Innovative Applications of O.R.
Designing robust rollout plan for better rural perinatal care system in Korea

https://doi.org/10.1016/j.ejor.2018.10.018Get rights and content

Highlights

  • We develop a location model to design a rollout plan of perinatal care providers in Korea.

  • Our model considers health care consumers’ preference and future demand uncertainty.

  • We empirically find that a strong requirement for robustness has its own price.

  • We propose a framework that uses the surplus budget to reduce the price of robustness.

Abstract

Strengthening perinatal care provision in medically under-served areas is an important public health task in Korea. Motivated by the ongoing efforts by the Korean government, this paper studies a multi-period capacitated location problem to design an optimal rollout plan for the government’s support program. The proposed model incorporates (1) health care consumers’ preference for care providers and (2) uncertainty in future demand for perinatal care. If not properly accounted for, these factors render location solutions at risk for under- or over-use, which will result in a continual need for extra budget spending to sustain healthy operation of the care capacities. In the proposed formulation we integrate a discrete choice model that describes the provider choice behavior by women in under-served areas in Korea. In addition, we address the demand uncertainty by using the robust optimization framework. By applying the proposed model to Korea’s under-served area support program, we show that both the demand uncertainty and choice behavior significantly influence the solution performance. Furthermore, we find that a strong requirement for robustness drives the model to not open all care provider sites allowed by the program’s budget to ensure that the capacity constraints are respected. With this surplus budget, we can relax the robustness requirement to open more perinatal care providers by using the surplus to absorb the cost associated with expected constraint violations. In other words, the surplus budget can pay the price of reducing the price of robustness.

Introduction

Many countries around the world are experiencing difficulties in providing sufficient perinatal care services in rural areas (Grzybowski, Stoll, Kornelsen, 2011, Kornelsen, Stoll, Grzybowski, 2011, Larimore, Davis, 1995). One of the major causes of this problem is a shortage of health care providers in rural areas, which translates into a lack of access to perinatal health care services. Women in rural areas often have to travel farther to obtain an appropriate level of service for their perinatal care. In the United States, for instance, only 6.4% of obstetricians, specialists who provide perinatal care, practice in rural areas (American College of Obstetricians & Gynecologists, 2014). As a result, more than half of the women living in rural areas have to travel longer than 30 minutes to reach the nearest perinatal care provider (Rayburn, Richards, & Elwell, 2012). It is well known that the lack of adequate and timely perinatal care increases the likelihood of experiencing serious medical conditions (Agency for Health Care Research and Quality, 2009, The National Advisory Committee on Rural Health and Human Services). As such, improving the status quo of the rural perinatal care is an important public health problem.

Korea is also suffering from its insufficient perinatal care networks in rural areas. Owing to several causes, such as the low fertility rate1 and increasing financial burden of operating hospitals, the infrastructure of rural perinatal care has been steadily weakened (Lim, Choi, Lim, Seo, & Park, 2012). According to a report by the Korean government, the number of obstetrics and gynaecology (OB/GYN) hospitals available for labor and delivery care services has been decreasing during the past decade (Lee et al., 2015). Specifically, the total number of OB/GYN hospitals in Korea declined from 1027 in 2007 to 675 in 2014; about 34% of OB/GYN hospitals closed over this seven-year period. One of its consequences is that one quarter of the municipalities across the country do not have OB/GYN hospitals to provide labor and delivery services. Deterioration of the rural perinatal care system has caused many medical and socioeconomic problems for pregnant women and their families. Enhancing a perinatal care system is an urgent and critical task for the Korean government.

To resolve this problem, the Korean government has established various support programs. One such program is to increase the level of accessibility to perinatal care by allocating OB/GYN resources to rural areas. This was suggested by the nationwide study commissioned by the Korean Ministry of Health and Welfare (Lee et al., 2015). In this study, a group of experts, including the authors, conducted research to identify medically under-served areas for obstetric care (OUAs) and develop a plan to establish OB/GYN care capacities in the areas. This paper was motivated by the original study to further refine and improve the analyses conducted therein in the following aspects.

First, the original study did not consider the time aspect of the establishment plan and simply provided the total capacities to establish to achieve its expected coverage. For actual implementation, however, the public health authority in the government needs a rollout strategy. In the context of establishing health care capacities, a rollout plan refers to a master plan that specifies when and how many care provider sites are to be established throughout the program period. A rollout plan is important because establishing care providers requires substantial investment from the OUA support program over a long period of time. In particular, the demand for the service in OUAs is likely to change over the program period, and thus a careful consideration to properly handle such uncertainties is warranted.

Another important aspect that was not considered in the original study is the patients’ hospital choice behavior. There are few studies that incorporate an individual’s choice behavior in the area of health care facility location problem. Many studies simply assume that patients will use hospitals as allocated in their model, and assess the location solution’s performance based on this assumption. This assumption is quite unrealistic, and health systems planners run the risk of making under- or over-estimation in the respective objectives (e.g., coverage) that in turn would results in an over- or under-investment.

To tackle such issues, this paper develops a new location model. The goal is to provide information on how best to establish perinatal care capacities over a given planning horizon. We consider two important features in the model – uncertainties in future demand and health care consumers’ hospital choice behavior. In particular, we use a robust optimization framework to handle the demand uncertainties, which can provide a robust solution against the demand uncertainties. We also incorporate a discrete choice model to more realistically represent individuals’ preferences in care provider selection. A discrete choice model, which has been mainly studied in the field of economics, provides a mathematical description for consumers’ choice behavior. As will be shown in this paper, incorporating both of these features in the model provide useful insights for the OUA support program planners.

Our contribution in this paper is twofold. First, this is the first study to introduce a multi-period health care facility location model that incorporates both demand uncertainties over the planning horizon and the patients choice aspect. Since the resulting model is difficult to solve due to its non-linear terms, we reformulate the model to derive a mixed integer linear program. Second, we apply the proposed model to a perinatal care provider location problem for Korea’s OUA support program by using the nationwide data collected for obstetric care in Korea. From the experiments, we draw important implications for the planners of Korea’s OUA support program.

The rest of this paper is structured as follows. In Section 2, we review the literature related to our study. In Section 3, we describe the perinatal care provider location problem in detail. In Section 4, we introduce a proposed location model, followed by a short description of the patients’ provider choice model. In Section 5, we present the results from our experiments and discussions on their implications for designing a perinatal care provider rollout plan for the program. Finally, Section 6 concludes our paper.

Section snippets

Related literature

This section discusses the previous literature in three areas pertinent to our study. We first review facility location models on a multi-period location problem. Then, we review the location models with uncertain demand with a particular focus on the models that employ a robust optimization approach. Lastly, studies on the choice model are briefly introduced, and a few location models that incorporate the consumer choice aspect are discussed. For a general review on location models, refer to

Problem description

We consider a problem of establishing perinatal care capacities to cover under-served areas for perinatal care over a given planning horizon. Here, a perinatal care capacity refers to a clinical unit that provides perinatal care services including delivery, and in this paper, we use the terms “perinatal care capacity” and “perinatal care provider” interchangeably. The objective is to construct an optimal rollout plan that maximizes the total expected coverage for the women in the fertile age

Optimization model

We begin this section by introducing a brief explanation of a discrete choice model. Then, in Section 4.2, we build a basic location model without uncertainty. Thereafter, in Section 4.3, we propose a robust location model that considers uncertainties in the perinatal care demand.

Locating perinatal care capacities for OUA support program in Korea

In this section, we apply our model to the problem of designing a rollout plan to cover medically under-served population for obstetric care in Korea. In Section 5.1, we begin by introducing the data used in the study and explain the discrete choice model adopted in our location model. Then, we illustrate the experimental settings in Section 5.3. Results from the experiments are discussed in Section 5.4, with a particular focus on the effects of incorporating the demand uncertainty (

Concluding remarks

This paper addresses the problem of locating perinatal care capacities to provide perinatal care in the under-served areas in Korea. In particular, we solve a location problem over a planning horizon to develop an optimal rollout plan. In our model, we consider two features that are particularly important for its practical applications: (1) uncertainties in future demand for perinatal care in Korea and (2) the care consumers’ hospital choice behavior. Our technical contribution is to develop a

Acknowledgement

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government (MSIP) (No. 2016R1A2B4014323) and the National Medical Center of Korea (NMC) grant funded by the Korea government (MOHW) (No. 11-1352000-001406-10).

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