ABSTRACT
Chapter 11 introduces two popular methods in optimization, linear programming (LP) and quadratic programming (QP). QP is perhaps the simplest form of nonlinear programming (NLP). LP seeks to maximize or minimize an objective function subject to a set of constraints, and both the objective and constraints are expressed in linear functions. QP has a quadratic objective function, but its constraints remain linear. A case study uses a customized “WasteCommuteR” tool to solve the classic wasteful commuting problem by LP. The location-allocation models are a set of applications of integer linear programming (ILP), where the decision variables need to be integers. Another case study illustrates how to (1) solve popular location-allocation models, such as the p-median problem and the maximum covering location problem (MCLP), by the built-in Location Allocation Analysis tools in ArcGIS Pro, and (2) implements the minimax (p-center) problem in the “MinimaxR” tool. This chapter also proposes a new location-allocation problem, namely, the maximal accessibility equality problem (MAEP), to minimize inequality in accessibility of facilities across geographic areas. A MAEP tool in R is developed to solve the QP problem.
