Competitive facility location model with concave demand |
| |
Authors: | Robert Aboolian Oded Berman Dmitry Krass |
| |
Affiliation: | 1. College of Business Administration, California State University San Marcos, San Marcos, CA 92096, USA;2. Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, Ont., Canada M5S 3E6 |
| |
Abstract: | We consider a spatial interaction model for locating a set of new facilities that compete for customer demand with each other, as well as with some pre-existing facilities to capture the “market expansion” and the “market cannibalization” effects. Customer demand is assumed to be a concave non-decreasing function of the total utility derived by each customer from the service offered by the facilities. The problem is formulated as a non-linear Knapsack problem, for which we develop a novel solution approach based on constructing an efficient piecewise linear approximation scheme for the objective function. This allows us to develop exact and α-optimal solution approaches capable of dealing with relatively large-scale instances of the model. We also develop a fast Heuristic Algorithm for which a tight worst-case error bound is established. |
| |
Keywords: | Location Integer programming Competitive facility location models Non-linear Knapsack problem Alpha-optimal solutions Greedy heuristics Worst-case bounds |
本文献已被 ScienceDirect 等数据库收录! |
|