Determining The Optimal Location for CVD Clinics: A Mathematical Programming Approach

Introduction The development of developing and underdeveloped countries is a topic discussed at the highest level of the United Nations. Although for this topic to become a reality, several economic and social situations are of high importance and need to be contained. To contain such situations, the working class and manpower of the state is needed to be active in economical and social activities. It is estimated that untimely deaths due to cardiovascular disease (CVD) in people of working age 35 - 64 years are expected to increase by 41% between 2007 and 2030. The economic impact is expected to be negatively enormous. This study investigates using a mathematical programming approach for selecting optimal locations for new specialized CVD clinics, and/ or improvements to current clinics within optimal locations in remote regions. Research Problem, Scope and Objective Most African states and developing countries have failed to provide an impetus to eradicate CVD as it mostly affects the poor. Even in some countries where CVD specialized clinics exist access to these facilities is severely limited. The objective of this research is to utilize a model to determine the optimal locations of specialized CVD treatment facilities to deal with the epidemic of the disease. In order to accurately evaluate our model, we select the Western Cape of South Africa as a case study because it excels at bringing us to an understanding of the complex issue being tackled. This will also provide a potential insight into the effectiveness of designing a system to deal with CVD at locations for maximum population coverage. Research Approach This research is initiated by analyzing the current state of CVD treatment, location of clinics and demographics of the Province of the Western Cape (Chapter 2). Based on the information we executed a stakeholder mapping and established performance measures (Chapter 2). We followed with a literature review on location theory (Chapter 3). We developed our models based on p-Median models and variants of the model (Chapter 4) and executed computational experiments (Chapter 5) and an extensive sensitivity analysis to verify the feasibility of our model and to test how sensitive our models are to changes that may occur. In (Chapter 6) we present the conclusions and recommendations to successfully implement our solutions. Findings The mathematical model presented in this research is a tool for the location of specialized CVD clinics. Our developed model is applied to the case of the Western Cape, utilizing demographical data, such as, population groups, age distribution, disease occurrence rate etc. that was provided by the ministry of health and private organizations and NGOS partaking in creating awareness for heart disease. We proceed by estimating the population using a uniform distribution within each municipality and its density. The traveling distances are computed as the straight line distances between each population i and potential clinic j. The distance between point i (1...309) and j (1...309) are computed and inputted into the Advanced Interactive Multidimensional Modeling System (AIMMS) software used for computational experiments to obtain the optimal locations (co-ordinates) for CVD clinics. An analysis carried out on the current situation showed that the current location of the hospitals do not effectively cover over 36% of the population. Using the mathematical models in this research, we maximized the total population of the Western Cape being covered within specific distance limit. We also minimized the distance traveled and also minimized the number of clinics required to cover the whole population. We obtained different configurations for which maximum population coverage is possible (See Table 1). Comparing the current situation of coverage of 64% with 16 CVD clinics, it can be seen from Table 1 that re-locating these clinics to appropriate co-ordinates as in Chapter 5 of this research leads to maximum coverage of the population in the Western Cape given a specific distance limit as seen in the table below. Conclusions In this research, we propose different mathematical programming models to solve the location problem for specialized CVD clinics. The models are based on p-Median models and are objective techniques to identify population not being covered and to identify potential new CVD specialist treatment facilities. Our findings may also be applicable to patients with other kinds of diseases that require specialist care. The methods utilized in this research can also be applied to other types of facilities or resource networks, such as government buildings, schools, businesses and other service related networks. This can be done with very little adaptations or changes to the constraints or parameters, such as the population, distance between facilities and population or other facilities.