On a branch-and-bound approach for a Huff-like Stackelberg location problem

Modelling the location decision of two competing firms that intend to build a new facility in a planar market can be done by a Huff-like Stackelberg location problem. In a Huff-like model, the market share captured by a firm is given by a gravity model determined by distance calculations to facilities. In a Stackelberg model, the leader is the firm that locates first and takes into account the actions of the competing chain (follower) locating a new facility after the leader. The follower problem is known to be a hard global optimisation problem. The leader problem is even harder, since the leader has to decide on location given the optimal action of the follower. So far, in literature only heuristic approaches have been tested to solve the leader problem. Our research question is to solve the leader problem rigorously in the sense of having a guarantee on the reached accuracy. To answer this question, we develop a branch-and-bound approach. Essentially, the bounding is based on the zero sum concept: what is gain for one chain is loss for the other. We also discuss several ways of creating bounds for the underlying (follower) sub-problems, and show their performance for numerical cases

Bilevel models on the competitive facility location problem

Facility location and allocation problems have been a major area of research for decades, which has led to a vast and still growing literature. Although there are many variants of these problems, there exist two common features: finding the best locations for one or more facilities and allocating demand points to these facilities. A considerable number of studies assume a monopolistic viewpoint and formulate a mathematical model to optimize an objective function of a single decision maker. In contrast, competitive facility location (CFL) problem is based on the premise that there exist competition in the market among different firms. When one of the competing firms acts as the leader and the other firm, called the follower, reacts to the decision of the leader, a sequential-entry CFL problem is obtained, which gives rise to a Stackelberg type of game between two players. A successful and widely applied framework to formulate this type of CFL problems is bilevel programming (BP). In this chapter, the literature on BP models for CFL problems is reviewed, existing works are categorized with respect to defined criteria, and information is provided for each work.WOS:000418225000002Scopus - Affiliation ID: 60105072Book Citation Index- Science - Book Citation Index- Social Sciences and HumanitiesArticle; Book ChapterOcak2017YÖK - 2016-1

Incorporating waiting time in competitive location models: Formulations and heuristics

In this paper we propose a metaheuristic to solve a new version of the Maximum Capture Problem. In the original MCP, market capture is obtained by lower traveling distances or lower traveling time, in this new version not only the traveling time but also the waiting time will affect the market share. This problem is hard to solve using standard optimization techniques. Metaheuristics are shown to offer accurate results within acceptable computing times.Market capture, queuing, ant colony optimization

An Alternating Heuristic for Medianoid and Centroid Problems in the Plane

This paper develops two heuristics for solving the centroid problem on a plane with discrete demand points. The methods are based on the alternating step well known in location methods. Extensive computational testing with the heuristics reveals that they converge rapidly, giving good solutions to problems that are up to twice as large as those reported in the literature. The testing also provides some managerial insight into the problem and its solution

On The Use of Genetic Algorithms to Solve Location Problems

This paper seeks to evaluate the performance of genetic algorithms (GA) as an alternative procedure for generating optimal or near-optimal solutions for location problems. The specific problems considered are the uncapacitated and capacitated fixed charge problems, the maximum covering problem, and competitive location models. We compare the performance of the GA-based heuristics developed against well-known heuristics from the literature, using a test base of publicly available data sets. Scope and purpose Genetic algorithms are a potentially powerful tool for solving large-scale combinatorial optimization problems. This paper explores the use of this category of algorithms for solving a wide class of location problems. The purpose is not to prove that these algorithms are superior to procedures currently utilized to solve location problems, but rather to identify circumstances where such methods can be useful and viable as an alternative/superior heuristic solution method