### Solving a Novel Multi-Objective Inventory Location Problem by Means of a Local Search Algorithm

Abstract

Problems in operations research are usually modelled as single objective ones even though there exist several goals that should be attained. Multiple reasons of why inherently multi-objective problems are modelled as single objective can be identified: better understanding of the problem features, simplification of the mathematical formulation of the problem, among others. However, summarising (usually conflicting) objectives into one objective function can be a sign of over-simplification in the problem modelling process. In this paper we extend a single objective inventory location problem formulation to a multi-objective one. We consider two conflicting objectives, namely, location cost and inventory cost. As a result, we obtain a complex multi-objective non-linear integer programming problem. Like its single objective formulation, this multi-objective problem cannot be solved by exact methods as the number of decision variables increases. Thus, a simple yet effective multi-objective local search algorithm is implemented in this paper.