Solving quadratic assignment problems with rectangular distances and integer programming

Abstract

The problem considered involves the assignment of n facilities to n specified locations. Each facility has a given nonnegative flow from each of the other facilities. The objective is to minimize the sum of transportation costs.Assume these n locations are given as points on a two-dimensional plane and transportation costs are proportional to weighted rectangular distances. Then the problem is formulated as a binary mixed integer program. The number of integer variables (all binary) involved equals the number of facilities squared. Without increasing the number of integer variables, the formulation is extended to include "site costs." Computational results of the formulation are presented.

Exact and heuristic procedures for the material handling circular flow path design problem

“…The Love and Wong (1976) model for the quadratic assignment problem can be regarded as the basis for later models in which distances between cells are computed on the basis of their size and dimensions. Montreuil (1990) initiated a modeling framework to integrate all the three components of the facility layout problem: the cell location problem, the P/D station location problem, and the flow path design problem.…”

Geographic and process information for chemical plant layout problems

“…A mixed-integer linear model version of the QAP was formulated such that locations are given as points in a two-dimensional plane, and Manhattan distances were used to describe the separa-Ž . tion between points Love and Wong, 1976 . In other mixedinteger linear models Manhattan distances are used and models usually require a priori known locations using a grid-Ž .…”

The Quadratic Assignment Problem

“…The QAP is a combinatorial optimization problem stated for the first time by Koopmans and Beckmann (1957). Early papers on the subject include Gilmore (1962), Pierce and Crowston (1971), Lawler (1973), and Love and Wong (1976). The problem is defined as follows.…”