Linear and Quadratic Programming and Applications in Examining Wasteful Commuting and Allocating Healthcare Providers - Liu, Lingbo; Wang, Fahui (Computational Methods and GIS Applications in Social Science - Lab Manual, 2024)
This chapter introduces two popular methods in optimization, linear programming (LP) and quadratic programming (QP). QP is perhaps the simplest form of non-linear programming (NLP). LP and QP seek to maximize or minimize an objective function subject to a set of constraints. LP has both the objective and the constraints in linear functions. QP has a quadratic objective function, but its constraints remain linear. This chapter uses case studies to illustrate their applications in measuring wasteful commuting and location-allocation analysis. This chapter introduces two popular methods in optimization, linear programming (LP) and quadratic programming. It utilizes case studies to illustrate their applications in measuring wasteful commuting and location-allocation analysis. The chapter examines the issue of wasteful commuting in Columbus, Ohio to illustrate the formulation of LP and its solution. It provides various location-allocation problems to plan healthcare providers in a rural county in China. The Maximal Accessibility Equality Problem (MAEP) seeks to minimize inequality in accessibility of facilities across geographic areas, and by extension, across population groups, and has great potential in applications in both private and public sectors. The planning problem is where to build three new hospitals and how large for each. The MAEP is formulated to allocate health care resources among the three selected candidate hospitals in order to maximize accessibility equality.