OR Spectrum

, Volume 34, Issue 2, pp 319–348 | Cite as

Organizing hospitals into networks: a hierarchical and multiservice model to define location, supply and referrals in planned hospital systems

  • Ana Maria Mestre
  • Mónica Duarte Oliveira
  • Ana Barbosa-Póvoa
Regular Article


Health care planners in countries with a system based on a National Health Service (NHS) have to make decisions on where to locate and how to organize hospital services, so as to improve the geographic equity of access in the delivery of care while accounting for efficiency and cost issues. This study proposes a hierarchical multiservice mathematical programming model to inform decisions on the location and supply of hospital services, when the decision maker wants to maximize patients’ geographical access to a hospital network. The model considers the multiservice structure of hospital production (with hospitals producing inpatient care, emergency care and external consultations) and the costs associated with reorganizing the hospital network. Moreover, it considers the articulation between different hospital services and between hospital units, and the ascendant and descendent flows related to two-way referrals of patients in the hospital hierarchy. The proposed approach differs from previous literature by accounting simultaneously for these issues and provides crucial information for health care planners on referral networks, on hospital catchment areas, on the location and structure of hospital supply as well as on the costs required to improve access. The results from applying the model are illustrated in an application to the South region of the Portuguese NHS. Three scenarios are portrayed to describe how the model can be used in distinct institutional settings and policy contexts and when there is uncertainty concerning the key parameters of the model.


Public facility planning Location models Network design Health care management 

List of symbols



District hospital


Central hospital


\({i\in I}\)

Demand points

\({j,l\in J}\)

Potential locations for DH

\({k\in K}\)

Potential locations for CH

\({w,v,a\in W}\)

Hospital services (w = 1 for inpatient care, w = 2 for emergency service and w = 3 for external consultation)


\({d_{ij}^{1}\, d_{ik}^2 }\)

Travel time between a demand point iand a DH j/CH k


Travel time between DH j and CH k


Demand for service w in demand point i


Share of demand transferred from service w in a DH to service v in a CH


Share of demand transferred from service v in a CH to service w in a DH


Share of demand transferred from service w to v within the same hospital

adw acw

Length of stay spent in service w in a DH/CH


Maximum capacity allowed for service w operating in a DH and in a CH

dhw chw

Minimum capacity required for service w operating in a DH and in a CH

α (0 ≤ α ≤ 1)

Weighting factor to differentiate first from second attendances (expressing planners’ preferences)

βw(0 ≤ βw ≤ 1)

Weighting factor to differentiate hospital services (expressing planners’ preferences)


Population located in demand point j


Minimum population located in a demand point required to open a new hospital


Number of facilities to be opened


Maximum travelling time allowed for a population to access a hospital

\({{\rm DHc}_j^w \,{\rm CHc}_k^w }\)

Total unit costs for delivering care in a DH j and in a CH k

DHecj DHicj

Cost of expanding/investing one bed in an existing/new DH located in j

\({{\rm icap}\_X_j^w }\)

Current capacity of DH j


Total annual operating costs for all DHs


Total investment costs for all DHs


\({X_j^w }\)

Determines the opening (=1) or closure (=0) of a DH in location j that provides service w

\({Y_k^w }\)

Determining the opening (=1) or closure (=0) of a CH in location k that provides service w

\({{\rm fd}_{ij}^w }\)

Flow from population point i to DH j for service w

\({{\rm fc}_{ik}^w }\)

Flow from population point i to CH k for service w

\({{\rm zdc}_{jk}^{wv}}\)

Ascendant flow from service w in DHj to service v in CH k

\({{\rm zcd}_{kj}^{wv}}\)

Descendent flow from service w in CH k to service v in DH j

\({{\rm td}_j^{wv}}\)

Flow between service w and v inside DH j (auxiliary variable)

\({{\rm tc}_k^{wv}}\)

Flow between service w and v inside CH k (auxiliary variable)

\({{\rm cap}\_X_j^w }\)

Capacity for service w in a DH j

\({{\rm cap}\_Y_k^w }\)

Capacity for service w in a CH k


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Ana Maria Mestre
    • 1
  • Mónica Duarte Oliveira
    • 1
  • Ana Barbosa-Póvoa
    • 1
  1. 1.Centre for Management Studies of Instituto Superior TécnicoTechnical University of LisbonLisbonPortugal

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