Robust Storage Assignment in Unit-Load Warehouses

Assigning products to and retrieving them from proper storage locations are crucial in minimizing the operating cost of a unit-load warehouse. The problem becomes intractable when the warehouse faces variable supply and uncertain demand in a multi-period 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 travel in the warehouse with distributional ambiguity of demand. Under a linear decision rule, we 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 linear policy achieves close to the expected value given perfect information, and significantly outperforms existing heuristics in the literature.