Decomposition Approach for a Two-Echelon Inventory Management System

Warehouses of the first echelon in a two-echelon system are designed to satisfy customerorders. In the second echelon, we have a central warehouse for restocking the first-echelonwarehouses. Customer orders can be partially satisfied, but the total fraction of completed ordersshould not be less than the specified threshold. We need to minimize the total cost of storing theitems in all warehouses. We use a deterministic simulation to calculate the order satisfaction ratioand the storage cost during the planning period. The simulation depends on inventorymanagement policies at each warehouse for each type of items. We develop a decompositionmethod for solving the problem. It is based on solution of subproblems for each type of items.Also, we propose some approaches to exact solution of the problem. The results of numericalexperiments with instances with 100 warehouses and 1000 types of items are presented. Oninstances with known exact solutions, we have the optimum in two cases, while in the other casesthe deviation from the optimal values is at most 1.9%.