Heuristic Methods for Centralized Control of One-Warehouse, N-Retailer Inventory Systems

This paper considers a periodic-review, two-echelon inventory system with one central warehouse and several retailers facing stochastic demand. The retailers replenish their stock from the warehouse, which in turn places orders at an outside supplier with infinite capacity. Transportation times and costs are constant. No ordering costs are considered, but warehouse replenishments must be multiples of a given batch quantity. The objective is to find policies that minimize holding and backorder costs. The standard approach to approximately solve this problem is to use a “balance” assumption, meaning that negative stock allocations to the retailers are possible. This approach may lead to considerable errors for problems with large differences between the retailers in terms of service requirements and demand characteristics. To handle such situations we suggest and evaluate two computationally tractable heuristics: the Virtual Assignment ordering rule for warehouse replenishments and the Two-step Allocation rule for allocating stock from the warehouse to the retailers. Numerical evidence shows that, especially when combining these heuristics, we obtain considerable improvements for many problems over the standard approach. Savings of up to 50% have been recorded.