Piecewise linear functions have been used to model and solve non-linear problems in science, social science, and technology fields since the 1950‟s. Multi-choice goal programming (MCGP) has been widely used to solve multiple objective decision-making (MODM) problems in which each goal mapping with multiple aspiration levels is allowed, expanding the original feasible region to obtain better solutions in the MODM problems. This paper integrates the efficient S-shaped penalty method, arbitrary piecewise linear utility functions, trapezoidal utility functions, and MCGP to solve a topology design problem in a remote patient monitoring system (RPMS) by providing universal senior citizen coverage in which quantitative (e.g., patient satisfaction-related cost) and qualitative (e.g., satisfaction) issues are considered simultaneously. In addition, some novel utility functions such as the force utility function, indicator utility function, and arbitrary utility function are proposed to improve the usefulness of MCGP in the field of management science. These proposed utility functions can be easily used to model qualitative issues in real-world problems. A topology design problem for an RPMS is demonstrated to justify the feasibility, usefulness, and compatibility of the proposed methods. Further, sensitivity analysis and managerial implications are provided using an RPMS in Taiwan.

Introduction

Given the aging society and falling birth rate, Taiwan has been classified as an “aged” society since 2018 and will turn into a “hyper-aged” society by 2025. The increasing healthcare costs for the growing population of elderly, chronic diseases, as well as the demand for new technologies and treatments in addition to the decrease in the number of healthcare professionals compared to the elderly increase make the traditional healthcare service model inadequate. Conventional healthcare model inadequacy can be explained by the following two aspects: (1) large hospitals (e.g., accredited hospitals and medical centers) are always overcrowded, and as a result, people often don‟t have access to outpatient clinics and must wait a long time for inpatient care; and (2) increasing healthcare costs also place a considerable burden on the government‟s finances. Nowadays, establishing an efficient remote patient monitoring system (RPMS) to take care of the greater number of elderly people as well as reduce healthcare costs is essential in Taiwan. Moreover, it is very important to build an RPMS with a more complete topology network under a limited budget to take care of senior citizens. To implement the RPMS for serving senior citizens, several goals and criteria should be considered simultaneously. These goals and criteria contain both quantitative (e.g., the RPMS setup cost and investment cost) and qualitative (e.g., satisfaction of senior citizens) issues, and the balance between them (e.g., balancing the setup cost and the satisfaction of senior citizens), complicates the problem. This is a typical multiple objective decision making (MODM) problem with conflicting goals.