Linear and Quadratic Programming and Applications in Examining Wasteful Commuting and Allocating Healthcare Providers

• Published in: Computational Methods and GIS Applications in Social Science - Lab Manual pp. 204 - 219
• Main Authors: Liu, Lingbo, Wang, Fahui
• Format: Book Chapter
• Language: English
• Published: United Kingdom CRC Press 2024; Taylor & Francis Group
• Edition: 1
• Subjects: Solver Node; Site Selection; Distance Decay; NLP; Distance Matrix; Kernel Density Estimation; Road Network Dataset; Pivot Node; Candidate Facilities; QP; Network Travel Time; Row Id; Input Port; Point Feature Class; Joiner Nodes; Health Informatics; 2SFCA Method; Distance Decay Parameter; Case Study 11B; CSV File; Case Study 11A; Resident Workers; MCLP; Groups Tab; Filter Node
• ISBN: 9781032302430; 1032302437
• DOI: 10.1201/9781003304357-11

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.