Health service network design: a robust possibilistic approach

• DOI: http://doi.org/10.1111/itor.12417
• Author: F. Abolhassani,M. S. Pishvaee,S. A. Torabi,M. Mousazadeh
• Published date: 01 January 2018
• Date: 01 January 2018

Intl. Trans. in Op. Res. 25 (2018) 337–373

DOI: 10.1111/itor.12417

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Health service network design: a robust possibilistic approach

M. Mousazadeha,S.A.Torabi

a,M.S.Pishvaee

band F. Abolhassanic

aSchool of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

bSchool of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

cDepartment of Health Services, National Institute of Health Research,Tehran University of Medical Sciences, Iran

E-mail: mousazadeh@ut.ac.ir [Mousazadeh]; satorabi@ut.ac.ir[Torabi]; pishvaee@iust.ac.ir [Pishvaee];

abolhassanif@tums.ac.ir [Abolhassani]

Received 15 May2016; received in revised form 17 March 2017; accepted 23 March 2017

Abstract

In this paper, a biobjective mixed-integer nonlinear programming model is developed for a hierarchical

three-level health service network design problem, which is then transformed to its linear counterpart. The

model aims to minimize the total establishment cost and total weighted distance between patient zones and

health facilities simultaneously. In order to cope with inherent epistemic uncertainty in input parameters,

four variants of a novel hybrid robust possibilistic programming (HRPP) approach are introduced. Finally,a

real case study is provided to illustrate the performance and applicability of the proposed HRPP models in

practice.

Keywords:health services; hierarchical location–allocation; referral system; biobjective programming; robustpossibilistic

programming

1. Introduction

A major prerequisite for health systems to reach their ultimategoal called “reducing health inequal-

ities” is to make health services available to all people. Hence, the design of a health service network

is a critical strategic decision, which affects the performance of the related national health system’s

operations to greatextent. Important decisions such as locations of health service providers/centers,

type of services and capacity of provided services, allocation of geographical regions to health ser-

vice providers, and design of referral system in a hierarchical configuration are some of the main

strategic decisions that must be made when configuring the health service network. It is obvious

that health networks are much extensive than they were 30 years ago, however many groups are

not properly covered yet. As a result, the fair extension of health service networks is a priority

nowadays, as it was the case 30 years ago (WHO, 2008).

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338 M. Mousazadeh et al. / Intl. Trans. in Op. Res. 25 (2018) 337–373

Facility location could be regarded as an old research area whose applications are still receiving

more attention. This area is a branch of operationsresearch, which is related to positioning/locating

at least a new facility among several existing facilities in order to optimize (minimize or maximize)

at least one objective function, for example, cost, profit, revenue, travel distance, service, waiting

time, coverage, and market shares (Farahani et al., 2010).

Daskin and Dean (2005) classified healthcare facility location problemsinto three basic categories,

that is, set covering, the maximal covering and the p-median models. In the set covering problems,

one tries to minimize the total opening cost of required facilities so that all demand nodes are fully

covered. In the maximal covering models, by defining a prespecified number of locations that can

be opened, the aim is to find the best locations so that the coverage rate by the opened facilities is

maximized. In fact, the notion of coverage is at the heart of both set covering and maximal covering

models. Finally, the p-median problem is about locating pfacilities on a network so that the total

weighted distance of serving all demand points is minimized.

One of the major extensions of classical facility location problem is the well-known location–

allocation problem. This extension refers to the problem of identifying the optimal location of one

or more facilities alongside the optimal assignment of the demand zones to the active facilities.

Location–allocation decisions have already been incorporated in several health-related problems,

such as the location–allocation of health service providers in rural (Mehrez et al., 1996; Smith et al.,

2009) and city areas (Harper et al., 2005), location–allocation of preventive healthcare facilities

(Verter and Lapierre, 2002; Zhang et al., 2009; 2012), community healthcare facilities (Griffin

et al., 2008), clinics (Beheshtifar and Alimoahmmadi, 2015), public hospitals (Chu and Chu, 2000),

specialty care providers (Syam and Cˆ

ot´

e, 2010; Benneyan et al., 2012), and long-term care services

(Song et al., 2015) as well as other healthcare-related topics such as blood supply chain network

design (Zahiri et al., 2015), pharmaceutical supply chain network design (Mousazadeh et al., 2015),

and organ transplantation network design (Zahiri et al., 2014b).

Many healthcare systems in developed and developing countries are organized as the three-level

hierarchical systems that include three types of healthcare facilities (Rahman and Smith, 2000).

At the outset of such hierarchical system, patients visit a general physician or nurse in a primary

health center (PHC), which is fairly close to their residential area in order to get first aid and/or

primary care and/or preventive health services. If necessary, following a referral system, they

might be directed to the second level of this hierarchy (i.e., regional health centers, RHCs)

to receive those services that are not available at the first level (e.g., therapeutic and limited

curative services). Also, some patients might be referred to the last level (i.e., specialty hospitals

or district health centers, DHCs) in which some specialized care services are provided for

patients. For more information about typical classification of general hierarchical facility location

problems, the interested readers can also consult S¸ahin and S¨

ural (2007) and Farahani et al.

(2014).

Although the study of hierarchical location–allocation problem outside the healthcare service

context is less limited (e.g., S¸ahin and S ¨

ural, 2007; Teixeira and Antunes, 2008), in the health

service context, hierarchical configuration of healthcare facilities is often disregarded and the

whole system is either analyzed as a single-level (Verter and Lapierre, 2002; Ndiaye and Alfares,

2008; Smith et al., 2009; Syam and Cˆ

ot´

e, 2010; Benneyan et al., 2012; Shariff et al., 2012; Syam and

Cˆ

ot´

e, 2012; Shishebori and Babadi, 2015; Song et al., 2015) or rarely as a bilevel system (Mestre

et al., 2012).

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International Transactionsin Operational Research C

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M. Mousazadeh et al. / Intl. Trans. in Op. Res. 25 (2018) 337–373 339

Among few research works that address the hierarchical location–allocation problem in the

healthcare context, Yasenovskiy and Hodgson (2007) propose a 0-1 linear programming model

for designing an optimal three-hierarchical facility system. The proposed model decides on the

locations of low-level, mid-level,and high-level facilities and the allocation of geographical zones to

the established facilities. It is assumed that the distance, facility size, and neighborhood accessibility

are the main criteria for traveling preferences of patients and the model aims at maximizing the

overallpatrons’ benefit. In another study,Mestre et al. (2012) propose a two-hierarchical multiservice

model in which decisions on the location of central hospitals (CHs) and district hospitals (DHs),

capacity of each health service provider and ascendant/descendent flowof patients via the network

are made with the aim of minimizing the total travel time for patients’ access to hospital services.

For more information about the health service network design problem, the interested readers can

also consult Mousazadeh et al. (2016).

In this paper, motivated by a real decision problem that the Ministry of Health and Medical Edu-

cation (MoHME) of Iran is facing with, a novel biobjective mixed-integer nonlinear programming

(BO-MINLP) model is proposed for designing a three-level hierarchical health system, which is

then transformed to its linear counterpart. This model is able to make the best decisions about the

locations and capacities of health service providers, the allocation of patientzones to the established

facilities in the first level of hierarchy (PHCs), designing the referral system from PHCs to the

second level of hierarchy (i.e., RHCs), and from RHCs to the third level of hierarchy (i.e., DHCs)

simultaneously. In addition, the model finds the optimal specialty service portfolio in DHCS and

patients’ flow pattern throughout the whole health network.

In most of the real situations, there might be no adequate historical data in order to model

uncertain parameters as random data, hence one should rely on experts’ judgments for reasonable

estimation of uncertain data. As a result, a suitable possibility distribution typically in the form of

a triangular/trapezoidal fuzzy number can be provided for each imprecise (i.e., possibilistic) data.

In this situation, possibilistic programming (PP) approaches are applied to solve the mathematical

programming models tainted with possibilistic data. Nevertheless, the robustness of final solution

is of particular importance, especially for the long-lasting decisions such as the location of facilities

that cannot be changed easily in a long-term horizon (Torabi et al., 2016). Accordingly, in this

paper, a novel hybrid robust possibilistic approach is introduced to handle epistemic uncertainty

in parameters as well as finding the most robust solution over the possible fluctuation of uncertain

parameters. To the best of our knowledge, among the reviewed papers, data uncertainty is only

taken into account in the research done by Shishebori and Babadi (2015). In detail, they proposed

a mathematical model for a robust and reliable medical services network design problem in a

single-level health system.

Given the currentliterature and identified gaps, the main contributions of this paperdifferentiating

it from other relevant papers can be summarized as follows.

rDeveloping a novel BO-MINLP (that is transformed to an equivalent biobjective MILP) model

for a three-level health service network design (3-LHSND) problem motivated by a real decision

problem. The model accounts for a number of crucial decisions including the location of health

service providers at different levels, the capacity of established facilities, allocation of regions to

PHCs, referral pattern of patients throughout the network, and specialty health service portfolio

in DHCs simultaneously.

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2017 The Authors.

International Transactionsin Operational Research C

2017 International Federation of OperationalResearch Societies