The Facility Location Problem with Fuzzy Parameters

Abstract

There is a variety of studies about Facility Location Problems (FLP) in Operations Research (OR) literature. The studies in the literature generally assume a deterministic environment. However studies relaxing the deterministic assumption are not rare. One way of incorporating uncertainties in these problems is through fuzzy parameters. While incorporating uncertainties into the problem Fuzzy set theory has some advantages over the other popular approach to handle uncertainties which is probabilistic theory. Unlike probabilistic theory the fuzzy set theory yields a logical manner to model uncertainties without the need for any historical data. Our focus in this work is to survey the collection of the recent publications on FLP with fuzzy parameters. Uncertain demands variable costs and travel durations as well as some subjective factors that are scaled in linguistic values can be given as examples for fuzzy parameters. As a methodology of this work firstly we start by listing parameters of the classical FLP and then present studies which consider these parameters as fuzzy sets and classify them accordingly. Secondly we group these studies based on the solution methodology implemented. Our search domain for the literature is primarily the Web of Science database. However we do not limit ourselves to that database in general. Our contribution is to provide knowledge about the properties of the fuzzy environments in facility location models.