A joint inventory reliable capacitated facility location problem using a continuum approximation

Abstract

This paper considers a continuum approximation to deal with a joint inventory reliable capacitated facility location problem within a two-echelon supply chain structure, whereas the majority of related studies assume facilities with infinite capacity and neglect inventory cost. The scope of the supply chain is restricted to distribution-centers (DCs) and customers, whereas they are spatially distributed over the market area. As DCs are vulnerable to permanent failure, different assignment levels are regarded for customers. The resulting model formulation partitions the market area into the different districts of DCs and consequently obtains the total required number of DCs. It also allocates a portion of the districts to the assignment levels. Since the model formulation is a nonlinear programming problem with box-constraint variables, we employ a trust region algorithm (TRA) as the solution procedure. A genetic algorithm (GA) is used as a benchmark for the proposed solution procedure. The computational results demonstrate the superiority of the TRA in terms of cost and time savings. Numerically, TRA improves the objective function by about 10% compared with the GA. The sensitivity analysis also indicates the enlargement of the number of districts as a result of increasing the vulnerability of DCs. Finally, the amount of enlargement is affected by a trade-off between transportation, inventory, and penalty costs on the one hand and fixed costs on the other.