A multi‐period multi‐criteria districting problem applied to primary care scheme with gradual assignment

• DOI: http://doi.org/10.1111/itor.12633
• Author: Stefan Nickel,Joerg Kalcsics,Seda Yanık,Burcin Bozkaya
• Published date: 01 September 2019
• Date: 01 September 2019

Intl. Trans. in Op. Res. 26 (2019) 1676–1697

DOI: 10.1111/itor.12633

INTERNATIONAL

TRANSACTIONS

IN OPERATIONAL

RESEARCH

A multi-period multi-criteria districting problem applied to

primary care scheme with gradual assignment

Seda Yanıka,JoergKalcsics

b, Stefan Nickelcand Burcin Bozkayad

aDepartment of Industrial Engineering, Istanbul TechnicalUniversity, Istanbul 34367, Turkey

bSchool of Mathematics, The University of Edinburgh, EdinburghEH9 3FD, United Kingdom

cInstitute for Operations Research,Karlsruhe Institute of Technology, Karlsruhe 76131, Germany

dSchool of Management, Sabanci Universitesi, Istanbul 34956, Turkey

E-mail: sedayanik@itu.edu.tr [Yanık]; joerg.kalcsics@ed.ac.uk [Kalcsics]; stefan.nickel@kit.edu [Nickel];

bbozkaya@sabanciuniv.edu[Bozkaya]

Received 21 March 2018; receivedin revised form 22 January 2019; accepted 22 January 2019

Abstract

Wepresent a modeling and optimization approach for the planning of primary healthcare services in order to

efficiently directpatient admissions to general practitioners (GP) and to leverage the capacity of the healthcare

system. Wepropose a multi-period multi-criteria districting model for the problem of designing GP districts in

the presence of six criteria: workload balance,capacity, accessibility, compactness, income equity,and district

similarity. We combine the last three criteria into a single objective function and formulate the problem as

a mixed integer program with binary location decision variables and relaxed allocation decision variables

for gradual assignments. To assess the usefulness of the model, we test it on real-case scenarios in Istanbul,

Tur key.

Keywords:health service; integer programming; multi-criteria; multi-period; location; districting

1. Introduction

The role of primary care thatis provided by general practitioners (GP) is the first level in a healthcare

system where many patient needs can already be treated and the admission of patients to secondary

care healthcare facilities (e.g., hospitals) is not required. As the demand for healthcare services is

rapidly increasing due to factors such as aging societies, increasing life standards and expectations

for healthy-living, an effective GP scheme plays a crucial role in leveraging the capacity of the

healthcare system (Buja et al., 2015).

The main premise of the GP scheme is to direct the admissions of patients to GPs instead of

hospitals. While some countries enforce patients to visit a GP first, it is the ease of access to a

GP that mainly determines the effectiveness of the scheme (Yiannakoulias et al., 2013; Buja et al.,

C

2019 The Authors.

International Transactionsin Operational Research C

2019 International Federation ofOperational Research Societies

Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA02148,

USA.

S. Yanık et al. / Intl. Trans. in Op. Res.26 (2019) 1676–1697 1677

2015). Either enforced or volunteered, the patient is motivated and more satisfied to visit a GP if

the GP is easily reachable. On the other hand, doctors are also selective in locating their practices

since their income is typically proportional to the number of patient visits as well as their age

distributions.

In practice, the GP scheme is usually planned by traditional, judgmental, and heuristic methods.

Systematic approaches based on Operations Research techniques using the available data rather

than the traditional regulatory approaches may result in significant efficiency improvements in

a healthcare system. In a well-planned scheme, the primary care service should be consistently

available and easily accessible over a geographical region with different population densities and

characteristics, and should also respect equity for the patients and the doctors. Thus, the design of

a GP scheme is closely related to location-based organizational planning and decision problems.

There are two fundamentally different types of GP schemes. In the first, inhabitants are assigned

to a GP in advance by a public healthcare administration unit. In the second, patients choose by

themselves which GP to visit. Two examples for the first are Turkey and the United Kingdom.

Although patients have in principle the freedom to visit a GP they are not assigned to, they have

to ask the administration for permission to do that in Turkey (Health Ministry of Turkey [HMT],

2010) or the non-designated GP in the United Kingdom may refuse to register an inhabitant on the

grounds that the inhabitant is living outside their district (NHS Choices, 2016). For these countries,

the GP scheme design can be defined as a districting problem related to planning services and

operations over a geographical region subject to various requirements. A solution to this problem

will identify districts with inhabitants that are (expected) to visit a doctor’s practice positioned at

the center of the corresponding district. An example for a free of choice scheme is Germany. See

Haase and M¨

uller (2015) and Carello and Lanzarone (2014) for moredetails on the ensuing models

and problems.

In this study, we focus on the first type of GP schemes where inhabitants are assigned to districts

by the administration. We formulate the problem of designing a GP scheme first as a multi criteria

districting model in the presence of the workload balance, capacity, accessibility, compactness,

income equity requirements; of which the last two are combined into a single objective function.

In this weighted sum objective function, “compactness” ensures the ease of travel for the patients

by minimizing the distances to GP locations, as previously done by Steiner et al. (2015) and Datta

et al. (2013), and “income equity” equalizes the attractiveness of each district for the doctors

by balancing the income generated in all districts, which is a concept commonly used in the sales

territory design applications (Zoltners and Sinha, 2005; Lei et al., 2015). Then, we extend this model

into a multi-period model, which searches effective district plans for multiple periods considering

the future values of the parameters. This model includes a third criterion, “district similarity,” into

the weighted sum objective function aiming to generate similar district plans between periods for

achieving the continuity of care of patients with the same GP.

One issue in district planning for the GP scheme in Turkey and the United Kingdom is to

incorporate to some extent the possibility that patients do not want to visit their designated GP.

Nevertheless, one of the most influential factors affectingthe patient’s choice is the distance between

the location of the patient and the doctor’s practice. If all other factors are almost the same, it is very

likely that a patient will still want to patronize a doctor’s practice located very close to his/her own

location. Hence, typically only patients located close to the border of a district may be inclined to

visit neighboring doctors, as the marginal utility frompatronizing the closest doctor diminishes. For

C

2019 The Authors.

International Transactionsin Operational Research C

2019 International Federation of OperationalResearch Societies