Decomposition Approach for a Two-Echelon Inventory Management System

Warehouses of the first echelon in a two-echelon system are designed to satisfy customer orders. In the second echelon, we have a central warehouse for restocking the first-echelon warehouses. Customer orders can be partially satisfied, but the total fraction of completed orders should not be less than the specified threshold. We need to minimize the total cost of storing the items in all warehouses. We use a deterministic simulation to calculate the order satisfaction ratio and the storage cost during the planning period. The simulation depends on inventory management policies at each warehouse for each type of items. We develop a decomposition method 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 numerical experiments with instances with 100 warehouses and 1000 types of items are presented. On instances with known exact solutions, we have the optimum in two cases, while in the other cases the deviation from the optimal values is at most 1.9%.