A Linear Storage-Retrieval Policy for Robust Warehouse Management

Assigning products to and retrieving them from proper storage locations in a unit-load warehouse are crucial in minimizing its operating cost. The problem becomes intractable when the warehouse faces uncertain demand in a dynamic setting. We assume a factor-based demand model in which demand for each product in each period is affinely dependent on some uncertain factors. The distributions of these factors are only partially characterized. We introduce a robust optimization model that minimizes the worst-case expected total operating cost of a warehouse under distributional ambiguity. Under a linear decision rule, we can obtain a storage and retrieval policy by solving a moderate-size linear optimization problem. Surprisingly, despite imprecise specification of demand distributions, our computational studies suggest that the simple linear policy achieves close to the expected value given perfect demand information, and significantly outperforms existing heuristics in the literature.