Location problem of medical institutions in the medically under-served areas in Korea considering demand patterns using choice model

Abstract

Medically under-served areas (MUAs) are areas where natural medical resources are lacking due to insufficient demand. In Korea, the government designates MUAs, selects hospitals in the area, and supports facility/equipment/labor costs. This provides medical services to the local residents. The government selected institutions that maximize the number of visitors within 60 minutes to relieve MUAs. This could be a facility location problem considering only potential accessibility, geographical information. However, it can be a bad decision if people with good accessibility do not actually visit. Ultimately, it is necessary to estimate the actual use of people to select the support hospitals that address MUAs. There are many ways to estimate the usage patterns of people, but the choice model is widely used in economics. The choice model can estimate the choice probability for a particular alternative, assuming a choice rule that chooses the alternative that gives the greatest utility when people make a choice. The goal of this dissertation is to propose a model that determines optimal location by reflecting the demand pattern. The choice model is chosen to reflect the demand pattern. Next, we want to expand it in the direction that can decide both choice attribute and location simultaneously. Finally, we propose a model that can reflect various preferences of attribute for each person. Chapter 2 proposes an obstetrics care unit choice model of Korea. The logit model, which is a simple form of the choice probability, is selected as the basic choice model. The actual birth data and the hospital data are used to construct the obstetrics care unit choice model. As a result, Korean mothers prefer to visit the obstetrics care unit of the hospital in the downtown area, which is close from residence and inexpensive and has a large number of obstetrics specialists. As out-of-sample validation results, proposed model is closer to reality than benchmark assignment rules, such as nearest, distance-based, and choice models of previous research. We also constructed a latent class model using the same data. The latent class model assumes that people belongs to several classes with various preferences than a homogeneous group. As a result of constructing the model, Korean mothers were able to divide into groups that placed more emphasis on accessibility to the obstetrics care unit and more important on the size of the obstetrics care unit. Chapter 3 proposes location model incorporated choice model. The non-linear term generated in this process is linearized by adopting the previously proposed linearization method using IIA(independence from irrelevant alternatives) property. Since the purpose of the model is to address the MUAs, the objective function is to maximize the number of MUAs relieved unlike maximizing the market share and a constraint to judge whether MUAs are relieved is added. In addition, lower bounds have been added in the process of linearized equality constraints. In the literature, only the upper bound exists because of the objective function. Next, we considered choice attributes as a design variable and proposed a model that can determine both at the same time. If the choice attribute can be determined at the same time as the location, many small vs. few large problems can be answered. As the choice attribute becomes a decision variable, an additional non-linear term is generated, which is linearized by 2 step: RLT(Reformation-Linearization Technique) after piecewise linearization. If the attribute variable is an integer, the optimal solution, not an approximate solution, can be obtained by a commercial LP solver. This model was the first to be completed. As a result of applying the above model to MUAs about obstetrics care in Korea, many small strategy is valid. In chapter 4, we develop the above model to reflect various preferences. One of the disadvantages of the logit model is that people's preferences are homogeneous. The goal is to propose a model to relax homogeneous preference assumption and apply a general problem. To do this, we propose a location model to obtain the almost robust optimal solution under given uncertainty configured from latent class model. We could deal with more realistic scenarios than previous study. In this dissertation, 1) Korean pregnant women's choice behaviors are analyzed through a choice model, 2) a location model that can simultaneously determine the attribute that affect choice and location of the facility, and that can obtain an optimal solution than an approximate solution with a commercial LP solver was proposed. 3 ) We propose a location model that can obtain almost robust optimal solutions when a distribution of uncertainty set is given.