A heuristic algorithm for solving large location–inventory problems with demand uncertainty

In this paper, we analyze a location–inventory problem for the design of large supply chain networks with uncertain demand. We give a continuous non-linear formulation that integrates location, allocation and inventory decisions, and includes the costs of transportation, cycle inventory, safety stock, ordering and facility opening. Then, relying on the fact that the model becomes linear when certain variables are fixed, we propose a heuristic algorithm that solves the resulting linear program and uses the solution to improve the variable estimations for the next iteration. In order to show the efficiency of the algorithm, we compare our results with those of the conic quadratic formulation of the problem. Computational experiments show that the heuristic algorithm can be efficiently used to find fast and close to optimal solutions for large supply chain networks. Finally, we provide managerial insights regarding the ways in which demand uncertainty, risk pooling and safety stocks at retailers affect the design of a supply chain.