FACILITY LOCATION PROBLEM MATHEMATICAL MODELS - SUPPLY CHAIN PERSPECTIVE

Background: Supply chains are the networks linking sources of supply with demand points and composed of so-called actors, i.e., producers, distributors/wholesalers, retailers, and customers/consumers. As in every network, supply chains contain vertices and arcs, the former represented by factories and warehouses (including distribution centers). Such facilities cause long-term and expensive investments. As a result, decisions on location and number of them belong to the strategic level of management and require quantitative analysis. To do this, mathematical models of the Facility Location Problem (FLP) are constructed to allow an application of optimization methods.

Methods: Mathematical optimization or programming is the selection of the best solution, with regard to some criterion, from a set of feasible alternatives. The fundamental of mathematical optimization is the formulation of mathematical models of analyzed problems. Mathematical models are composed of objective function, decision variables, constraints, and parameters. These components are presented and compared in the paper concerning FLP from a supply chain perspective.

Results: The ten mathematical models of the FLP are presented, including the two original ones. The models are classified according to such features as facility type they concern, including the desirable, neutral, and undesirable ones. The models and their components are characterized. In addition, their applicability and elasticity are analyzed. Finally, the models are compared and discussed from the supply chain point of view.

Conclusions: However, the FLP mathematical models are relatively similar; the most important element of them for supply chain appropriate representation is an objective function. It strongly influences the possible applicability of FLP models and their solutions, as well. The objective functions having broader applicability turned out to be the maximized number of supply/demand points covered by facilities and the minimized number of facilities necessary to cover supply/demand points. However, not to locate all allowed facilities (use all the location sites) or as many as supply/demand points, but an appropriate number of them, it is necessary to take into account facility fixed costs. Thus, when locating logistics facilities, the minimized total cost of serving supply/demand points is the most appropriate objective function.