1. Introduction

Health care professionals face the challenging task to organize their processes more effectively and efficiently. The pressure on health care systems rises as both demand for health care and expenditures are increasing steadily [329]. Within a health care organization, professionals of different functions jointly organize health care delivery with the objective to provide high-quality care using the limited resources that are available [56]. Designing and organizing processes is known as planning and control, which involves setting goals and deciding in advance what to do, how to do it, when to do it and who should do it. Health care planning and control comprises multiple managerial functions, making medical, financial and resource decisions. In this paper we address the managerial function of resource capacity planning and control as defined in [200]: ‘Resource capacity planning and control addresses the dimensioning, planning, scheduling, monitoring, and control of renewable resources’.

Operations Research and Management Sciences (OR/MS) is an interdisciplinary branch of applied mathematics, engineering and sciences that uses various scientific research-based principles, strategies, and analytical methods including mathematical modeling, statistics and algorithms to improve an organization's ability to enact rational and meaningful management decisions [228]. OR/MS has been applied widely to resource capacity planning and control in manufacturing. Since the 1950s, the application of OR/MS to health care also yields significant contributions in accomplishing essential efficiency gains in health care delivery. Many different topics have been addressed, such as operating room planning, nurse staffing and appointment scheduling. Owing to the interdisciplinary nature of OR/MS applied to health care, there is an extensive base of literature published across various academic fields. Tailored reference databases prove to be valuable in retrieving references from this broad availability. For example, Dexter provides a comprehensive bibliography on operating room management [111]. The Center for Healthcare Operations Improvement and Research (CHOIR) of the University of Twente has introduced and maintains the online literature database ‘ORchestra’ [ 226, 328], in which references in the field of OR/MS in health care are categorized by medical and mathematical subject. All the articles mentioned in this review are included and categorized in ORchestra.

Contribution

We aim to guide health care professionals and OR/MS researchers through the broad field of OR/MS in health care. We provide a structured overview of the typical decisions to be made in resource capacity planning and control in health care, and provide a review of relevant OR/MS articles for each planning decision.

The contribution of this paper is twofold. First, to position the planning decisions, we present a taxonomy. This taxonomy provides health care managers and OR/MS researchers with a method to identify, break down and classify planning and control decisions. The taxonomy contains two axes. The vertical axis reflects the hierarchical nature of decision making in resource capacity planning and control, and the horizontal axis the various health care services. The vertical axis is strongly connected, because higher-level decisions demarcate the scope of and impose restrictions on lower-level decisions. Although health care delivery is generally organized in autonomous organizations and departments, the horizontal axis is also strongly interrelated as a patient pathway often consists of several health care services from multiple organizations or departments.

Second, following the vertical axis of the taxonomy, and for each health care service on the horizontal axis, we provide a comprehensive specification of planning and control decisions in resource capacity planning and control. For each planning and control decision, we structurally review the key OR/MS articles and the OR/MS methods and techniques that are applied in the literature to support decision making. No structured review exists of this nature, as existing reviews are typically exhaustive within a confined scope, such as simulation modeling in health care [240] or outpatient appointment scheduling [76], or are more general to the extent that they do not focus on the concrete specific decisions.

This paper is organized as follows. Section 2 presents our taxonomy, Section 3 identifies, classifies and discusses the planning and control decisions. Section 4 concludes this paper with a discussion of our findings.

2. Taxonomy

Taxonomy is the practice and science of classification. It originates from biology where it refers to a hierarchical classification of organisms. The National Biological Information Infrastructure [318] provides the following definition of taxonomy: “Taxonomy is the science of classification according to a pre-determined system, with the resulting catalog used to provide a conceptual framework for discussion, analysis, or information retrieval; … a good taxonomy should be simple, easy to remember, and easy to use”. With exactly these objectives, we present a taxonomy for resource capacity planning and control in health care.

Planning and control decisions are made by health care organizations to design and operate the health care delivery process. It requires coordinated long-term, medium-term and short-term decision making in multiple managerial areas. In Hans et al [200], a framework is presented to subdivide these decisions in four hierarchical, or temporal, levels and four managerial areas. These hierarchical levels and the managerial area of resource capacity planning and control form the basis for our taxonomy. For the hierarchical levels, [200] applies the well-known breakdown of strategic, tactical and operational [9]. In addition, the operational level is subdivided in offline and online decision making, where offline reflects the in advance decision making and online the real-time reactive decision making in response to events that cannot be planned in advance. The four managerial areas are: medical planning, financial planning, materials planning and resource capacity planning. These are defined as follows. Medical planning comprises decision making by clinicians regarding medical protocols, treatments, diagnoses and triage. Financial planning addresses how an organization should manage its costs and revenues to achieve its objectives under current and future organizational and economic circumstances. Materials planning addresses the acquisition, storage, distribution and retrieval of all consumable resources/materials, such as suture materials, blood, bandages, food, etc. Resource capacity planning addresses the dimensioning, planning, scheduling, monitoring and control of renewable resources. Our taxonomy is a refinement of the health care planning and control framework of [200] in the resource capacity planning area.

The taxonomy contains two axes. The vertical axis reflects the hierarchical nature of decision making in resource capacity planning and control, and is derived from [200]. On the horizontal axis of our taxonomy we position different services in health care. We identify ambulatory care services, emergency care services, surgical care services, inpatient care services, home care services and residential care services. The taxonomy is displayed in Figure 1. We elaborate on both axes in more detail below.

Figure 1
figure 1

The taxonomy for resource capacity planning and control decisions in health care.

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Vertical axis

Our taxonomy is intended for planning and control decisions within the boundaries of a health care delivery organization. Every health care organization operates in a particular external environment. Therefore, all planning and control decisions are made in the context of this external environment. The external environment is characterized by factors such as legislation, technology and social factors.

The nature of planning and control decision making is such that decisions disaggregate as time progresses and more information becomes available [460]. Aggregate decisions are made in an early stage, while more detailed information supports decision making with a finer granularity in later stages. Because of this disaggregating nature, most well-known taxonomies and frameworks for planning and control are organized hierarchically [ 200, 460]. As the impact of decisions decreases when the level of detail increases, such a hierarchy also reflects the top-down management structure of most organizations [39].

For completeness we explicitly state the definitions of the four hierarchical levels [200], which we position on the vertical axis of our taxonomy. The definitions are adapted to specifically fit the managerial area of resource capacity planning and control.

  • Strategic planning addresses structural decision making. It involves defining the organization's mission (i.e., ‘strategy’ or ‘direction’), and the decision making to translate this mission into the design, dimensioning and development of the health care delivery process. Inherently, strategic planning has a long planning horizon and is based on highly aggregated information and forecasts. Examples of strategic planning are determining the facility's location, dimensioning resource capacities (e.g., acquisition of an MRI scanner, staffing) and deciding on the service and case mix.

  • Tactical planning translates strategic planning decisions to guidelines that facilitate operational planning decisions. While strategic planning addresses structural decision making, tactical planning addresses the organization of the operations/execution of the health care delivery process (i.e., the ‘what, where, how, when and who’). As a first step in tactical planning, patient groups are characterized based on disease type/diagnose, urgency and resource requirements. As a second step, the available resource capacities, settled at the strategic level, are divided among these patient groups. In addition to the allocation in time quantities, more specific timing information can already be added, such as dates or time slots. In this way, blueprints for the operational planning are created that allocate resources to different tasks, specialties and patient groups. Temporary capacity expansions like overtime or hiring staff are also part of tactical planning. Demand has to be (partly) forecasted, based on (seasonal) demand, waiting list information, and the ‘downstream’ demand in care pathways of patients currently under treatment. Examples of tactical planning are staff-shift scheduling and the (cyclic) surgical block schedule that allocates operating time capacity to patient groups.

  • Operational planning (both ‘offline’ and ‘online’) involves the short-term decision making related to the execution of the health care delivery process. Following the tactical blueprints, execution plans are designed at the individual patient level and the individual resource level. In operational planning, elective demand is entirely known and only emergency demand has to be forecasted. In general, the capacity planning flexibility is low on this level, since decisions on higher levels have demarcated the scope for the operational level decision making.

  • Offline operational planning reflects the in advance planning of operations. It comprises the detailed coordination of the activities regarding current (elective) demand. Examples of offline operational planning are patient-to-appointment assignment, staff-to-shift assignment and surgical case scheduling.

  • Online operational planning reflects the control mechanisms that deal with monitoring the process and reacting to unplanned events. This is required due to the inherent uncertain nature of health care processes. An example of online operational planning is the real-time dynamic (re)scheduling of elective patients when an emergency patient requires immediate attention.

Note that the decision horizon lengths are not explicitly given for any of the hierarchical planning levels, since these depend on the specific characteristics of the application. For example, an emergency department inherently has shorter planning horizons than a long-stay ward in a nursing home. Furthermore, there is a strong interrelation between hierarchical levels. Top-down interaction exists as higher-level decisions demarcate the scope of and impose restrictions on lower-level decisions. Conversely, bottom-up interaction exists as feedback about the health care delivery realization supports decision making in higher levels.

Horizontal axis

On the horizontal axis of our taxonomy we position the different services in health care. The complete spectrum of health care delivery is a composition of many different services provided by many different organizations. From the perspective of resource capacity planning and control, different services may face similar questions. To capture this similarity, we distinguish six clusters of health-care services. The definitions of the six care services are obtained from the corresponding MeSH terms provided by PubMed [310]. For each care service we offer several examples of facilities that provide this service.

  • Ambulatory care services provide care to patients without offering a room, a bed and board, and they may be free-standing or part of a hospital. In ambulatory care services, we position primary care services and community services as well as hospital-based services such as the outpatient clinic, since these services face similar questions from a resource capacity planning perspective. Examples of ambulatory care facilities are outpatient clinics, primary care services and the hospital departments of endoscopy, radiology and radiotherapy.

  • Emergency care services are concerned with the evaluation and initial treatment of urgent and emergent medical problems, such as those caused by accidents, trauma, sudden illness, poisoning or disasters. Emergency medical care can be provided at the hospital or at sites outside the medical facility. Examples of emergency care facilities are hospital emergency departments, ambulances and trauma centers.

  • Surgical care services provide operative procedures (surgeries) for the correction of deformities and defects, repair of injuries, and diagnosis and cure of certain diseases. Examples of surgical care facilities are the hospital's operating theater, surgical daycare centers and anesthesia facilities.

  • Inpatient care services provide care to hospitalized patients by offering a room, a bed and board. Examples are intensive care units, general nursing wards and neonatal care units.

  • Home care services are community health and nursing services that provide multiple, coordinated services to a patient at the patient's home. Home care services are provided by a visiting nurse, home health agencies, hospitals or organized community groups using professional staff for health care delivery. Examples are medical care at home, housekeeping support and personal hygiene assistance.

  • Residential care services provide supervision and assistance in activities of daily living with medical and nursing services when required. Examples are nursing homes, psychiatric hospitals, rehabilitation clinics with overnight stay, homes for the aged, and hospices.

Note that the horizontal subdivision is not based on health care organizations, but on the provided care services. Therefore, it is possible that a single health care organization offers services in multiple clusters. It may be that a particular facility is used by multiple care services, for example a diagnostics department that is used in both ambulatory and emergency care services. In addition, a patient's treatment often comprises of consecutive care stages offered by multiple care services. The health care delivery realization within one care service is impacted by decisions in other services, as inflow and throughput strongly depend on these other services. Therefore, resource capacity planning and control decisions are always made in the context of decisions made for other care services. Hence, like the interrelation in the vertical levels, a strong interrelation exists between the horizontal clusters.

This taxonomy provides a method to identify, break down and classify planning and control decisions in health care. This is a starting point for a complete specification of planning decisions and helps to gain understanding of the interrelations between various planning decisions. Hence, health care professionals can identify lacking, insufficiently defined and incoherent planning decisions within their department or organization. It also gives the opportunity to identify planning decisions that are not yet addressed often in the OR/MS literature. Therefore, in the next section, with our taxonomy as the foundation, we provide an exhaustive specification of planning decisions for each care service, combined with a review of key OR/MS literature.

3. Identification and classification of planning and control decisions

In this section, we identify the resource capacity planning and control decisions for each of the six care services in our taxonomy. The decisions are classified according to the vertical hierarchical structure of our taxonomy. For each identified planning decision, we will discuss the following in our overview:

  • What is the concrete decision?

  • Which performance measures are considered?

  • What are the key trade-offs?

  • What are main insights and results from the literature?

  • What are general conclusions?

  • Which OR/MS methods are applied to support decision making?

The identified planning decisions are in the first place obtained from available books and articles on health care planning and control. Our literature search method will be explained in more detail below. In addition, to be as complete as possible, expert opinions from health care professionals and OR/MS specialists are obtained to identify decisions that are not yet well-addressed in the literature and for this reason cannot be obtained from the literature. In this introduction, we first discuss the scope of the identified planning decisions and the applied OR/MS methods, and next we present the applied literature search method.

Scope

Numerous processes are involved in health care delivery. We focus on the resource capacity planning and control decisions to be made regarding the primary process of health care delivery. In the management literature, the primary process is defined as the set of activities that are directly concerned with the creation or delivery of a product or service [343]. Thus, we do not focus on supporting activities, such as procurement, information technology, human resource management, laboratory services, blood services and instrument sterilization.

We focus on OR/MS methods that quantitatively support and rationalize decision making in resource capacity planning and control. Based on forecasting of demand for care (see [330] for forecasting techniques), these methods provide optimization techniques for the design of the health care delivery process. Outside our scope is statistical comparison of performance of health care organizations, so-called benchmarking, of which Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) are well-known examples [91]. Quantitative decision making requires measurable performance indicators by which the quality of health care delivery can be expressed. A comprehensive survey of applied performance measures in health care organizations is provided in [277]. Next, practical implementation of OR/MS methods may require the development of Information Communications Technology (ICT) solutions (that are possibly integrated in health care organizations’ database systems); this is also outside the scope of this paper.

The spectrum of different OR/MS methods is wide (see for example [ 218, 394, 406, 448] for introductory books). In this review, we distinguish the following OR/MS methods: computer simulation [272], heuristics [1], Markov processes (which includes Markov reward and decision processes) [406], mathematical programming [ 331, 371], queueing theory [363]. For a short description of each of these OR/MS methods, the reader is referred to Appendix A.

Literature search method

As the body of literature on resource capacity planning and control in health care is extensive, we used a structured search method and we restricted to articles published in ISI-listed journals to ensure that we found and filter key and state-of-the-art contributions. Table 1 displays our search method. To identify the search terms as listed in Appendix B and to create the basic structure of the planning decision hierarchy for each care service, we consulted available literature reviews [ 45, 53, 55, 65, 72, 76, 84, 141, 156, 157, 192, 196, 197, 233, 240, 244, 246, 259, 287, 301, 311, 316, 336, 342, 345, 350, 353, 385, 386, 411, 422] and books [ 56, 199, 267, 309, 330, 433]. Additional search terms were obtained from the index of Medical Subject Headings (MeSH) [310] and available synonyms. With these search terms, we performed a search on the database of Web of Science (WoS) [440]. WoS was chosen as it contains articles from all ISI-listed journals. It is particularly useful as it provides the possibility to select Operations Research and Management Science as a specific subject category and to sort references on the number of citations.

Table 1 The search method applied to each care service
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We identify a base set containing the 10 most-cited articles in the predefined subject category of Operations Research and Management Science. Starting from this base set, we include all articles from ISI-listed journals that are referred by or refer to one of the articles in the base set and deal with resource capacity planning and control decisions. As such, we ensure that we also review recent work that may not have been cited often yet. In addition, we include articles published in Health Care Management Science (HCMS), which is particularly relevant for OR/MS in health care and obtained an ISI listing in 2010. To be sure that by restricting to WoS and HCMS, we do not neglect essential references, we also performed a search with our search terms on the databases of Business Source Elite [135], PubMed [346] and Scopus [372]. This search did not result in significant additions to the already found set of papers. The literature search was updated up to 10 May 2012.

The review is organized as follows. Section 3.1 is devoted to ambulatory care services, the Section 3.2 to emergency care services, Section 3.3 to surgical care services, Section 3.4 to inpatient care services, Section 3.5 to home care services and Section 3.6 to residential care services. For each care service, the review is subdivided in strategic, tactical, offline operational and online operational planning. In Appendix C, tables are included in which the identified planning decisions are listed for each care service, together with applied OR/MS methods and literature references per planning decision. When for different care services a similar planning decision is involved, we use the same term. Our intention is that all the following sub-sections are self-contained, so that they can be read in isolation. Therefore, minor passages are overlapping. When in the description of a planning decision a paper is cited, while it does not appear in the ‘methods’-list, it means that this paper contains a relevant statement about this planning decision, but the particular planning decision is not the main focus of the paper.

3.1. Ambulatory care services

Ambulatory care services provide medical interventions without overnight stay, that is, the patient arrives at the facility and leaves the facility on the same day. These medical interventions comprise for example diagnostic services (e.g., CT scan, MRI scan), doctor consultations (e.g., general practitioner, hospital specialist), radiotherapy treatments or minor surgical interventions. Demand for ambulatory care services is growing in most western countries since 2000 [324]. The existing literature has mainly focused on the offline operational planning decision of appointment scheduling.

Strategic planning

Regional coverage

Ambulatory care planning on a regional level aims to create the infrastructure to provide health care to the population in its catchment area. This regional coverage decision involves determining the number, size and location of facilities in a certain region to find a balanced distribution of facilities with respect to the geographical location of demand [130]. The main trade-off in this decision is between patient accessibility and efficiency. Patient accessibility is represented by access time and travel distance indicators. Efficiency is represented by utilization and productivity indicators [ 130, 385]. Common regional planning models incorporate the dependency of demand on the regional demographic and socioeconomic characteristics [2].

Methods: computer simulation [ 298, 359, 388, 404], heuristics [ 2, 130], literature review [385].

Service mix

An organization decides the particular services that the ambulatory care facility provides. The service mix stipulates which patient types can be consulted. In general, the service mix decision is not made at an ambulatory care service level, but at the regional or hospital level, as it integrally impacts the ambulatory, emergency, surgical and inpatient care services. This is also expressed in the literature, in which for example inpatient resources, such as beds and nursing staff, are indicated as ‘following’ resources [431]. This may be the reason that we have not found any references focusing on service mix decisions for ambulatory care services in specific.

Methods: no papers found.

Case mix

Every ambulatory care facility decides on a particular case mix, which is the volume and composition of patient groups that the facility serves. The settled service mix restricts the decisions to serve particular patient groups. Patient groups can be classified based on disease type, age, acuteness, home address, etc. The case mix influences almost all other planning decisions, such as a facility's location, capacity dimensions and layout. Also, demand for different patient groups in the case mix may vary, which influences required staffing levels significantly [ 384, 392]. However, case mix decision making has not received much attention in the OR/MS literature. In the literature, the case mix is often treated as given.

Methods: computer simulation [392], mathematical programming [384].

Panel size

The panel size is the number of potential patients of an ambulatory care facility [187]. Since only a fraction of these potential patients, also called calling population, actually demands health care, the panel size can be larger than the number of patients a facility can serve. The panel size is particularly important for general practitioners, as they need an accurate approximation of how many patients they can subscribe or admit to their practice. A panel size should be large enough to have enough demand to be profitable and to benefit from economies of scale, as a facility's costs per patient decrease when the panel size increases [388]. On the other hand, when the panel size is too large, access times may grow exponentially [187].

Methods: computer simulation [388], queueing theory [187].

Capacity dimensioning

Ambulatory care facilities dimension their resources, such as staff, equipment and space, with the objective to (simultaneously) maximize clinic profit, patient satisfaction and staff satisfaction [392]. To this end, provider capacity must be matched with patient demand, such that performance measures such as costs, access time and waiting time are controlled. Capacity is dimensioned for the following resource types:

  • Consultation rooms. The number of consultation rooms that balances patient waiting times and doctor idle time with costs for consultation rooms [ 227, 385, 391, 392].

  • Staff. Staff in the ambulatory care services concern for example doctors, nurses and assistants [ 32, 240, 298, 360, 384, 385, 388, 391, 392, 438, 444].

  • Consultation time capacity. The total consultation time that is available, for example for an MRI scanner or a doctor [ 98, 136, 138].

  • Equipment. Some ambulatory care services require equipment for particular consultations, for example MRI scanners, CT scanners and radiotherapy machines [ 161, 298, 404].

  • Waiting room. The waiting room is dimensioned such that patients and their companions waiting for consultation can be accommodated [392].

When capacity is dimensioned to cover average demand, variations in demand may cause long access and waiting times [404]. Basic rules from queueing theory demonstrate the necessity of excess capacity to cope with uncertain demand [182]. Capacity dimensioning is a key decision, as it influences how well a facility can meet demand and manage access and waiting times.

Methods: computer simulation [ 136, 138, 161, 227, 298, 360, 388, 391, 392, 404, 444], Markov processes [438], mathematical programming [384], queueing theory [ 32, 98, 138, 227], literature review [ 240, 385].

Facility layout

The facility layout concerns the positioning and organization of various physical areas in a facility. A typical ambulatory care facility consists of a reception area, a waiting area and consultation rooms [164]. The facility layout is a potentially cost-saving decision in ambulatory care facilities [ 164, 330], but we found no papers that used an OR/MS approach to study the layout of an ambulatory care facility. Yet, the handbook [330] discusses heuristics for facility layout problems in health care.

Methods: heuristics [330].

Tactical planning

Patient routing

Ambulatory care typically consists of multiple stages. We denote the composition and sequence of these stages as the route of a patient. An effective and efficient patient route should match medical requirements, capacity requirements and restrictions, and the facility's layout. For a single facility, identifying different patient types and designing customized patient routes for each type prevents superfluous stages and delays [298]. For example, instead of two visits to a doctor and a medical test in between, some patient types may undergo a medical test before visiting the doctor, which saves valuable doctor time. Parallel processing of patients may increase utilization of scarce resources (e.g., a doctor or a CT scanner) [ 161, 227]. When parallel processing is applied, idle time of the scarce resource is reduced by preparing patients for consultation during the consultation time of other patients. Performance is typically measured by total visit time, waiting time and queue length.

Methods: computer simulation [ 82, 161, 227, 298, 388], queueing theory [ 227, 461].

Capacity allocation

On the tactical level, resource capacities settled on the strategic level are subdivided over all patient groups. To do so, patient groups are first assigned to resource types:

  • Assign patient groups to resource types. The assignment of patient groups to available resources requires knowledge about the capabilities of for example clinical staff, support staff or medical equipment, and the medical characteristics of patients. The objective is to maximize the number of patients served, by calculating the optimal assignment of patient groups to appropriately skilled members of clinical staff [384]. Efficiency gains are possible when certain tasks can be substituted between clinical staff, either horizontally (equally skilled staff) or vertically (lower skilled staff) [385].

  • Time subdivision. The available resource capacities, such as staff and equipment, are subdivided over patient groups. For example, general practitioners divide their time between consulting patients and performing prevention activities for patients [195]. When patient demand changes over time (e.g., seasonality), a dynamic subdivision of capacity, updated based on current waiting lists, already planned appointments and expected requests for appointments, performs better than a long-term, static subdivision of resource capacity [429].

Methods: computer simulation [429], mathematical programming [ 195, 384], literature review [433].

Temporary capacity change

The balance between access times and resource utilization may be improved when resource capacities can temporarily be increased or decreased, to cope with fluctuations in patient demand [429]. For example, changing a CT scanner's opening hours [429] or changing doctor consultation time [138].

Methods: computer simulation [ 138, 429].

Access policy

In appointment-driven facilities, the access policy concerns the waiting list management that deals with prioritizing waiting lists so that access time is equitably distributed over patient groups. In the traditional approach, there is one queue for each doctor, but when patient queues are pooled into one joint queue, patients can be treated by the first available doctor, which reduces access times [427]. Another policy is to treat patients without a scheduled appointment, also called ‘walk-in’ service. In between scheduled and walk-in service is ‘advanced access’ (also called ‘open access’, or ‘same-day scheduling’). With advanced access, a facility leaves a fraction of the appointment slots vacant for patients that request an appointment on the same day or within a couple of days. The logistical difficulty of both walk-in service and advanced access is a greater risk of resource idle time, since patient arrivals are more uncertain. However, implementation of walk-in/advanced access can provide significant benefits to patient access time, doctor idle time and doctor overtime, when the probability of patients not showing up is relatively large [ 334, 358]. A proper balance between traditional appointment planning and walk-in/advanced access further decreases access times and increases utilization [ 356, 461]. The specification of such a balanced design will be discussed below.

Methods: computer simulation [ 12, 152, 284, 334, 356, 427], heuristics [284], Markov processes [334], queueing theory [ 358, 461].

Admission control

Given the access policy decisions, admission control involves the rules according to which patients are selected to be admitted from the waiting lists. Factors that are taken into account are for example resource availability, current waiting lists and expected demand. Clearly, this makes admission control and capacity allocation mutually dependent. This is for example the case in [429], where the capacity subdivision for a CT scanner is settled by determining the number of patients to admit of each patient group. Access times can be controlled by adequate admission control [ 168, 173, 238, 429]. Admission control plays a significant role in advanced access or walk-in policies. Successful implementation of these policies requires a balance between the reserved and demanded number of slots for advanced access or walk-in patients. Too many reserved slots results in resource idle time, and too little reserved slots results in increased access time [ 348, 349].

Methods: computer simulation [429], heuristics [173], Markov processes [ 168, 173], mathematical programming [ 238, 348, 349].

Appointment scheduling

Appointment schedules are blueprints that can be used to provide a specific time and date for patient consultation (e.g., an MRI scan or a doctor visit). Appointment scheduling comprises the design of such appointment schedules. Typical objectives of this design are to minimize patient waiting time, maximize resource utilization or minimize resource overtime. A key trade-off in appointment scheduling is the balance between patient waiting time and resource idle time [ 76, 219, 245]. Appointment scheduling is comprehensively reviewed in [ 76, 197]. In an early paper [443], the Bailey-Welch appointment scheduling rule is presented, which is a robust and well-performing rule in many settings [ 219, 241, 253]. References differ in the extent in which various aspects are incorporated in the applied models. Frequently modeled aspects that influence the performance of an appointment schedule are patient punctuality [ 152, 276, 446], patients not showing up (‘no-shows’) [ 152, 153, 220, 241], walk-in patients or urgent patients [ 12, 152, 356, 461], doctor lateness at the start of a consultation session [ 152, 153, 283, 360], doctor interruptions (e.g., by comfort breaks or administration) [ 153, 276] and the variance of consultation duration [219]. These factors can be taken into account when modeling the following key decisions that together design an appointment schedule:

  • Number of patients per consultation session. The number of patients per consultation session is chosen to control patient access times and patient waiting times. When the number of patients is increased, access times may decrease, but patient waiting times and provider overtime tend to increase [ 73, 152, 219].

  • Patient overbooking. Patients not showing up, also called ‘no-shows’, cause unexpected gaps, and thus increase resource idleness [219]. Overbooking of patients, that is, booking more patients into a consultation session than the number of planned slots is suggested to compensate no-shows in [ 254, 258, 273, 317, 387]. Overbooking can significantly improve patient access times and provider productivity, but it may also increase patient waiting time and staff overtime [ 254, 258]. Overbooking particularly provides benefits for large facilities with high no-show rates [254].

  • Length of the appointment interval. The decision for the length of the planned appointment interval or slot affects resource utilization and patient waiting times. When the slot length is decreased, resource idle time decreases, but patient waiting time increases [153]. For some distributions of consultation time, patient waiting times and resource idle time are balanced when the slot length equals the expected length of a consultation [76]. The slot length can be chosen equal for all patients [ 153, 219, 443], but using different, appropriate slot lengths for each patient group may decrease patient waiting time and resource idle time when expected consultation times differ between patient groups [136].

  • Number of patients per appointment slot. Around 1960, it was common to schedule all patients in the first appointment slot of a consultation session [158]. This minimizes resource idle time, but has a negative effect on patient waiting times [ 342, 360]. Later, it became common to distribute patients evenly over the consultation session to balance resource idle time and patient waiting time. In [158], various approaches in between these two extremes are evaluated, such as two patients in one time slot and zero in the next.

  • Sequence of appointments. When different patient groups are involved, the sequence of appointments influences waiting times and resource utilization. Appointments can be sequenced based on patient group or expected variance of the appointment duration. In [253], various rules for patient sequencing are compared. Alternatively, when differences between patients exist with respect to the variation of consultation duration, sequencing patients by increasing variance (i.e., lowest variance first) may minimize patient waiting time and resource idle time [76].

  • Queue discipline in the waiting room. The queue discipline in the waiting room affects patient waiting time, and the higher a patient's priority, the lower the patient's waiting time. The queue discipline in the waiting room is often assumed to be first-come-first-serve (FCFS), but when emergency patients and walk-in patients are involved, the highest priority is typically given to emergency patients and the lowest priority to walk-in patients [76]. Priority can also be given to the patient that has to visit the most facilities on the same day [298].

  • Anticipation for unscheduled patients. Facilities that also serve unscheduled patients, such as walk-in and urgent patients, require an appointment scheduling approach that anticipates these unscheduled patients by reserving slack capacity. This can be achieved by leaving certain appointment slots vacant [128], or by increasing the length of the appointment interval [76]. Reserving too little capacity for unscheduled patients results in an overcrowded facility, while reserving too many may result in resource idle time. Often, unscheduled patients arrive in varying volumes during the day and during the week. When an appropriate number of slots is reserved for unscheduled patients, and appointments are scheduled at moments that the expected unscheduled demand is low, patient waiting times decrease and resource utilization increases [ 326, 356, 461]. In the online operational level of this section, we discuss referring unscheduled patients to a future appointment slot when the facility is overcrowded.

Methods: computer simulation [ 14, 73, 77, 110, 136, 152, 153, 205, 219, 220, 245, 258, 276, 283, 284, 298, 326, 356, 392, 433, 434, 443, 446], heuristics [ 73, 241, 284], Markov processes [ 158, 188, 241, 253, 280, 317, 387], mathematical programming [ 25, 73, 106, 357], queueing theory [ 52, 98, 128, 254, 273, 357, 433, 461], literature review [ 76, 197, 240, 385].

Staff-shift scheduling

Shifts are duties with a start and end time [65]. Shift scheduling deals with the problem of selecting what shifts are to be worked and how many employees should be assigned to each shift to meet patient demand [141]. More attractive schedules promote job satisfaction, increase productivity and reduce turnover. While staff dimensioning on the strategic level has received much attention, shift scheduling in ambulatory care facilities seems underexposed in the literature. In [63], shift schedules are developed for physicians, who often have disproportionate leverage to negotiate employment terms, because of their specialized skills. Hence, physicians often have individual arrangements that vary by region, governing authority, seniority, specialty and training. Although these individual arrangements impose requirements to the shift schedules, there is often flexibility for shifts of different lengths and different starting times to cope with varying demand during the day or during a week. In this context, the handbook by [330] discusses staggered shift scheduling and flexible shift scheduling. In the first alternative, employees have varying start and end times of a shift, but always work a fixed number of hours per week. In the latter, cheaper alternative, a core level of staff is augmented with daily adjustments to meet patient demand.

Methods: computer simulation [338], mathematical programming [63], literature review [ 65, 141, 199, 330].

Offline operational planning

Patient-to-appointment assignment

Based on the appointment scheduling blueprint developed on the tactical level, patient scheduling comprises scheduling of an appointment in a particular time slot for a particular patient. A patient may require multiple appointments on one or more days. Therefore, we distinguish scheduling a single appointment, combination appointments and appointment series:

  • Single appointment. Patients requiring an appointment often have a preference for certain slots. When information is known about expected future appointment requests and the expected preferences of these requests, a slot can be planned for this patient to accommodate the current patient, but also to have sufficient slots available for future requests from other patients. This can for example be necessary to ensure that a sufficient number of slots is available for advanced access patients [ 198, 439], or to achieve equitable access for all patient groups to a diagnostic facility [335].

  • Combination appointments. Combination appointments imply that multiple appointments for a single patient are planned on the same day, so that a patient requires fewer hospital visits. This is the case when a patient has to undergo various radiotherapy operations on different machines within one day [340].

  • Appointment series. For some patients, a treatment consisting of multiple (recurring) appointments may span a period of several weeks or months. The treatment is planned in an appointment series, in which appointments may have precedence relations and certain requirements for the time intervals in between. In addition, the involvement of multiple resources may further complicate the planning of the appointment series. The appointment series have to fit in the existing appointment schedules, which are partly filled with already scheduled appointments. Examples of patients that require appointment series are radiotherapy patients [ 93, 94, 95] and rehabilitation patients [85].

Methods: heuristics [ 85, 340, 439], Markov processes [ 198, 335, 439], mathematical programming [ 93, 94, 95].

Staff-to-shift assignment

On the tactical level, staff-shift scheduling results in shifts that have to be worked. In staff-to-shift assignment on the offline operational level, a date and time are given to staff members to perform particular shifts. For example, a consultation session is scheduled for a doctor on a particular day and time, and with a certain duration. For an endoscopy unit, in [238] a model is presented to schedule available doctors to endoscopy unit shifts.

Methods: mathematical programming [238], literature review [199].

Online operational planning

Dynamic patient (re)assignment

After patients are assigned to slots in the appointment schedule, the appointments are carried out on their planned day. During such a day, unplanned events, such as emergency or walk-in patients, extended consultation times, and equipment breakdown, may disturb the planned appointment schedule. In such cases, real-time dynamic (re)scheduling of patients is required to improve patient waiting times and resource utilization in response to acute events. For example, to cope with an overcrowded facility walk-in patients can be rescheduled to a future appointment slot to improve the balance of resource utilization over time [351]. Dynamic patient (re)assignment can also be used to decide which patient group to serve in the next time slot in the appointment schedule [188], for example based on the patient groups’ queue lengths. When inpatients are involved in such decisions, they are often subject to rescheduling [76], since it is assumed that they are less harmed by a rescheduled appointment as they are already in the hospital. However, longer waiting times of inpatients may be more costly, since it may mean they have to be hospitalized longer [100].

Methods: computer simulation [351], Markov processes [ 100, 188, 280], mathematical programming [100].

Staff rescheduling

At the start of a shift, the staff schedule is reconsidered. Before and during the shift, the staff capacities may be adjusted to unpredicted demand fluctuations and staff absenteeism by using part-time, on-call nurses, staff overtime and voluntary absenteeism [ 191, 342].

Methods: no papers found.

3.2. Emergency care services

Emergency care services have the goal to reduce morbidity and mortality resulting from acute illness and trauma [ 352, 454]. To attain this goal, rapid response of an ambulance and transportation to an emergency care center (e.g., an emergency department in a hospital, or an emergency location near a disaster) is required [ 37, 352]. Patients arrive to the emergency department (ED) of a hospital as a self-referral, through ambulatory care services or by ambulance [54]. A frequently reported and studied problem in emergency care is that of long ED waiting times. One of the causes of long ED waiting time is treatment of a high number of self-referrals that could also be treated in ambulatory care services (e.g., by general practitioners). To cope with this problem, EDs increasingly cooperate with ambulatory care services, for example by combining the ED with a service that provides primary care outside office hours, or by opening an ambulatory walk-in center to which these patients can be referred [270]. The body of OR/MS literature directed to emergency care services is large. The existing literature mainly focuses on the strategic decisions regional coverage and capacity dimensioning for ambulances, and the tactical decision staff-shift scheduling.

Strategic planning

Regional coverage

To be able to provide rapid response to an acute illness or trauma, emergency care services need to be geographically close to their customer base, where emergencies can potentially occur [342]. Given a geographical region with a certain spatial distribution of service requests (i.e. emergency demand), the locations, types and number of emergency care facilities have to be decided. The objective is to find a balanced distribution of facilities to guarantee a desired level of service [ 36, 279]. This level of service can for example be measured by the maximum time it takes for a patient to travel to the closest ED, or the maximum response time that an ambulance requires to reach a specified region. The main trade-off in the decision where to locate emergency care centers and ambulances is between the level of service for emergency patients and costs [ 36, 41, 68, 203, 237]. Below, we will elaborate on this trade-off for both emergency care centers and ambulances.

  • Emergency care centers. The decision where to locate emergency care centers, such as an ED in a hospital, is determined such that locations where emergencies may occur have at least one emergency care center within a target travel time or distance [353]. When a large-scale emergency or disaster occurs, an emergency care center may be unable to provide emergency care services (e.g., the facility is destroyed). In [222], this possibility is incorporated in regional coverage models that can be used to determine good locations for (temporary) emergency care centers after a disaster.

  • Ambulances (e.g., vans, motorcycles, helicopters, airplanes). The decision where to locate ambulances is determined such that a specified region can be reached within a target response time by one or more ambulances, or that the average or maximum response time to a potential emergency is minimized [ 41, 68, 134, 140, 237]. The response time of an ambulance concerns the time elapsed from notification of an emergency until an ambulance arrives at the emergency location [154]. Other factors to take into account in planning the locations of ambulances are the likelihood of timing and location of an emergency, staff availability, location constraints (e.g., a place where staff can rest), and the emergency care center where patients are potentially transported to [ 33, 56, 68, 134, 154, 175, 230, 237, 342, 352, 454].

Methods: computer simulation [ 56, 140, 154, 160, 174, 203, 230, 352, 366, 393, 454], heuristics [ 20, 33, 35, 139, 170, 229], Markov processes [ 19, 222], mathematical programming [ 16, 33, 35, 36, 37, 41, 68, 99, 134, 140, 160, 175, 177, 203, 222, 237, 352, 353, 380, 393, 407], queueing theory [ 33, 170, 229, 269, 290, 380], literature review [ 61, 183, 237, 279, 342, 353].

Service mix

An organization decides the particular services that the emergency care facility provides. Facilities may provide services for particular types of emergency patients, which are possibly classified by severity of trauma. For example, a first-aid center may provide services that are adequate for minor emergencies, while an academic medical center is equipped to treat the most complex and severe traumas. In this case, treating minor emergencies at the first-aid center may alleviate the use of expensive resources in the academic medical center, and may be more cost-effective from a societal viewpoint. In order to balance provided emergency care and the cost of emergency care resources within a region or country, the service mix decision may be governed by societal influences and governmental regulations.

In general, the service mix decision is not made at an emergency care service level, but at the hospital level, as it integrally impacts the ambulatory, emergency, surgical and inpatient care services. The decided service mix dictates the case mix of emergency patients that can be served by the emergency care facility. Emergency care facilities in general do not decide a particular case mix, as they are often obliged to serve arriving emergency patients with any type of injury or disease [ 78, 336].

Methods: no papers found.

Ambulance districting

A covered region may be subdivided into several districts to which available ambulances are assigned. In subdividing a region and assigning ambulances to districts, it is the objective to minimize response times, while balancing the workload [ 33, 74, 269]. When an emergency occurs in a district, one of the available ambulances within that district is dispatched to the emergency [ 33, 269]. When none are available (e.g., when all ambulances are responding to a call), an ambulance from a different district may be dispatched to the emergency [269]. Such interdistrict dispatching decreases average response times, especially for relatively smaller districts. This is the effect of so-called pooling of resources [366]. Owing to this possibility of interdistrict dispatching, only predicting the workload generated within the assigned district may not lead to a well-balanced ambulance districting decision. In the analysis of the districting problem, overlapping districts, mobile locations and interdistrict dispatching should be included for an accurate prediction of workload balance [269].

Methods: computer simulation [ 174, 366], heuristics [33], mathematical programming [33], queueing theory [ 33, 74, 269].

Capacity dimensioning

Emergency care facilities dimension their resources with the objective to attain a reliable level of service while minimizing costs [ 36, 37, 323]. Often, this level of service is represented by a response target, for example x% of the emergency patients should be reached (ambulance) or seen (ED) within y minutes. An imbalance in supply and demand can lead to congestion or overcrowding in the ED [56]. ED overcrowding results in long waiting times, patients who leave the ED without being seen, and ambulance diversions [ 78, 189, 336]. This leads to patient dissatisfaction, medical errors and decreased staff satisfaction [336]. A typical cause of congestion in the ED is the delay in admitting emergency patients to an inpatient bed due to congested medical care units and ICUs [ 15, 78, 90, 322, 323, 422]. Congestion may also be caused by insufficient available resources in the surgical care services (e.g., operating time capacity) and ambulatory care services (e.g., diagnostic equipment). Moreover, coordinated decision making for resource capacity dimensioning both within, and in services relating to emergency care services, reduces delays for emergency patients [ 15, 54, 78, 90, 266, 422]. The following resources are dimensioned:

  • Ambulances. Ambulances exist in different transport modalities (helicopters, vans, cars) carrying different types of equipment and staff [ 35, 36, 37, 140, 160, 230, 352, 366, 380, 401, 454]. Ambulances collect emergency patients, but also perform less urgent transfers of patients between care facilities [401]. The number of ambulances should be chosen to include buffer capacity, to cope with fluctuations in demand and ambulance availability. Fluctuations in demand may be caused by expected demand peaks, such as large events, or unexpected demand peaks, such as large-scale accidents [454].

  • Waiting room. The waiting rooms is possibly separated for patients awaiting results and patients awaiting initiation of service [ 90, 336].

  • Treatment rooms. Treatment rooms comprise treatment beds or treatment chairs [ 78, 90, 266, 336]. Occupation of treatment rooms can be alleviated by letting patients await their lab test results in the waiting room and not in the treatment room [ 78, 90].

  • Emergency wards. These are observation wards for a temporary stay, possibly before admission to the general wards [ 15, 90, 322, 323], also called Acute Admission Unit (AAU). Capacity is generally given in the number of beds.

  • Equipment. Equipment may be required for emergency procedures, including treatment beds, treatment chairs and diagnostic equipment [ 78, 90, 336]. In general, diagnostic testing is considered outside the control of the emergency care services [155]. Emergency patients may require an X-ray or other diagnostic testing, and may have to compete with inpatients and outpatients for diagnostic resource capacity. Ineffective management of the diagnostic department causes delays in the emergency care services [155]. Installing diagnostic equipment in the ED may decrease the waiting time for diagnostic results, and therewith the overall length of stay of a patient in the ED [336].

  • Staff. Staff in emergency care services is composed of different skill and responsibility levels, for example doctors, emergency nurses and support staff [ 54, 155, 189, 240, 266, 322, 323, 336, 458]. Required staffing dimensions, and thereby staff costs, may be reduced by passing on non-critical patients from doctors to lower-qualified, less-costly staff, releasing doctors to work on the critical cases [54]. Moreover, flexibility in staffing can be used to cost-effectively match uncertain emergency demand with resource capacity. For example, staff members may be ‘on call’ while working elsewhere or being off-duty, and they are called upon when additional staff is required in the ED to cope with unexpected demand peaks [323].

Methods: computer simulation [ 15, 37, 54, 78, 140, 155, 160, 230, 266, 270, 322, 352, 366, 454, 458], heuristics [35], mathematical programming [ 35, 36, 140, 322, 323, 352], queueing theory [ 90, 189, 380, 401], literature review [ 56, 240, 336].

Facility layout

The facility layout concerns the positioning and organization of different physical areas in a facility. Hospital managers aim to find the layout of the emergency care facility that maximizes the number of emergency patients that can be examined, given the budgetary and building constraints. Letting patients wait for their lab results in a waiting area instead of the treatment room enables the treatment rooms to be used more effectively, which can decrease patient waiting time [90]. Moreover, integration of the facility layout decision and the patient routing decision may decrease costs.

Methods: computer simulation [458], heuristics [330], literature review [336].

Tactical planning

Patient routing

An emergency patient process consists of multiple stages. We denote the composition and sequence of these stages as the route of a patient. Patient routes are designed to minimize patient waiting time, maximize patient throughput and increase staff utilization [ 54, 240]. A typical patient process is as follows. Patients arrive to the hospital as a self-referral, through ambulatory care services or by ambulance [54]. Generally, upon arrival at the ED, patients see a ‘triage-nurse’, who prioritizes these patients into urgency categories [78]. After triage and possibly a wait in the waiting room, patients see a medical staff member that aims to establish a diagnosis of the patient's condition timely and cost-effectively. In this phase, diagnostic tests (e.g., laboratory, X-ray) are typically required. Although more expensive, it may be decided to directly administer multiple diagnostic tests, to reduce the time to establish a diagnosis and patient waiting time [240]. When a diagnosis is determined, possibly a treatment is carried out at the ED. This treatment may be continued in the operating room or a medical care unit in the hospital. If (further) treatment is not required, the patient is discharged, possibly with a referral to an ambulatory care clinic [265].

To minimize patient waiting time, maximize patient throughput and increase staff utilization, alternative patient routing systems within the emergency care services may be developed. For example, a ‘fast-track system’ in the ED separates the patients with minor injuries and illnesses from the more severe traumas [ 90, 240, 299]. It reduces waiting time for patients with minor injuries and illnesses [299], but may lead to increased waiting time for the other patient groups, since less resources are available for these groups [155]. This may be acceptable, when the effect is not too large [299] and the increased waiting times are still within the set targets for each patient group [ 54, 240]. As relatively many steps in the emergency care process depend on effective and efficient processing in other care services (e.g., diagnostic services, surgical care services, and inpatient care services), coordinated decision making between the services involved in the emergency care process reduces delays for emergency patients [ 54, 78, 90, 155].

Methods: computer simulation [ 54, 78, 155, 265, 299, 425], queueing theory [ 90, 302], literature review [ 240, 336].

Admission control

Admission control involves the rules according to which patients are selected to be served. The admission control rules first prescribe that the highest priority (life-threatened) patients are seen immediately, and that other patients can be deferred to the waiting room until they can be seen by a clinician [54]. Secondly, they define the order in which waiting patients are selected to be served. In the triage process, mentioned earlier in the patient routing decision, emergency patients are classified into ‘triage categories’ (often five) during an assessment by a qualified medical practitioner [78]. Typically, waiting time targets are set for each triage category, as a particular waiting time has a different impact on the health status of two patients in different urgency groups [302]. In general, patients are served in the order of triage category of decreasing urgency. However, applying more dynamic rules that take into account the number of waiting patients per triage category can enhance the compliance to the waiting time targets per category [54].

Methods: computer simulation [ 54, 78], queueing theory [302].

Staff-shift scheduling

Shifts are hospital duties with a start and end time [65]. Shift scheduling deals with the problem of selecting what shifts are to be worked and how many employees should be assigned to each shift to meet patient demand [141]. The objective of shift scheduling is to generate shifts that minimize the number of staff hours required to cover the desired staffing levels [345]. The required staffing levels are determined by calculating how much staff is required to reach a given service level target, for example x% of the patients should be seen in y minutes.

For an ED, patient demand varies significantly throughout the week and throughout the day. Therefore, identical staffing schedules each day and each hour may seem convenient and practical, but they are likely suboptimal [185]. Implementing different staffing levels based on patient arrival rates for different moments within the day and week may decrease patient waiting times and reduce the number of patients that leave an ED without being seen [189]. To calculate the required staffing levels on each moment of the day, the working day is typically divided into planning intervals [184]. The required staffing level in each interval is dependent on the patient arrivals in that interval, but also by delayed congestion effects from prior intervals [ 184, 189]. Therefore, it can be beneficial to let a change in staffing level follow a change in patient arrival rate after a certain delay in time [184].

When staffing levels are determined, a set of shifts can be developed to meet those staffing levels as close as possible. Staggered shift scheduling is when shifts do not have to start and finish at the same time. This results in more flexibility to accommodate shifts to the required staffing levels at specific intervals, leading to improved utilization of resources [381]. Shift schedules are impacted by the preferences of staff and by laws prescribing emergency staff is only available for a limited number of hours [ 139, 189].

Methods: computer simulation [ 230, 381, 382, 458], heuristics [ 381, 382], queueing theory [ 184, 185, 189], literature review [ 199, 240, 336].

Offline operational planning

Staff-to-shift assignment

In staff-to-shift assignment, a date and time are given to a staff member to perform a particular shift. The objective is to attain the tactically settled staffing levels for each shift while minimizing costs, such as overtime by regular staff or staff hired temporarily from an agency [18]. Staff-to-shift assignments can be noncyclic and cyclic, where in the latter a staff member constantly repeats the same shift pattern [75]. In staff-to-shift assignment, labor laws, staff availability and staff satisfaction have to be taken into account [ 18, 23, 103]. In [139], the staff-to-shift assignment for ambulance staff is coordinated with the regional coverage decision for ambulances, to maximize the provided service level for patients in a region.

Methods: heuristics [75], mathematical programming [ 18, 23, 75, 103, 139].

Online operational planning

Ambulance dispatching

Ambulance dispatching concerns deciding which ambulance to send to an emergency patient [8]. When calls to report an emergency event come in, a physician, nurse or paramedic assesses whether the reported emergency requires an ambulance. If so, the call is transferred to the dispatcher, who decides which ambulance will respond [380]. Many dispatching rules exist, and a commonly used rule is to send the ambulance closest to the emergency [281]. However, when predictions on future emergency calls are incorporated, sending the closest ambulance is not always optimal, as dispatching an ambulance makes it temporarily unavailable to respond to other calls. Shorter overall response times can be achieved when future demand is also incorporated in the dispatching decision [274]. When multiple calls come in, prioritizing calls and dispatching accordingly may balance ambulance workload [174]. Prioritizing and dispatching based on urgency improves response rates for the high-urgent calls [281]. After the dispatching decision has been made and an ambulance is traveling to the emergency, a request for emergency care may be canceled, leading to resource idle time [203].

Methods: computer simulation [ 8, 274, 281, 454], heuristics [274], mathematical programming [281], queueing theory [401].

Facility selection

When an ambulance has collected a patient, the emergency facility to which to bring a collected emergency patient has to be decided [454]. It is the aim to select the facility that minimizes the patient's travel time and is ‘adequate’ to serve the patient. The prospective emergency facility may for example be a local health clinic, a first-aid center or a hospital ED, and its appropriateness depends on the match between the facility's services, resources and bed availability, and the services required for the medical condition of the patient [366]. Delivering the emergency patient to the closest appropriate ED also leads to higher ambulance availability, as ambulance travel time is minimized [366].

Methods: computer simulation [366].

Ambulance routing

When an ambulance is dispatched to a particular emergency, the fastest route between an ambulance's location and the emergency location needs to be determined with the aim to minimize ambulance response times. Information with respect to distance, traffic, road work, accessibility can be taken into account. No specific contributions have been found for ambulance routing with our search method, but note that a wide range of contributions in the general problem of vehicle routing exists [408].

Methods: no papers found.

Ambulance relocation

When ambulances are unavailable, for example because they are dispatched to emergency cases or they are in repair, they may leave a significant fraction of population without ambulance coverage [167]. In this case, to maximize regional coverage and to decrease response times, ambulances may be relocated [ 8, 61, 167, 300]. Relocation improves flexibility to respond to fluctuating patient demand [454] and dynamic traffic conditions [368]. When relocating ambulances dynamically, one aims to control the number of relocations to avoid successively relocating the same set of ambulances, long travel times between the initial and final location, and repeated round trips between the same two locations [ 61, 167]. However, the increased movements of ambulances caused by dynamic relocation may also pose advantages. There is a higher chance of receiving a call while on the road, which may result in a decrease in response times caused by shorter turn-out times, that is, the time for a crew to get ready before they can drive to an emergency when they are dispatched [300]. Real-time dynamic relocation is increasingly implementable, due to the increased availability of location information and the decreasing price of computing power [300].

Methods: computer simulation [ 8, 167, 454], Markov processes [ 300, 368], mathematical programming [167], literature review [61].

Treatment planning and prioritization

Each patient may follow a tailored set of stages through the ED, for example patients may receive different diagnostic tests and visit different types of doctors [78]. It is the objective to dynamically plan these stages, such that resource utilization is maximized and waiting time between stages is minimized. Planning the sequence of these stages and the selection of which task for which patient is performed at each point in time includes various factors, such as urgency, medical requirements, resource availability and patient waiting time. This planning decision is highly interrelated with the strategic and tactical level decisions facility layout, patient routing and admission control. As these decisions shape the process flow for a particular patient and set the priority rules applying to the patient. Furthermore, there is a significant interdependence between medical decision making and resource capacity planning in this planning decision.

Methods: computer simulation [ 78, 155].

Staff rescheduling

When emergency demand for ambulances or in the emergency care facility is significantly higher than predicted or when staff is lower than expected (e.g., absent due to illness), additional staff may be required. Especially when senior doctors, who are required for key decisions such as discharge and particular treatments of a patient, are unexpectedly unavailable, it is recommended to call in an additional senior doctor [322].

Methods: computer simulation [458], mathematical programming [322].

3.3. Surgical care services

Surgeries are physical interventions on tissues, generally involving cutting of a patient's tissues or closure of a previously sustained wound, to investigate or treat a patient's pathological condition. Surgical care services have a large impact on the operations of the hospital as a whole [ 29, 46, 72], and they are the hospital's largest revenue center [ 72, 108]. Surgical care services include ambulatory surgical wards, where patients wait and stay before and after being operated. We do not classify such wards as inpatient care services, since patients served on ambulatory basis do not require an overnight stay. The proportion of ambulatory surgeries, which are typically shorter, less complex and less variable [341], is increasing in many hospitals [301]. There is a vast amount of literature on OR/MS in surgical care services, comprehensively surveyed in [ 45, 72, 111, 192, 196, 197, 287, 301, 345, 386, 436]. These surveys are used to create the taxonomic overview of the planning decisions.

Strategic planning

Regional coverage

At a regional level, the number, types and locations of surgical care facilities have to be determined to find a balanced distribution of facilities with respect to the geographical location of demand [130]. The main trade-off in this decision is between patient accessibility and facility efficiency. Coordination of activities between hospitals in one region can provide significant cost reductions at surgical care facilities and downstream facilities [ 50, 365].

Methods: computer simulation [50], mathematical programming [365].

Service mix

An organization selects the particular services that the surgical care facility provides. The service mix stipulates which surgery types can be performed, and therefore impacts the net contribution of a facility [221]. Specific examples of services are medical devices to perform noninvasive surgeries and robotic services for assisting in specialized surgery [107]. In general, the service mix decision is not made at a surgical care service level, but at the regional or hospital level, as it integrally impacts the ambulatory, emergency, surgical and inpatient care services.

Methods: no papers found.

Case mix

The case mix involves the number and types of surgical cases that are performed at the facility. Often, diagnosis-related groups (DRGs), which classify patient groups by relating common characteristics such as diagnosis, treatment, and age to resource requirements, are used to identify the patient types included in the case mix [225]. The case mix is chosen with the objective to optimize net contribution while considering several internal and external factors [ 192, 225]. Internal factors include the limited resource capacity, the settled service mix, research focus, and medical staff preferences and skills [ 46, 192, 239]. External factors include societal preferences, the disease processes affecting the population in the facility's catchment area [46], the case mix of competing hospitals [127], and the restricted budgets and service agreements in government-funded systems [46]. High profit patient types may be used to cross-subsidize the unprofitable ones, possibly included for research or societal reasons [46].

Methods: computer simulation [239], mathematical programming [ 46, 225], literature review [192].

Capacity dimensioning

Surgical care facilities dimension their resources with the objective to optimize hospital profit, idle time costs, surgery delays, access times and staff overtime [ 285, 370]. Therefore, provider capacity must be matched with patient demand [370] for all surgical resource types. The capacity dimensioning decisions for different resource types are highly interrelated and performance is improved when these decisions are coordinated both within the surgical care facility and with capacity dimension decisions in services outside the surgical care facility, such as medical care units and the Intensive Care Unit (ICU) [ 56, 369, 421, 422]. The following resources are dimensioned:

  • Operating rooms. Operating rooms can be specified by the type of procedures that can be performed [ 21, 196, 240, 370].

  • Operating time capacity. This concerns the number of hours per time period the surgical care services are provided [ 239, 301, 369, 402, 421]. Operating time capacity is determined by the number of operating rooms and their opening hours [285].

  • Presurgical rooms. These rooms are used for preoperative activities, for example induction rooms for anesthetic purposes [301].

  • Recovery wards. At these wards, patients recover from surgery [ 255, 256, 257, 369, 370]. The recovery ward is also called Post Anesthesia Care Unit (PACU) [192].

  • Ambulatory surgical ward. At this ward, outpatients stay before and after surgery.

  • Equipment. Equipment may be required to perform particular surgeries. Examples are imaging equipment [197] or robotic equipment [107]. Equipment may be transferable between rooms, which increases scheduling flexibility.

  • Staff. Staff in surgical care services include surgeons, anesthesiologists, surgical assistants and nurse anesthetists [ 5, 64, 107, 221]. Staffing costs are a large portion of costs in surgical care services [ 10, 107]. Significant cost savings can be achieved by increasing staffing flexibility [107], for example by (i) cross-training surgical assistants for multiple types of surgeries [196], (ii) augmenting nursing staff with short-term contract nurses [107], and (iii) drawing nurses from less critical parts in the hospital during demand surges [107].

Methods: computer simulation [ 239, 255, 256, 257, 285, 369, 370, 421], heuristics [ 64, 107, 221], mathematical programming [ 21, 64, 107, 402], queueing theory [285], literature review [ 240, 301].

Facility layout

The facility layout concerns the positioning and organization of different physical areas in a facility. The aim is to determine the layout of the surgical care facility that maximizes the number of surgeries that can take place, given the budgetary and building constraints. A proper integration of the facility layout decision and the patient routing decision decreases costs and increases the number of patients operated [291]. For example, when patients are not anesthetized in the operating room, but in an adjacent induction room, patients can be operated with shorter switching times in between. In [301], contributions that model a facility layout decision for surgical care services are reviewed.

Methods: computer simulation [291], heuristics [330], literature review [301].

Tactical planning

Patient routing

A surgical process consists of multiple stages. We denote the composition and sequence of these stages as the route of a patient. The surgical process consists of a preoperative, perioperative and postoperative stage [ 192, 196, 341]. The preoperative stage involves waiting and anesthetic interventions, which can take place in induction rooms [291] or in the operating room [301]. The perioperative stage involves surgery in the operating room, and the postoperative stage involves recovery at a recovery ward [192]. Recovery can also take place in the operating room when a recovery bed is not immediately available [13]. Surgical patients requiring a bed are admitted to a (inpatient or outpatient) medical care unit before the start of the surgical process, where they return after the surgical process [235]. Efficient patient routes are designed with the objective to increase resource utilization [291].

Methods: computer simulation [291], heuristics [13], mathematical programming [ 13, 341], literature review [ 192, 301].

Capacity allocation

On the tactical level, resource capacities settled on the strategic level are subdivided over patient groups. The objectives of capacity allocation are to trade off patient access time and the utilization of surgical and postsurgical resources [ 45, 123, 192, 287, 402], to maximize contribution margin per hour of surgical time [72], to maximize the number of patients operated, and to minimize staff overtime [201]. Capacity allocation is a means to achieve an equitable distribution of access times [402]. Hospitals commonly allocate capacity through block scheduling [ 151, 192, 433]. Block scheduling involves the subdivision of operating time capacity in blocks that are assigned to patient groups [ 192, 196]. Capacity is allocated in three consecutive steps. First, patient groups are identified. Second, resource capacities, often in the form of operating time capacity, are subdivided over the identified patient groups. Third, blocks of assigned capacity are scheduled to a specified date and time.

  • Patient group identification. In general, patient groups are classified by (sub)specialty, medical urgency, diagnosis or resource requirements. Identification by medical urgency distinguishes elective, urgent and emergent cases [ 72, 145, 192, 196]. Elective cases can be planned in advance, urgent cases require surgery urgently, but can incur a short waiting period, and emergency patients require surgery immediately [ 51, 72]. Examples of patient grouping by resource requirements are inpatients, day-surgery patients [196] and grouping patients by the equipment that is required for the surgery [107].

  • Time subdivision. With the earlier mentioned objectives, operating time is subdivided over the identified patient groups based on expected surgery demand. This is often a politically charged and challenging task, since various surgical specialties compete for a profitable and scarce resource. What makes it even more complex is that hospital management and surgical specialties may have conflicting objectives [48]. When allocating operating time capacity to elective cases, a portion of total operating time capacity is reserved for emergency cases, which arrive randomly [169]. Staff overtime is the result when the reserved capacity is insufficient to serve all arriving emergency patients, but resource idle time increases when too much capacity is reserved, causing growth in elective waiting lists [ 51, 262, 263, 339, 462]. Capacity can be reserved by dedicating one or more operating rooms to emergency cases, or by reserving capacity in elective operating rooms [ 72, 261, 379].

  • Block scheduling. In the last step of capacity allocation, a date and time are assigned to blocks of allocated capacity [29]. Several factors have to be considered in developing a block schedule. For example, (seasonal) variation in surgery demand, the number of available operating rooms, staff capacities, surgeon preferences, and material and equipment requirements [ 29, 365]. Block schedules are often developed to be cyclic, meaning the block schedule is repeated periodically. A (cyclic) block schedule is also termed a Master Surgical Schedule (MSS) [420]. Cyclic block schedules may not be suitable for rare elective procedures [ 192, 420]. For these procedures, capacity can be reserved in the cyclic block schedule [436], or non-cyclical plans may provide an outcome. When compared with cyclic plans, non-cyclic [ 107, 120, 121], or variable plans [240], increase flexibility, decrease staffing costs [107] and decrease patient access time [ 199, 240]. However, cyclic block schedules have the advantage that they make demand more predictable for surgical and downstream resources, such as the ICU and general wards, so that these resources can increase their utilization by anticipating demand more structurally [420].

In addition to block scheduling, the literature also discusses open scheduling and modified block scheduling. Open scheduling involves directly scheduling all patient groups in the total available operating time capacity, without subdividing this capacity first. Although open scheduling is more flexible than block scheduling, open scheduling is rarely adopted in practice [ 48, 192], because it is not practical with regards to doctor schedules and increases competition for operating time capacity [ 287, 345]. Modified block scheduling is when only a fraction of operating time capacity is allocated by means of block scheduling [ 117, 192]. Remaining capacity is allocated and scheduled in a later stage, which increases flexibility to adapt the capacity allocation decision based on the latest information about fluctuating patient demand [192].

Capacity allocation decisions in surgical care services impact the performance of downstream in-patient care services [ 29, 31, 45, 72, 107, 287, 344, 422, 423, 424]. Variability in bed utilization and staff requirements can be decreased by incorporating information about the required inpatient beds for surgical cases in allocating surgical capacity [ 4, 29, 31, 186, 365, 419, 420]. In contributions that model downstream services, it is often the objective to level the bed occupancy in the wards or the ICU, to decrease the number of elective surgery cancellations [ 29, 72, 344, 365, 395, 402, 419, 420], or to minimize delays for inpatients waiting for surgery [459].

Methods: computer simulation [ 51, 117, 120, 121, 262, 339, 459], heuristics [ 29, 30, 31, 395, 431], Markov processes [ 169, 423, 424, 462], mathematical programming [ 29, 30, 31, 47, 48, 80, 107, 199, 262, 344, 365, 395, 402, 403, 419, 420, 459], queueing theory [462], literature review [ 45, 72, 192, 196, 240, 287, 330, 422, 433, 436].

Temporary capacity change

Available resource capacity could be temporarily changed in response to fluctuations in demand [285]. When additional operating time capacity is available, it can be allocated to a particular patient group, for example based on contribution margin [ 196, 436] or access times [402], or it can be proportionally subdivided between all patient groups [ 48, 402].

Methods: computer simulation [117], mathematical programming [ 48, 107, 402], literature review [ 196, 199, 436].

Unused capacity (re)allocation

Some time periods before the date of carrying out a settled block schedule, capacity allocation decisions may be reconsidered in order to reallocate capacity that remains unused [ 125, 196, 215] and to allocate capacity not allocated before (for example in modified block scheduling, discussed in capacity allocation). When unused capacity is released sufficiently early before the surgery time is planned, better quality reallocations are possible than when the unused capacity is released on the same day it is available [215]. Unused capacity is (re)allocated with the same objectives as the capacity allocation decision.

Methods: computer simulation [ 117, 125], heuristics [125], Markov processes [215], literature review [196].

Admission control

Admission control involves the rules according to which patients from different patient groups are selected to undergo surgery in the available operating time capacity. There is a strong reciprocal relation between admission control decisions and capacity allocation decisions: capacity allocation decisions demarcate the available operating time capacity for surgeries, and admission control decisions influence the required operating time capacity. Admission control has the objective to balance patient service, resource utilization and staff satisfaction [45]. It is established by developing an admission plan that prescribes how many surgeries of each patient group to perform on each day, taking the block schedule into account [4]. Balancing the number of scheduled surgical cases throughout the week prevents high variance in utilization of involved surgical resources, such as operating rooms and recovery beds, and downstream inpatient care resources, such as ICU and general ward beds [ 3, 4, 29, 247, 287, 410]. Resource utilization can be improved by using call-in patients [45] and overbooking [51]. Call-in patients are given a time frame in which they can be called in for surgery when there is sufficient space available in the surgical schedule. Overbooking of patients involves planning more surgical cases than available operating time capacity to anticipate for no-shows [29]. Most patients requiring surgical care enter the hospital through the ambulatory care services. Although this makes admission control and capacity allocation policies for both ambulatory and surgical care services interdependent, not much literature is available on the interaction between ambulatory and surgical care services [422].

Methods: computer simulation [ 51, 115, 247, 410], Markov processes [313], mathematical programming [ 3, 4], literature review [ 45, 192].

Staff-shift scheduling

Shifts are hospital duties with a start and end time [65]. Shift scheduling deals with the problem of selecting what shifts are to be worked and how many employees should be assigned to each shift to meet patient demand [141]. The objective of shift scheduling is to generate shifts that minimize the number of staff hours required to cover the desired staffing levels [345]. The desired staffing levels are impacted by the capacity allocation decisions. Hence, integrated decision making for capacity allocation and staff-shift scheduling minimizes required staff [30]. Flexible shifts can improve performance [ 48, 116]. One example is staggered shift scheduling, which implies that employees have varying start and end times of shifts [330]. It can be used to plan varying, but adequate staffing levels during the day, and to decrease overtime [ 48, 116].

Methods: heuristics [112], mathematical programming [ 30, 63, 126], literature review [ 199, 345].

Offline operational planning

Staff-to-shift assignment

In staff-to-shift assignment, a date and time are given to a staff member to perform a particular shift. The literature on shift scheduling and assignment in health care mainly concerns inpatient care services [141], which we address in the section ‘Inpatient care services’.

Methods: no papers found.

Surgical case scheduling

Surgical case scheduling is concerned with assigning a date and time to a specific surgical case. Availability of the patient, a surgeon, an anesthetist, nursing and support staff, and an operating room is a precondition [45]. Surgical case scheduling is an offline operational planning decision, since it results in an assignment of individual patients to planned resources and not in blueprints for assigning surgical cases to particular slots. The objectives of surgical case scheduling are numerous: to achieve a high utilization of surgical and postsurgical resources, to achieve high staff and patient satisfaction, and to achieve low patient deferrals, patient cancellations, patient waiting time and staff overtime [ 72, 107, 150, 235, 289, 341, 361, 379, 441]. The execution of a surgical case schedule is affected by various uncertainties in the preoperative stage duration, surgical procedure duration, switching time, postsurgical recovery duration, emergency patient interruption, staff availability and the starting time of a surgeon [ 192, 341]. These uncertainty factors should be taken into account in surgical case scheduling.

Although surgical case scheduling can be done integrally in one step [ 13, 119, 120, 151, 287, 341, 361, 389], it is often decomposed in several steps. In the latter case, first, the planned length of a surgical case is decided. Second, a date and an operating room are assigned to a surgical case on the waiting list. (also termed the ‘advance scheduling’ [287]). Third, the sequence of surgical cases on a specific day is determined [ 193, 287] (also termed the ‘allocation scheduling’ [287]). Fourth, starting times for each surgical case are determined. Below, we explain these four steps in more detail.

  • Planned length of a surgical case. The planned length of a surgical case is the reserved operating time capacity in the surgical schedule for the surgical case duration, switching time and slack time. Surgical case duration, which is often estimated for each patient individually [327], is impacted by factors as the involved surgeon's experience, and the acuteness, sex and age of the patient [ 113, 327]. Switching time between surgical cases includes cleaning the operating room, performing anesthetic procedures or changing the surgical team [124]. Slack capacity is reserved as a buffer to deal with longer actual surgery durations than expected in advance [201]. When too little time is reserved, staff overtime and patient waiting time occur, and when too much time is reserved, resources incur idle time [ 124, 327, 441].

  • Assigning dates and operating rooms to surgical cases. Dates and operating rooms are assigned to the elective cases on the surgical waiting list, following the settled admission control decisions [ 21, 149, 150, 201, 235, 292, 355]. The available blocks of operating time capacity are filled with elective cases. When too few cases are planned, utilization decreases, leading to longer waiting lists. Conversely, when too many cases are planned, costs increase due to staff overtime [ 51, 355]. Assigning dates and operating rooms to surgical cases can be done by assigning an individual surgical case, or by jointly assigning multiple cases to various possible dates and times. The latter is more efficient as more assignment possibilities can be considered [120].

  • Sequencing of surgical cases. When the set of surgical cases for a day or for a block is known, the sequence in which they are performed still has to be determined. Factors to consider in the sequencing decision are doctor preference [192], medical or safety reasons [ 69, 235], patient convenience [ 69, 70], and resource restrictions [71]. Various rules for sequencing surgical cases are known [ 21, 69, 70, 194, 341, 355, 379]. In general, the traditional first-come-first-serve (FCFS) rule is outperformed by a longest-processing-time-first (LPTF) rule [ 45, 255, 257, 330]. When the variation of surgical case duration is known, sequencing surgical cases in the order of increasing case duration variation (i.e., lowest-variance-first) may yield further improvements [ 108, 441].

  • Assigning starting times to surgical cases. The planned start time of each surgical case is decided [194]. This provides a target time for planning the presurgical and postsurgical resources, and for planning the doctor schedules [441]. The actual start time of a surgical case is impacted by the planned and actual duration of all preceding surgical cases [ 21, 441] and the completion time of the preoperative stage [122].

Emergency cases may play a significant role during the execution of the surgical case schedule [192]. Hence, incorporating knowledge about emergency cases, for example predicted demand, in surgical case scheduling decreases staff overtime and patient waiting time [ 51, 169, 261, 262, 263]. Often, surgical case scheduling is done in isolation. However, efficiency gains may be achieved by also considering decisions in other care services [ 69, 72, 86, 235, 341]. For example, without coordination with the ICU, a scheduled case may be rejected on its day of surgery due to a full ICU [341]. The contributions [ 13, 69, 86, 151, 221, 288, 314, 341, 370] do incorporate other care services, such as the patient wards and ICUs.

Methods: computer simulation [ 10, 51, 86, 114, 117, 119, 120, 123, 145, 194, 255, 257, 261, 262, 370, 403, 441], heuristics [ 10, 13, 71, 108, 113, 149, 151, 193, 194, 221, 261, 263, 292, 355, 361, 389, 418], Markov processes [ 169, 196, 313, 327], mathematical programming [ 13, 21, 69, 70, 71, 80, 86, 106, 107, 108, 149, 150, 151, 193, 235, 261, 262, 263, 289, 292, 339, 341, 355, 361, 379, 402], queueing theory [441], literature review [ 45, 72, 197, 287, 301, 330, 385].

Online operational planning

Emergency case scheduling

Emergency cases requiring immediate surgery are assigned to reserved capacity or to capacity obtained by canceling or delaying elective procedures [420]. It is the objective to operate emergency cases as soon as possible, but also to minimize disturbance of the surgical case schedule [197]. When emergency cases cannot be operated immediately, prioritizing of emergency cases is required to accommodate medical priorities or to minimize average waiting time of emergency cases [ 118, 341].

Methods: mathematical programming [ 118, 341], literature review [197].

Surgical case rescheduling

When the schedule is carried out, unplanned events, such as emergency patients, extended surgery duration and equipment breakdown, may disturb the surgical case schedule [ 3, 289]. Hence, the surgical case schedule often has to be reconsidered during the day to mitigate increasing staff overtime, patient waiting time and resource idle time. Rescheduling may involve moving scheduled surgeries from one operating room to another and delaying, canceling or rescheduling surgeries [289].

Methods: mathematical programming [ 3, 289], literature review [ 196, 197].

Staff rescheduling

At the start of a shift, the staff schedule is reconsidered. Before and during the shift, the staff capacities may be adjusted to unpredicted demand fluctuations and staff absenteeism by using part-time, on-call nurses, staff overtime and voluntary absenteeism [ 191, 342].

Methods: no papers found.

3.4. Inpatient care services

Inpatient care refers to care for a patient who is formally admitted (or ‘hospitalized’) for treatment and/or care and stays for a minimum of one night in the hospital [325]. Owing to progress in medicine inpatient stays have been shortened, with many admissions replaced by more cost-effective outpatient procedures [ 324, 330]. Resource capacity planning has received much attention in the OR/MS literature, with capacity dimensioning being the most prominently studied decision.

Strategic planning

Regional coverage

At a regional planning level, the number, types and locations of inpatient care facilities have to be decided. To meet inpatient service demand, the available budget needs to be spent such that the population of each geographical area has access to a sufficient supply of inpatient facilities of appropriate nature and within acceptable distance [56]. Coordinated regional coverage planning between various geographical areas supports the realization of equity of access to care [ 43, 364]. To achieve this, local and regional bed occupancies need to be balanced with the local and regional probability of admission refusals resulting from a full census. The potential pitfall of deterministic approaches as used in [364] is that resource requirements are underestimated and thus false assurances are provided about the expected service level to patients [209].

Methods: computer simulation [209], mathematical programming [ 56, 364], queueing theory [43].

Service mix

The service mix is the set of services that health care facilities offer. health care facilities that offer inpatient care services can provide a more complex mix of services and can accommodate patient groups with more complex diagnoses [385]. In general, the inpatient care service mix decision is not made at an inpatient care service level, but at the regional or hospital level, as it integrally impacts the ambulatory care facilities, the operating theater and the wards. This may be the reason that we have not found any references focusing on service mix decisions for inpatient care services in specific.

Methods: no papers found.

Case mix

Given the service mix decision, the types and volumes of patients that the facility serves need to be decided. The settled service mix decision restricts the decisions to serve particular patient groups. Patient groups can be classified based on disease type, demographic information and resource requirements [190]. In addition, whether patient admissions are elective or not is an influential characteristic on the variability of the operations of inpatient care services [414]. The case mix decision influences almost all other decisions, in particular the care unit partitioning and capacity dimensioning decisions [24].

Methods: computer simulation [190], heuristics [ 24, 414].

Care unit partitioning

Given the service and case mix decisions, the hospital management has to decide upon the medical care units in which the inpatient care facility is divided. We denote this decision as care unit partitioning. It addresses both the question which units to create and the question which patient groups to consolidate in such care units. Each care unit has its designated staff, equipment and beds (in one or more wards). The objective is to guarantee care from appropriately skilled nurses and required equipment to patients with specific diagnoses, while making efficient use of scarce resources [ 24, 132, 133, 176, 209, 216, 374, 430].

First, the desirability of opening shared higher-level care units like Intensive Care Units (ICU) or Medium Care Units (MCU) should be considered [412]. Second, the general wards need to be specified. Although care unit partitioning is traditionally done by establishing a care unit for each specialty, or sometimes even more diagnosis specific [385], specialty-based categorization is not necessarily optimal. Increasingly, the possibilities and implications of consolidating inpatient services for care related groups is investigated to gain from the economies-of-scale effect, so-called ‘pooling’ [450]. For example, many hospitals merge the cardiac and thoracic surgery unit [186], or allow gynecologic patients in an obstetric unit during periods of low occupancy [303]. In such cases, the overflow rules need to be specified on the tactical level. For geriatric departments, it has to be decided whether to separate or consolidate assessment, rehabilitation and long-stay care [ 307, 308]. Also, multi-specialty wards can be created for patients of similar length of stay, such as day-care, short, week- and long-stay units [ 374, 430], or for acute patients [ 224, 414]. Concentrating emergency activities in one area (a Medical Assessment Unit) can improve efficiency and minimize disruption to other hospital services [323]. One should be cautious when pooling beds for patient groups with diverging service level [186] or nursing requirements [264]. A combined unit would require the highest service and nurse staffing level for all patient groups. As a result, acceptable utilization may be lower than with separate units. Also, pooling gains should be weighed against possible extra costs for installing extra equipment on each bed [264]. To conclude, the question whether to consolidate or separate clinical services from a logistical point of view is one that should be answered for each specific situation, considering demand characteristics but also performance preferences and requirements [209]. Obviously, the care unit partitioning decision is highly interrelated with the capacity dimensioning decisions, to be discussed next.

Methods: computer simulation [ 132, 133, 176, 209, 224, 374], heuristics [ 24, 264, 414], mathematical programming [323], queueing theory [ 186, 216, 303, 307, 308, 412, 450].

Capacity dimensioning

In conjunction with the care unit partitioning, the size of each care unit needs to be determined. Care unit size is generally expressed in the number of staffed beds, as this number is often taken as a guideline for dimensioning decisions for other resources such as equipment and staff.

  • Beds. The common objective is to dimension the number of beds of a single medical care unit such that occupancy of beds is maximized while a predefined performance norm is satisfied [ 178, 319, 321, 354, 428, 447]. The typical performance measure is the percentage of patients that have to be rejected for admission due to lack of bed capacity: the admission refusal rate. Several other consequences of congested wards can be identified, all being a threat to the provided quality of care. First, patients might have to be transferred to another hospital in case of an emergency [ 92, 248, 297, 452]. Second, patients may (temporarily) be placed in less appropriate units, so-called misplacements [ 96, 132, 133, 186, 208, 213, 452]. Third, backlogs may be created in emergency rooms or surgical recovery units [ 88, 176, 186, 322, 323]. Fourth, elective admissions or surgeries may have to be postponed, by which surgical waiting lists may increase [ 7, 96, 178, 451, 452], which negatively impacts the health condition of (possibly critical) patients [ 410, 416]. Finally, to accommodate a new admission in critical care units, one may predischarge a less critical patient to a general ward [ 129, 445]. The number of occupied beds is a stochastic process, because of the randomness in the number of arrivals and lengths of stay [251]. Therefore, slack capacity is required and thus care units cannot operate at 100% utilization [ 102, 186]. Often, inpatient care facilities adopt simple deterministic spreadsheet calculations, leading to an underestimation of the required number of beds [ 88, 96, 102, 204, 209]. Hospitals commonly apply a fixed target occupancy level (often 85%), by which the required number of beds is calculated. Such a policy may result in excessive delays or rejections [ 17, 186, 209, 251, 319]. The desirable occupancy level should be calculated as a complex function of the service mix, the number of beds and the length of stay distribution [ 208, 209]. This nonlinear relationship between number of beds, mean occupancy level and the number of patients that have to be rejected for admission due to lack of bed capacity is often emphasized [ 7, 102, 208, 213, 251, 319, 320, 354]. In determining the appropriate average utilization, the effect of economies-of-scale due to the so-called portfolio effect plays a role: larger facilities can operate under a higher occupancy level than smaller ones in trying to achieve a given patient service level [ 186, 209, 210, 251], since randomness balances out. However, possible economies of scope due to more effective treatment or use of resources should not be neglected [186]. Units with a substantial fraction of scheduled patients can in general operate under a higher average utilization [186]. The effect of variability in length of stay on care unit size requirements is shown to be less pressing than often thought by hospital managers [ 186, 416]. Reducing the average length of stay shows far more potential. For care units that have a demand profile with a clear time-dependent pattern, these effects are preferably explicitly taken into account in modeling and decision making, to capture the seasonal [ 213, 286], day-of-week [ 129, 162, 213, 223] and even hour-of-day effects [ 27, 62, 88, 208]. This especially holds for units with a high fraction of emergencies admissions [385]. Capacity decisions regarding the size of a specific care unit can affect the operations of other units. Therefore, the number of beds needs to be balanced among interdependent inpatient care units [ 7, 60, 88, 89, 190, 209, 216, 224, 278, 297, 385]. Models that consider only a single unit neglect the possibility of admitting patients in a less appropriate care unit and thus the interaction between patient flows and the interrelationship between care units. Next to estimating utilization and the probability of admission rejections or delays, models that do incorporate multiple care units, also focus on the percentage of time that patients are placed in a care unit of a lower level or less appropriate care unit, or in a higher level care unit [ 11, 92, 172, 186, 278, 374]. The first situation negatively impacts quality of care as it can lead to increased morbidity and mortality [410] and the second negatively impacts both quality of care, as it may block admission of another patient, and efficient resource use [ 186, 374]. Some multi-unit models explicitly take the patient's progress through multiple treatment or recovery stages into account and try to dimension the care units such that patients can in each stage be placed in the care units that are most suitable regarding their physical condition [ 88, 92, 102, 146, 166, 171, 206, 211, 212, 224, 297, 374, 412].

  • Equipment. In [430], it is stated that pooling equipment among care units can be highly beneficial. However, no references have been found explicitly focusing on this planning decision. This might be explained by the fact that the care unit partitioning and size decisions are generally assumed to be translatable to equipment capacity requirements. Therefore, many of the references mentioned under these decisions are useful for the capacity dimensioning of equipment.

  • Staff. The highest level of personnel planning is the long-term workforce capacity dimensioning decision. This decision concerns both the number of employees that have to be employed, often expressed in the number of full time equivalents, and the mix in terms of skill categories [ 207, 322]. For inpatient care services it mainly concerns nursing staff. To deliver high-quality care, the workforce capacity needs to be such that an appropriate level of staff can be provided in the different care units in the hospital [ 141, 172]. In addition, holiday periods, training, illness and further education need to be addressed [65]. Workforce flexibility is indicated as a powerful concept in reducing the required size of workforce [ 65, 104, 172, 385]. To adequately respond to patient demand variability and seasonal influences, it pays off to have substitution possibilities of different employee types, to use overtime, and to use part-time employees and temporary agency employees [385]. Just as with pooling bed capacity, economies-of-scale can be gained when pooling nursing staff among multiple care units. Nurses cross-trained to work in more than one unit can be placed in a so-called floating nurse pool [ 65, 172, 264, 385]. Note that flexible staff can be significantly more expensive [191]. Also, [271] indicates that to maintain the desired staff capacity, it is necessary to determine the long-term human resource planning strategies with respect to recruiting, promotion and training. To conclude, integrating the staff capacity dimensioning decision with the care unit size decision yields a significant efficiency gain [172].

Methods: computer simulation [ 7, 17, 88, 92, 96, 132, 133, 176, 190, 191, 204, 207, 208, 209, 210, 224, 248, 251, 297, 319, 320, 321, 322, 354, 374, 410, 428, 445, 447, 451, 452], heuristics [264], Markov processes [ 7, 62, 146, 166, 171, 211, 212, 213, 286], mathematical programming [ 104, 172, 207, 271, 278, 322, 323], queueing theory [ 11, 27, 60, 88, 89, 102, 129, 162, 178, 186, 206, 216, 223, 248, 278, 354, 412, 416], literature review [ 65, 141, 342, 385].

Facility layout

The facility layout concerns the positioning and organization of different physical areas in a facility. To determine the inpatient care facility layout, it needs to be specified which care units should be next to each other [330] and which care units should be close to other services like the surgical, emergency and ambulatory care facilities [67]. Ideally, the optimal physical layout of an inpatient care facility is determined given the decisions on service mix, case mix, care unit partitioning and care unit size. However, in practice, it often happens vice versa: physical characteristics of a facility constraint service mix, care unit partitioning and care unit size decisions [ 67, 430]. Newly built hospitals are preferably designed such that they support resource pooling and have modular spaces so that they are as flexible as possible with respect to care unit partitioning and dimensioning [430].

Methods: computer simulation [67], heuristics [330], mathematical programming [67].

Tactical planning

Bed reallocation

Given the strategic decision making, tactical resource allocation needs to ensure that the fixed capacities are employed such that inpatient care is provided to the right patient groups at the right time, while maximizing resource utilization. Bed reallocation is the first step in tactical inpatient care service planning. Medium-term demand forecasts may expose that the care unit partitioning and size decisions fixed at the strategic level are not optimal. If the ward layout is sufficiently flexible, a reallocation of beds to units or specialties based on more specific demand forecast can be beneficial [ 24, 208, 431]. In addition, demand forecasts can be exploited to realize continuous reallocation of beds in anticipation for seasonality in demand [242]. To this end, hospital bed capacity models should incorporate monthly, daily and hourly demand profiles and meaningful statistical distributions that capture the inherent variability in demand and length of stay [204]. When reallocating beds, the implications for personnel planning, and involved costs for changing bed capacity, should not be overlooked [6].

Methods: computer simulation [ 208, 242], heuristics [ 24, 431], mathematical programming [6], queueing theory [242].

Temporary bed capacity change

To prevent superfluous staffing of beds, beds can temporarily be closed by reducing staff levels [186]. This may for instance be in response to predicted seasonal or weekend demand effects [ 204, 210]. The impact of such closings on the waiting lists at referring outpatient clinics and the operating room is studied by [ 450, 451]. Temporary bed closings may also be unavoidable as a result of staff shortages [297]. In such cases hospitals can act pro-actively, to prevent bed closings during peak demand periods [24].

Methods: computer simulation [ 204, 210, 297, 451], heuristics [24], queueing theory [ 186, 450].

Admission control

To provide timely access for each different patient group, admission control prescribes the rules according to which various patients with different access time requirements are admitted to nursing wards. At this level, patients are often categorized in elective, urgent and emergency patients. Admission control policies have the objective to match demand and supply such that access times, rejections, surgical care cancellations and misplacements are minimized while bed occupancy is maximized. The challenge is to cope with variability in patient arrivals and length of stay. Smoothing patient inflow, and thus workload at nursing wards, prevents large differences between peak and non-peak periods, and so realizes a more efficient use of resources [ 4, 204, 432].

Patient resource requirements are another source of variability in the process of admission control. Most references only focus on maximizing utilization of bed resources. This may lead to extreme variations in the utilization of other resources like diagnostic equipment and nursing staff [385]. Also, as with temporarily closing of beds, possible effects of admission control policies on the waiting lists at referring outpatient clinics and the operating room should not be neglected [378]. Admission control policies can be both static (following fixed rules) and dynamic (changing rules responding to the actual situation).

  • Static bed reservation. To anticipate for the estimated inflow of other patient groups, two types of static bed reservation can be distinguished. The first is refusing admissions of a certain patient type when the bed census exceeds a threshold. For example, to prevent the rejection of emergent admission requests, an inpatient care unit may decide to suspend admissions of elective patients when the number of occupied beds reaches a threshold [ 142, 163, 232, 243, 297, 303, 354, 378]. As such, a certain number of beds is reserved for emergency patients. This reservation concept is also known as ‘earmarking’. Conversely, [ 249, 410] indicate that earmarking beds for elective postoperative patients can minimize operating room cancellations. In the second static level the number of reserved beds varies, for example per weekday. Examples of such a policy are provided in [42], and [413] in which for each work day a maximum reservation level for elective patients is determined.

  • Dynamic bed reservation. Dynamic bed reservation schemes take into account the actual ‘state’ of a ward, expressed in the bed census per patient type. Together with a prediction of demand, the reservation levels may be determined for a given planning horizon [252] or it may be decided to release reserved beds when demand is low. Examples of the latter are found in [249], where bed reservations for elective surgery are released during weekend days, and [28], where admission quota are proposed per weekday. In [214], an extension to dynamic reservation is proposed which concerns calling in semi-urgent patients from an additional waiting list on which patients are placed who needs admission within 1–3 days.

  • Overflow rules. In addition to the bed reservation rules, overflow rules prescribe what happens in the case that all reserved beds for a certain patient type are occupied. In such cases, specific overflow rules prescribe which patient types to place in which units [209]. Generally, patients are reassigned to the correct treatment area as soon as circumstances permit [385]. By allowing overflow and setting appropriate rules, the benefits of bed capacity pooling are utilized (see capacity dimensioning: care unit size), while the alignment of patients with their preferred bed types is maximized [297]. Various references focus on predicting the impact of specific overflow rules [ 180, 209, 216, 297, 374].

  • Influence surgical schedule. For many inpatient care services the authority on admission control is limited due to the high dependency on the operating room schedule (see surgical care services). By adjusting the surgical schedule, extremely busy and slack periods can be avoided [ 4, 24, 129, 132, 145, 180, 186, 204, 402, 423, 424, 431, 432, 452] and cancellation of elective surgeries can be avoided [247]. In practice, the operating room planning is generally done under the assumption that a free bed is available for postoperative care [249], which may result in surgery cancellations. Therefore, both for inpatient and surgical care services coordinated planning is beneficial [ 3, 204].

Methods: computer simulation [ 3, 132, 145, 180, 204, 209, 247, 249, 297, 354, 374, 402, 410, 432, 452], heuristics [ 24, 431], Markov processes [ 42, 142, 214, 216, 252, 423, 424], mathematical programming [ 3, 4, 28, 402], queueing theory [ 28, 129, 163, 186, 232, 243, 303, 378, 413].

Staff-shift scheduling

Shifts are hospital duties with a start and end time [65]. Shift scheduling deals with the problem of selecting what shifts are to be worked and how many employees should be assigned to each shift to meet patient demand [ 141, 246]. For inpatient care services, it generally concerns the specification of 24-h-a-day-staffing levels divided in a day, evening and night shift, during which demand varies considerably [ 65, 141]. Typically, this is done for a period of one or two months [342]. Staffing levels need to be set both for each care unit's dedicated nurses and for flexible staff in floating pools [264]. Also, [ 104, 191] investigate the potential of on-call nurses who are planned to be available during certain shifts and only work when required.

The first step in staff shift scheduling is to determine staffing requirements with a demand model [ 141, 199, 246, 396], based on which the bed occupancy levels [385] and medical needs are forecasted [264]. The second step is to translate the forecasted demand in workable shifts and in the number of nurses to plan per shift, taking into account the staff resources made available at the strategic decision level [437]. Often, nurse-to-patient ratios are applied in this step [191], which are assumed to imply acceptable levels of patient care and nurse workload [453]. To improve the alignment of care demand and supply, shift scheduling is preferably coordinated with scheduled admissions and surgeries [342], which also helps avoiding high variation in nurse workload pressure [30].

Methods: computer simulation [191], heuristics [264], mathematical programming [ 30, 104, 437, 453], queueing theory [396], literature review [ 65, 141, 199, 246, 342, 385].

Offline operational planning

Admission scheduling

Governing the rules set by tactical admission control policies, on the operational decision level the admission scheduling determines for a specific elective patient the time and date of admission. We found one reference on this decision: [95] presents a scheduling approach to schedule admissions for a short-stay inpatient facility that only operates during working days, which takes into account various resource availabilities such as beds and diagnostic resources. We suggest two reasons for the lack of contributions on this decision. First, when admission control policies are thoroughly formulated, admission scheduling is fairly straightforward. Second, as described before, for postoperative inpatient care authority of admission planning is generally at the surgical care services [431].

Methods: mathematical programming [95].

Patient-to-bed assignment

Together with the admission scheduling decision, an elective patient needs to be assigned to a specific bed in a specific ward. Typically, this assignment is carried out a few days before the effective admission of the patient. The objective is to match the patient with a bed, such that both personal preferences (for example a single or twin room) and medical needs are satisfied [ 79, 105]. An additional objective may be to balance bed occupancy over different wards.

Methods: heuristics [ 79, 105], mathematical programming [ 79, 105].

Discharge planning

Discharge planning is the development of an individualized discharge plan for a patient prior to leaving the hospital. It should ensure that patients are discharged from the hospital at an appropriate time in their care and that, with adequate notice, the provision of other care services is timely organized. The aim of discharge planning is to reduce hospital length of stay and unplanned readmission, and improve the coordination of services following discharge from the hospital [376]. As such, discharge planning is highly dependent on availability downstream care services, such as rehabilitation, residential or home care. Therefore, a need is identified for integrated coherent planning across services of different health care organizations [ 426, 442]. Patients whose medical treatment is complete but cannot leave the hospital are often referred to as ‘alternative level of care patients’ or ‘bed blockers’ [ 422, 442]. Also in discharge planning it is worthwhile to anticipate for seasonality effects.

Methods: computer simulation [426], queueing theory [442], literature review [376].

Staff-to-shift assignment

Staff-to-shift assignment deals with the allocation of staff members to shifts over a period of several weeks [141]. The term ‘nurse rostering’ is also often used for this step in inpatient care services personnel planning [ 65, 84]. The objective is to meet the required shift staffing levels set on the tactical level, while satisfying a complex set of restrictions involving work regulations and employee preferences [ 40, 65, 84, 234, 246, 415]. Night and weekend shifts, days off and leaves have to be distributed fairly [ 342, 385, 453] and as much as possible according to individual preferences [ 40, 141]. In most cases, to compose a roster for each individual, first sensible combinations or patterns of shifts are generated (cyclic or non-cyclic), called ‘lines-of-work’, after which individuals are assigned to these lines-of-work [141]. Sometimes, staff-to-shift assignment is integrated with staff-shift scheduling [ 65, 453]. ‘Self-scheduling’ is an increasingly popular concept aimed at increased staff satisfaction which allows staff members to first propose individual schedules, which are taken as starting point to create a workable schedule that satisfies the staffing level requirement set on the tactical level [362].

Methods: heuristics [ 40, 415], mathematical programming [ 40, 234, 362, 415, 453], literature review [ 65, 84, 141, 246, 342, 385].

Online operational planning

Elective admission rescheduling

Based on the current status of both the patient and the inpatient care facility, it has to be decided whether a scheduled admission can proceed as planned. Circumstances may require postponing or canceling the admission, to reschedule it to another care unit, or to change the bed assignment. Various factors will be taken into consideration such as severity of illness, age, expected length of stay, the probable treatment outcome, the (estimated) bed availability, and the conditions of other patients (in view of the possibility of predischarging an other patient) [ 248, 282, 377]. This decision is generally made on the planned day of admission or a few days in advance. Rescheduling admissions can have a major impact on the operations at the surgical theater [248].

Methods: computer simulation [248], heuristics [282], queueing theory [ 248, 377].

Acute admission handling

For an acute admission request it has to be decided whether to admit the emergency patient and if so to which care unit, which bed, and on what notice. The tactical admission control rules act as guideline. As with rescheduling elective admissions, the status of both the patient and the inpatient care facility are taken into account [ 248, 377]. In [248], it is calculated how long the waiting will be if the patient is placed on ‘the admission list’ and [377] proposes and evaluates an admission policy to maximize the expected incremental number of lives saved from selecting the best patients for admission to an ICU.

Methods: computer simulation [248], queueing theory [ 248, 377].

Staff rescheduling

At the start of a shift, the staff schedule is reconsidered. Based on severity of need in each care unit, the float nurses and other flexible employees are assigned to a specific unit and a reassignment of dedicated nurses may also take place [