Modeling, Configuration and Assessment of Regeneration Supply Chains

Abstract

In contrast to the conventional manufacturing industry, the regeneration of complex capital goods is subject to additional information uncertainty and disturbances throughout the order processing phase. To achieve a high logistics performance despite these constraints, supply chain configurations and appropriate tools are required to address the resulting challenges. Along a roadmap, this report presents measures and tools that support the reduction of information uncertainty, the description of effects of uncertainty within regeneration planning and control and in regeneration logistics as well as a superordinate assessment and configuration of regeneration supply chains. For forecasting a Bayesian Network based approach is presented. The planning quality that is achieved based on these forecasts is assessed using a descriptive model based on the classic milestone trend analysis. To support logistics oriented regeneration supply chain assessment and configuration an extensive simulation model as well as a model for pool stock dimensioning is presented. These tools and models represent the results of the subproject D1 of the CRC871 that had the overall goal to empower regeneration service providers to establish robust regeneration supply chains.

1 Introduction

In recent years, a growing social, economic and political interest and striving for the sustainable use of resources and products in the sense of a circular economy can be observed worldwide (Cervelló-Royo et al. 2020; Liu et al. 2021). A prominent example of this kind of circular economy represents the regeneration of complex capital goods. The regeneration of complex capital goods, such as jet engines, stationary gas turbines or wind turbines, comprises maintenance, repair and overhaul (MRO) activities and serves to generate additional “life cycles” at the end of a use phase of the products (Guide et al. 1997). The terms “regeneration” and “MRO” will be used as synonyms below. Starting from an initial diagnosis, the generic regeneration process can be separated into the disassembly of the complex capital good, an inspection, the repair or replacement of damaged components, the subsequent reassembly as well as a final inspection and quality assurance (see Fig. 1) (Eickemeyer et al. 2011; Guide et al. 1997; Lucht et al. 2019; Lund 1984).

Fig. 1

Regeneration supply chain structure (based on Eickemeyer et al. 2011; Guide et al. 1997)

The diagnosis performed before physical induction forms the basis for the definition of the required depth of disassembly (full or partial) and the initial scheduling of the regeneration process (Eickemeyer et al. 2011; Seitz et al. 2020). Disassembly can be performed either on flow lines or in so-called docks (Burmeister et al. 2004). Flow line organization tends to offer advantages in efficiency, by allowing to synchronize processing of the regeneration orders along the supply chain. Disassembly in docks allows for a (limited) interchange of disassembly sequences—e.g., sorted by earliest repair start date of single components that have already been identified as damaged in the diagnosis. Further discussion on this can be found in Lucht et al. (2020).

The disassembled components then undergo a detailed inspection to gather reliable information about the repair measures required for regeneration and spare parts demands. Here, discrepancies between the predicted damage pattern and the final inspection result can occur. If this is not taken into account in supply chain design and planning, there is a risk of considerable turbulence in the form of schedule deviation or long waiting times for missing material or capacities (Dombrowski and Sendler 2016). The same may result if (additional) rework is required during repair, should damage only be detected or even caused there. Instead of repairing unserviceable components, the components required for reassembly can be provided from spare parts pools (Kuprat et al. 2016).

Both a pool containing serviceable (SA) components and a pool of repairable (RA) components are established in many MRO supply chains (Lucht et al. 2019). The pools offer the possibility to cushion uncertainties about spare parts stock levels and alternative supply paths (Kuprat 2018; Lucht et al. 2021a). However, these serviceable components are often very expensive, so spare parts inventories must be kept as low as possible. An order-specific provision via new parts procurement is also possible but mostly comes at very high costs and extensive delivery lead times. Once all components are ready for installation, reassembly and quality assurance can be performed. The capital good can then be handed back to the owner to continue service in another life cycle (Guide et al. 1997; Guide 2000; Lund 1984).

During regeneration, the capital goods are not available for the provision of services (e.g., the transport of passengers) and thus the generation of revenue. Hence, lead time extensions of the regeneration are directly linked to losses in revenue. It should be noted, however, that in most cases the capital goods could not be used without the MRO event either, as components have reached their operational limits or are no longer serviceable due to other influences. Nonetheless, the turnaround time (TAT) forms the basis for the operators’ operational planning. Using the example of an aircraft, this means that the aircraft is assigned to specific flights. If there are deviations from the planned TAT, this not only limits the ability to generate revenue, but at the same time leads to a major need for rescheduling by the operators (Herde 2013). Consequently, deviations from promised TAT or delivery dates are usually tied to strong penalties (Eickemeyer et al. 2013). As a result, achieving the highest possible planning reliability and accuracy is of primary importance while also ensuring short TAT. This is countered by a great uncertainty in information regarding the timing and scope of a regeneration order due to the variety of possible damage patterns in conjunction with a large number of components as well as the highly dynamic market and production environment (Reményi and Staudacher 2014).

The actual damage of the individual components can usually only be precisely determined during the inspection following disassembly or even during the repair process—for example, after coatings have been removed. However, unforeseen faults can still occur within the advanced regeneration process. To avoid negative impacts on the regeneration service providers’ logistics performance suitable measures are required to ensure the regeneration order can still be completed on time. In other words, regeneration service providers must design their production systems to be as robust as possible, while robustness in here refers to “stability against different varying conditions” (Stricker and Lanza 2014).

To support regeneration service providers, various tools and approaches have been developed in subproject D1 of the Collaborative Research Center 871. These are organized into three major fields of action. They also provide the structure of the remainder of this paper. Section 2 gives an overview of these fields of action that simultaneously represents the overall roadmap of the subproject. Based on this, the fields of action are presented separately in Sects. 3 (improving forecast quality), 4 (assessing planning quality) and 5 (assessing and configuring of regeneration supply chains). Section 6 sums up the outline of this paper and provides an outlook to further research and transfer activities.

2 Objective and Structure of the Fields of Action

Subproject D1 of CRC 871 focuses on the design of an efficient and robust regeneration logistics system through three major fields of action (see Fig. 2). These also form the overall structure of the following sections.

Fig. 2

Roadmap and modular structure of subproject D1

The first field of action addresses the uncertainty at the beginning of the regeneration process. The aim is to minimize this uncertainty to improve the planning basis for the subsequent regeneration process.

The second field of action focuses on increasing transparency of the logistics consequences of this uncertainty within the regeneration process. In particular the focus lies on assessing the planning quality of the planning processes as critical tasks both for the internal processes as well as for communication and coordination with customers, partners and suppliers and thus making them accessible for improvement measures.

Since random disruptions can still occur even with complete information availability, the third field of action aims to compensate for the remaining disruptive influences as efficiently as possible by means of a suitable design of the supply chain and configuration of production planning and control. The supply chain design and the configuration of production planning and control (subsequently subsumed as “production configuration”) must take these challenges into account and provide suitable tools to reduce or compensate for any turbulence to ensure a high level of logistics efficiency.

3 Reducing Uncertainty Using Data-Based Forecasting

The first of the three fields of action focuses on the forecast of the capacity load expected from a regeneration order upstream of the actual regeneration process. This is of essential importance for the planning of the regeneration process, as it supports the definition of realistic delivery times and at the same time the demand-oriented dimensioning of capacities and material stock and allows a higher precision (Reményi et al. 2011). However, due to the unique nature of regeneration orders, conventional, time series-based forecasting approaches are unsuitable for making a forecast with acceptable accuracy for practical applications. Instead, order-specific forecasting approaches allow to take into account the information available at a specific point in time from a specific usage profile of a regeneration object and knowledge from past regeneration orders for the forecast. These order-specific forecasts can then be used to aggregate the total load resulting from the order spectrum. A schematic representation of the described prognosis method developed within the subproject shown in Fig. 3.

Fig. 3

Data-based forecasting of capacity demand (based on (Eickemeyer et al. 2013; Eickemeyer 2014))

In order to make the data of different types and origins required for this purpose usable for forecasting, they can be merged into a higher-level database using data mining methods, as shown in Fig. 3 (Eickemeyer et al. 2013). In this context, the usage profile of the capital goods is characterized, among other things, by information regarding the place as well as the time and type of operation. Following the example of an aircraft engine, the number of flown cycles (i.e. completed cycles consisting of take-off, flight phase, and landing) can be used for this purpose (Seitz et al. 2020). Potential further information is provided by temperature, pressure and speed curves (Weiss et al. 2022). Information from past regeneration runs, however, can include customer data, schematics, component information, and detailed data on regeneration paths (required repair processes, setup times, processing times etc.).

The damage library compiled in this way makes it possible to predict the existing but not yet identified damage to a capital good depending on the specific usage profile. The actual damage for individual usage profiles can be inferred by using databased fore-casting methods. Additionally, such database can also predict the resulting workload in the event of a need for regeneration. The knowledge stored in corresponding databases can be extracted using Bayesian networks (Berkholz 2012; Eickemeyer et al. 2013; Seitz et al. 2019). With these, a high forecasting quality can be achieved in practical applications. It has been shown that the application of Bayesian networks is useful for forecasting the workload of entire complex capital goods, individual assemblies and components as well as the loads on the workstation level in the regeneration of complex capital goods (Eickemeyer et al. 2013). Furthermore, beyond capacity planning and coordination, e.g., for dimensioning pool inventories, Bayesian networks have the potential to make helpful forecasts and increase planning reliability. A typical example is the decision to accept new orders (Eickemeyer and Herde 2012). The improved prediction of capacity demands of regeneration objects that are still in the utilization phase allows a better estimation of the arising efforts and costs of regeneration service providers. Thus, it forms the basis for a more precise (capacity) planning (Berkholz 2012) and a higher logistics efficiency. Improved throughput or delivery time forecasts are also possible as well taking into account information about the current workload in the regeneration supply chain (Hiller et al. 2021).

4 Assessment of Planning Quality in Regeneration

Even if a significant improvement of the information accuracy can be achieved using the increasing data availability described above (see dotted line in Fig. 4), uncertainties remain, which lead to turbulences in the regeneration process and thus to deviations from planned states and dates. Due to the regeneration-specific uncertainties in information and data basis, which only diminishes within the regeneration process (see Fig. 4), frequent adjustments of planned dates are required in practice to reflect the changing information within these.

Fig. 4

Qualitative development of information accuracy along the regeneration process (based on (Eickemeyer et al. 2012))

Although adjustments to the plans are necessary in practice to provide the operational order processing with the most up-to-date information, this also leads to “concealing” planning errors that—in consequence—cannot be assessed in an a posteriori performance controlling anymore (Lucht et al. 2021b). However, corresponding planning iterations can be systematically described using a so-called plan history diagram (PHD) and thus made accessible for analyses. For this purpose, the temporal distance between a planned date and the observation period is plotted over time (see Fig. 5). If a plan remains unchanged over time, this results in a straight line that continuously approaches the horizontal axis. For example, the remaining throughput time until the planned realization of a date is reduced by one day with each additional day that passes. This describes the ideal process by one day scheduling without further schedule adjustments during order processing. Shifts in dates are expressed accordingly as swings in a positive direction (shifting a date into the future) or in a negative direction (bringing a date earlier).

Fig. 5

Normalized plan history diagram of four regeneration orders with characteristic rescheduling patterns (based on (Lucht et al. 2021b))

Figure 5 shows the corresponding planned date curves of four orders of a real use case (regeneration service provider) in a PHD. Here, the planned date curves of the regeneration orders of one exemplary product group are normalized to a common start date. In addition to a comparison of different planned date curves, characteristic patterns in the planned date curves can also be identified. Characteristic planned date adjustments are recognizable within the time of reaching the marked milestone. In this example, this milestone represents the completion of the inspection of all disassembled components. At this time, for the first time, there are more or less reliable insights into the actual damage pattern of the regeneration good. The recurring planned date adjustments identified in this way can thus be made accessible to a root cause analysis and thus potential measures such as the adjustment of the scheduling algorithm on which these dates are based can be initiated. Typical causes found for recurring schedule delays at the completion of this milestone were found to be systematically underestimated workload of regeneration orders or recurringly required customer clarifications not considered in the planning.

Overall, the PHD allows for a systematic description and investigation of planning processes in turbulent production environments that require frequent planning iterations. In this way, schedule shifts can be described and the causal disruptive influences as well as weak points in the production configuration can be identified. The production configuration must be fundamentally suitable for achieving the required logistics performance and, accordingly, for compensating for external and internal disruptive influences. The definition of a suitable production configuration is an extremely complex task due to the large number of influencing factors to be taken into account and their mutual dependencies, and is therefore discussed in detail in the following section.

5 Configuration of Regeneration Supply Chains

Depending on the selected configuration of the supply chain, regeneration service providers are able to offer a certain logistics performance on the market. As described above, the customer perceives this via key figures for on-time delivery and the delivery time offered. For high profitability of the regeneration process, regeneration service providers must therefore realize a high on-time delivery and short delivery times with the lowest possible logistics costs. Even if the configuration is defined to a certain degree by the capital goods themselves and by the technologies required for regeneration, there remain degrees of freedom on the production logistics side with regard to the provision of capacity, scheduling and lot sizing procedures, and control and processing strategies. The design of these degrees of freedom directly impacts the logistics performance and the logistics costs of all individual processes. The parameterization of the individual processes directly influences the overall performance of the supply chain and thus on the performance perceived by the customer due to the existing interactions within the regeneration supply chain. The production configuration can be divided into four successive levels (see Fig. 6).

Fig. 6

levels of production configuration (based on (Mütze et al. 2022))

At the strategic levels 1 and 2, a distinction can be made between the definition of the goal and the structural configuration of the supply chain. The configuration of planning and control within the structure-forming macro processes represents the tactical level 3 of production configuration. Finally, the fourth level addresses production monitoring and root cause analysis for potential deviations as a starting point for adjustments to the existing production configuration. Among other things, the PHD already presented above can be used for this purpose (Mütze et al. 2022). The key configuration decisions are made at levels 2 and 3 so that these are the focus of the following subsections.

For this purpose, a simulation-based evaluation tool for the comparison of different supply chain configurations is presented (Sect. 5.1). On this basis, general cause-effect relationships with a focus on pooling as a regeneration-specific configuration option are modeled (Sect. 5.2) and approaches for the operational implementation of dynamic capacity and material planning are presented (Sect. 5.3).

6 Simulation-Based Support in Strategic and Tactical Configuration of Regeneration Supply Chains

The multitude of influencing factors, configuration options as well as their interactions along the supply chain (Lucht et al. 2019) makes production configuration and especially the selection of appropriate procedures for production planning and control (PPC) extremely complex. Often, decisions on the design of the supply chain structure cannot be made in isolation from configuration decisions such as the selection of specific order release or sequencing procedures at individual work systems (Mundt et al. 2020). At the same time, these usually are also dependent on boundary conditions and input variables that cannot be influenced or are difficult to influence, making it extremely difficult or even impossible to apply common logistics models to evaluate all possible configurations.

Therefore, effective support for regeneration service providers in this respect lies in making configuration decisions assessable and thus manageable. To allow corresponding evaluations without having to run simulations during operation, a model was developed to easily assess and compare potential configurations and scenarios. Simulation serves as a suitable tool for investigating various configurations in combination with variable boundary conditions and evaluating their logistics performance (Nyhuis et al. 2005). This section presents the simulation model for assessing the logistics effects of various production configurations and MRO-specific disturbances and uncertainties. The focus lies on the overall structure of the model, the design and configuration options modeled herein, and the aggregation of the simulation results within an assessment model, which serves to improve accessibility of the simulation results. This allows the comparison of different configurations and thus supports the selection of a suitable configuration depending on the respective boundary conditions. Thus, both structural design options, which lie in the regeneration in the introduction of one- or two-stage pooling, and parameterizable planning and control procedures of individual processes are made accessible to an evaluation.

6.1 Model and Supply Chain Structure, Disturbances and Uncertainties

To analyze the interdependencies and the logistics performance achievable with various supply chain and PPC configurations the simulation model is implemented as a time discrete model using Siemens Tecnomatix PlantSimulation v15.3. The basic supply chain structure follows the generic process model of regeneration presented in Sect. 1. At the top level, it comprises disassembly, inspection, repair, reassembly and a final test (see Fig. 7). The models features arranged below this macroscopic structure are described in the following section. Here, the focus is on the configuration options available.

Fig. 7

Macro level of the overall simulation model implemented in PlantSimulation

The capital goods to be regenerated are modeled as modular products consisting of six modules with defined precedence relationships for disassembly and reassembly. This structure is adapted from the modular design of an aircraft engine, which can be seen as a typical example of a capital good to be regenerated. The intermediate arrival time of the orders is assumed to be normally distributed and thus fluctuates around a definable mean value.

When generated, one of three different order configurations is assigned to each of them. These configurations are the “full disassembly” and two variants of “partial disassembly”. In the case of “full disassembly”, all modules are disassembled, inspected, repaired/replaced and reassembled. The partial disassembly represents a regeneration of only 3 of the 6 modules. The first variant of partial disassembly corresponds to a reduced workscope of the regeneration order that leaves the inner three modules assembled and untouched. In contrast, the second variant assumes the first three modules to be removed fully assembled to access the three remaining modules. While all modules are removed in this configuration, only the three inner modules are fully disassembled, inspected and repaired (if necessary).

Whether a module needs to be scrapped, is serviceable or repairable as well as its specific workscope is determined by a pre-defined damage pattern. This represents a damage diagnosis or prognosis performed prior to disassembly. This damage pattern information is again randomly assigned to the disassembled modules during order generation. For this purpose, five specific damage patterns (no damage, light, medium, heavy damage and scrap/irreparable) are distinguished. Based on the average damage pattern, the orders are assigned to one of three customer delivery time classes (short, regular, long) corresponding to an overall project workscope. Based on the regular delivery time that also represents a configuration parameter of the simulation model, 10% of the regular delivery time is deducted or given as a premium depending on the order-specific delivery time class. As an additional option, a defined proportion (0–100%) of the orders is randomly generated as a rush order which corresponds to a reduction of delivery time by 10 days.

For disassembly, the line principle as well as a construction-site principle is implemented. While the line principle leads to a fixed disassembly sequence of the modules, the construction-site principle allows for due date-oriented sequencing of the modules. The disassembled modules are then inspected in module-specific work systems. Here, information uncertainty regarding the initial workscope can be modeled by randomly inducing normally distributed deviations of the damage pattern. The initial damage pattern forms the mean value of this distribution. Modules found to be irreparable are removed from the system and must be replaced with a replacement component.

For this purpose, a new parts inventory is implemented, which is supplied by a new parts procurement. This is assumed to be inventory-controlled and allows setting the initial stock level, reorder point as well as the replenishment time and lot size for each module. The same applies to the RA and SA pools, which can be switched on and off separately and filled via procurement or by the regeneration process. Both pool stages can provide modules as scrap replacements or allow for rotating modules between the pool inventories and the capital goods to be regenerated. This requires to remove the link between the modules to be repaired and the original regeneration good. Removing this link opens up the possibility of rotating the modules whenever a delivery date cannot be met. The assignment of pool modules to a specific regeneration order is done when a specific demand is identified in the reassembly process.

In addition, there is a configuration option that allows SA or RA pool modules to be reserved as soon as irreparability is determined during inspection. The following repair shop forms the most complex section within the regeneration supply chain. It is modeled as an area consisting of four different workstations. These can have up to six parallel stations/capacities, each of which can process all modules. The respective work plans differ in the number and duration of work steps to be performed, depending on the damage pattern of the modules to be repaired. Since the compensation of disturbances and failures of the work systems are not subject of this work, they are not explained here.

When the repair is completed, demand for rework can be randomly assigned to a defined number of modules (0–100%). Modules that require rework are routed back to inspection and need to pass the repair process again following the work plan of the next higher damage pattern. Reassembly is modeled based on the construction-site principle and can also be scaled to up to six parallel stations. The final test represents a single work system testing the reassembled good.

6.2 Configuration Options in PPC

Along the supply chain structure, different configuration options as well as regeneration-specific disturbances and uncertainties are implemented. An aggregated overview of the main configuration parameters and options in the model is given in Fig. 8.

Fig. 8

Schematic overview of the configuration options implemented in the simulation model

The PPC procedures implemented cover the global order management, order scheduling, completion check, capacity control, order release and sequencing. The overall scheduling is implemented as a backward-oriented scheduling based on the order-specific arrival date and delivery time. The planned throughput times are determined on the basis of the predicted damage pattern respectively the corresponding work plans. To determine the planned inter-operation times, a multiple of the work system-specific processing time is defined. This allows for a much simpler and well automatable execution of different configurations but is of limited validity from a production logistic perspective in case of highly varying processing times (Schäfers 2020). Since the resource-specific processing times in this simulation are set comparatively homogeneous, this should only have a minor impact on the overall results.

The global order release, and thus the release into disassembly, can be triggered immediately, on the basis of the planned start date, or by means of the ConWIP (Hopp and Spearman 2000) procedure. For the latter, the maximum number of orders to be processed in the system at the same time can be set. Order release procedures in inspection, repair and reassembly can be set to the procedures already listed for the global order release. The procedure selected applies for all parallel or sequential work stations within the respective area. For the configuration of order sequencing, both the first-in-first-out (FIFO) principle and due date-oriented principles (comprising the earliest due date or least slack procedure) can be applied in each area. They are also applied for all parallel or sequential work stations within an area. A static completeness check can be set up at reassembly to ensure that reassembly is not started until all the required modules have been provided. If this is switched off, the simulation does not limit the order release to orders which already have the material completely physically ready for reassembly.

Overall, a two-shift system is applied for all work systems and stations, allowing capacity flexibility in additional shifts. These can be activated by a backlog control when exceeding a defined backlog limit per work system. This is reset either after a defined period or after the backlog falls below the defined limit.

The variety of configuration options for results in an almost infinite number of possible combinations and cause-effect relationships. Consequently, a detailed and comprehensive logistics modeling of interdependencies within the overall configurations does not appear to be reasonable. Instead, an assessment model is to be used to support and facilitate easy analysis and comparison of the logistics performance that can be achieved with a particular overall configurations.

6.3 Aggregation of Simulation Data and Comparison of Different Configurations

The assessment model visualizes the logistics performance of the entire supply chain as well as that of the individual work systems incorporating established logistics performance indicators at the most relevant measurement points along the supply chain. While the primary focus is on the punctuality of the reassembly as the crucial point for logistics performance within the supply chain, all the other processes are also covered. This allows to analyse customer-oriented indicators like punctuality and indicators relevant to the MRO service provider like capacity utilization.

While the simulation is implemented in Siemens Tecnomatix PlantSimulation the analysis is implemented in KNIME Analytics Platform to allow for (semi-)automated analyses of the simulation data. The results are structured in a Microsoft Excel spreadsheet that forms the database/lookup table for the presentation and comparison of the logistics perfomance achieved with different configurations in the assessment tool. Since a complete presentation of all simulation results is not possible within the limited space of this paper, an exemplary selection of key simulation results for four configurations is shown in Fig. 9 for discussion instead. This summarizes essential key performance indicators available within the evaluation tool as well as their presentation.

Fig. 9

Schematic representation of the assessment model

Because of the different scales of the incorporated performance indicators, a comparison is made based on a relative basis compared to a reference configuration. This also allows for a better comparison of the logistics effects of a change in configuration or disturbing influences that can be simulated using the simulation model. To do so, configuration CR is set as a reference. This configuration is chosen based on the findings and conclusions of former simulation and case studies on production configuration within MRO shops (besides others Georgiadis 2017; Guide, JR. 2000; Hoffmann et al. 2017; Liu et al. 2017; Reményi et al. 2011; Sendler 2020). It applies due date oriented sequencing and order release in all supply chain areas except the inspection and final test. Instead sequencing is done based on the FIFO-principle in these processes, since these are neither of particular relevance regarding the overall research goal nor do they significantly influence the logistic performance (due to the low material flow complexity within these). Order release is done immediately after the order’s arrival at the respective work station. In addition, configuration CR uses a disassembly based on the line principle and applies a static completeness check in reassembly. Configuration CR outperformes this configuration in nearly every aspect. This reconfirms the results of the previous simulation studies that can be found in scientific literature (e.g. Denkena et al. 2017; Reményi et al. 2011). Since configuration CR forms the basis for assessing the logistics-oriented impact of the disturbances and pooling mechanisms described above, these are not included in these configurations. Instead, these represent the two key differentiators to the other configuration shown in Fig. 9. Configuration C2 equals reference configuration CR but is subject to information uncertainty regarding the actual damage pattern of the capital goods respectively their modules. As a counter measure it also incorporates a SA pool stage, that is added upstream of the reassembly. The use of the components contained in this pool follows the descriptions in sections above.

The introduction of the disturbances in configuration C2 leads to a significantly increased standard deviation of the lateness parameters. Also, the mean work in progress (WIP) in reassembly increases due to the higher disturbed WIP waiting for components. Similarly, there is a drop in the repair capacity utilization, which can be attributed to the partially lower workload induced by the repair jobs. The mean value and standard deviation of the output lateness in repair and reassembly is significantly reduced introducing single-stage SA-components pooling. In addition, a considerable increase in repair capacity utilization can be achieved with a simultaneous reduction of the mean WIP. This can be explained by the due date-oriented provision of the pool components and the thus improved controllability of the workload within the repair.

Overall, the simulations confirm the potential of various configuration options, which are in line with the results, some of which have already been reported in earlier, separate studies. The evaluation model makes it easy to assess the effects of design or control changes on the logistics performance and cost indicators. The derivation of target-oriented measures for the configuration of regeneration supply chains is thus significantly simplified. It serves as decision support for the individual and requirement-oriented design and configuration of regeneration supply chains. In particular, the logistics-oriented potential of pooling is confirmed in terms of the opportunity to improve logistics performance and compensate for disruptive influences. Thus, the following section focuses on modeling the effects of pooling on logistics performance and costs.

7 Modeling of the Effects of Pooling on the Reassembly Process

The modeling of pooling as a regeneration-specific design and configuration option concerns both the dimensioning of corresponding pool stocks and the use of the available components in operational regeneration processes. This is addressed in the following sub-sections, building on each other.

7.1 Dimensioning of Pool Components

The simulation study confirms that the pooling of spare parts can positively influence on keeping due-dates in reassembly and the resulting missing parts situation (Kuprat et al. 2016). In order to be able to describe the missing parts situation in reassembly, which is supplied by several parallel supply processes (disassembly, repair, procurement, and pools), the supply diagram according to Beck 2013 was enhanced accordingly. This allows several supply processes to be taken into account simultaneously based on their respective schedule deviation distributions in the outgoing material flow (Kuprat et al. 2016; Kuprat 2018). This alternative improved approach of the supply diagram is thus suitable for evaluating the synchronicity of material flows in regeneration. For example, as an indicator for the evaluation, the disturbed WIP can be determined with the supply diagram. This forms the basis for describing general correlations identified in the simulation studies between the mean stock of SA pool components and the missing parts situation, expressed via the disturbed WIP. In principle, a high mean stock level of SA pool components can positively influence the disturbed WIP as well as the adherence to duedates in reassembly. However, the positive influence follows a digressive course, so that above a certain stock level no additional positive influence on the defective part situation can be achieved (see Fig. 10). This point can be determined mathematically under the assumption of ideal process conditions (this includes, in particular, deviations in entry and exit of the pools). In real environments, the boundary conditions on which this calculation is based are usually not given, so that a higher SA pool stock level is required to achieve the identical effect. This leads to a deviating curve (dotted line in Fig. 10).

Fig. 10

Effects of pooling on the disrupted WIP in reassembly (based on Kuprat 2018)

The choice of components to be included in the pooling also significantly influences the missing parts situation. In view of the logistics performance achieved, components that lie on the critical path of order should be provided from the pool and thus tend to cause a schedule deviation. A corresponding procedure for the selection of suitable pool components as well as further explanations of the modeling presented can be found in Kuprat 2018. To fully exploit the logistics potential bound up in the pool stocks built up in this way, they must be integrated into the regeneration operations in the best possible way. This requires integration and consideration of the interactions with the other processes of the regeneration supply chain.

7.2 Integrated Planning of Repair and Two-Stage Spare Parts Pooling

Mathematical optimization models offer a possibility to represent the resulting multitude of parameters and influences to be considered in the decision-making process. While only one SA pool level has been represented in the modeling in the previous section so far, both the SA pool level and—if available—an additional RA pool level upstream of the repair must be taken into account in an integrated manner to leverage the entire logistics potential of pooling. A corresponding mathematical optimization model is presented in Lucht et al. 2021a. This model couples classical repair scheduling, as presented in Hoffmann et al. 2017 with flexibility options opened up by pool stocks. This means that delays in the provision of materials caused, for example, by disruptions or deviations from the plan can be responded dynamically by demand-oriented replacing the original components to be repaired with pool components. While pool components from the SA pool in serviceable condition can be used for this purpose without throughput time, the repairable components held in the RA pool first require repair before they can be reinstalled in capital good. While they are, therefore, less flexible in terms of logistics, they usually have a significantly lower value than new or already repaired components [35] and thus also a significantly reduced capital tie-up. All in all, this results in various supply paths in Fig. 11 (Berkholz 2012; Heuer et al. 2020), that needs to be dynamically allocated to material demands from regeneration orders, which represents the elementary purpose of the model.

Fig. 11

Potential material provisioning paths with two-stage pooling (based on Heuer et al. 2020; Lucht et al. 2021a)

This approach thus forms a decision support system that allows integrated and time dynamic order and material coordination while simultaneously taking into account the multitude of relevant interactions in regeneration. Input variables of the model are the available pool stocks, their damages and values, if applicable, and the information about the order spectrum. On one hand, this includes the known date, planned and actual arrival date as well as the delivery date of the orders. On the other hand, additional information can be taken into account, including whether the use of pooling is permissible in the respective order, whether rework will be required at the end of the repair, and the damage class used as a basis for planning and the actual damage class determined in the findings.

This information can be used to map typical regeneration disturbances, which the model then takes into account in the decision-making process. Both predefined, completed scenarios and continuously updated data from practical applications can be processed. The objective function stored in the model minimizes the total costs, which consist of penalty costs for schedule deviations (caused by disruptive influences) in the reassembly as well as costs for the use of pool components. As a result, the model provides minimum-cost repair scheduling for the complete (but not necessarily punctual) servicing of material demand in reassembly.

A generalizable dependence of the cumulative delay on the stock level in the two pools was identified in simulation studies carried out with the model using synthetically generated scenarios. Thus, it can be seen that a reduction of the cumulative delay can be achieved with increasing stock levels in the respective pools. However, increasing the stock level in the SA pool shows a significantly higher impact—regarding schedule reliability but also capital commitment—than increasing the available stock level in the RA pool. This is due to the differences in the flexibility with which the respective components can be provided in the reassembly. In addition, however, it is also shown that the combined use of heterogeneous pool inventories makes it possible to achieve an identical cumulative delay with reduced use of new parts (Lucht et al. 2021a). The reduction in the number of new parts required to provide the desired logistics service that can be achieved in this way offers potential for a reduction in regeneration costs and a better evaluation and an increase in the reliability of regeneration service providers. In the long term, this also contributes to support a more sustainable and at the same time competitive use of resources.

8 Conclusions and Future Research

This section sums up the outline of this paper and gives an overview of potential future research activities. Future research focuses on the extension and transfer of the scientific results presented in this paper. The transfer addresses both the utilization of the scientific results in industry and the transfer of the results to other applications and industries.

9 Summary and Conclusions

The regeneration of complex capital goods is faced with both high customer demands on the logistics performance to be achieved and a simultaneous high degree of information uncertainty. Therefore, it is a highly demanding industry in terms of logistics, and the special boundary conditions prevailing here must be taken into account in its logistics design. In this respect, this article presents three fields of action that build upon each other to support regeneration service providers. These address the reduction of information uncertainty, the creation of transparency about the effects of interference and information uncertainty on essential planning tasks, and the design and configuration of efficient and robust regeneration supply chains.

Information uncertainty represents an essential perturbation impact on regeneration logistics. This concerns in particular the knowledge of the workload to be expected from a regeneration order, which is the basis for short-, medium- and long-term planning. To reduce this information uncertainty (field of action 1), Bayesian networks can be used to forecast the damage of future regeneration orders based on data from past regeneration orders enriched with information from the operation of the capital goods to be regenerated and structured in a damage library. Thus, the capacity load to be expected from these can also be determined.

In addition to the design of the capacity structure, this has a particular influence on the timing (scheduling) of the regeneration orders. Precise and stable scheduling is of great relevance for operational order processing and coordination and communication with customers. However, unclear information, internal and external disturbances, and other planning errors often lead to deviations from this planning so that planned dates are adjusted accordingly. A model for describing planning iterations was presented in the second field of action to make this planning behavior transparent and to uncover inefficiencies potentially hidden by planning iterations. This model serves both to visualize and to analyze the progress of planning due-dates so that, for example, recurring patterns in planning behavior can be identified and thus made accessible for the derivation of suitable countermeasures.

The third field of action addresses the support of regeneration service providers in the design and configuration of their supply chains. This can be supported by the presented simulation model and the evaluation model based on it. In particular, the pooling of spare parts was identified as a suitable measure to improve material supply. It was thus possible to model a generalizable influence of the average pool stock of SA components ready for installation on the disturbed WIP as a key figure for the missing parts situation in the reassembly. The use of the available pool components in the operative regeneration process requires the simultaneous consideration of many influencing factors and (mutual) dependencies. This is especially true when adding an additional pool stage with repairable RA components. The presented mathematical optimization model allows to consider these qualitatively heterogeneous pool conditions within the regeneration planning and thus to exploit their logistics potential in the best possible way. In the process, a further, potentially globalizable interdependency between the inventories of the two pool levels and the achievable adherence to delivery dates could be identified. This represents a central starting point for further research work.

10 Future Research

Future research focuses on the extension and transfer of the scientific results presented in this paper. While the developed optimization model addresses load adjustment in the form of pooling, its combination with the capacity adjustment modeling in Eickemeyer et al. 2014 offers the possibility to best exploit the joint flexibility or robustness potential of capacity flexibility and multi-level spares pooling. Further potential is promised by extending pooling as a regeneration-specific option for supply chain structure design. While the influence of single-stage pooling on disturbed WIP could already be modeled in a generally valid way, an extension of the modeling to two-stage pool structures as well as their influence on the robustness of material supply promises the potential to harness the joint logistics potential along supply chains of distributed inventories. This is of increasing importance, especially in the context of increasing supply uncertainty due to events that are difficult to predict, such as conflicts or natural catastrophes, to assess the actual material availability in the event of supply failures or to identify unnecessarily high (intermediate) material inventories. The application is not limited to regeneration service providers and promises great potential in the manufacturing industry. With regard to regeneration service providers, the increasing availability of operating data of capital goods opens up additional potential for a drastic reduction of information uncertainty about the material demand to be expected from a regeneration order and thus more precise input information for material management. A particular challenge here will be to allocate the forecast requirements to the respective available pool levels within the regeneration supply chain. For this purpose, the total demand must be broken down with regard to further requirements such as the available time for material provision per demand or the available stock of used but repairable components.