The EOQ problem with decidable warehouse capacity: Analysis, solution approaches and applications

The Economic Order Quantity (EOQ) problem is a fundamental problem in supply and inventory management. In its classical setting, solutions are not affected by the warehouse capacity. We study a type of EOQ problem where the (maximum) warehouse capacity is a decision variable. Furthermore, we assume that the warehouse cost dominates all the other inventory holding costs. We call this the EOQ-Max problem and the D-EOQ-Max problem, if the product is continuously divisible and discrete, respectively. The EOQ-Max problem admits a closed form optimal solution, while the D-EOQ-Max problem does not because its objective function may have several local minima. We present an optimal polynomial time algorithm for the discrete problem. Construction of this algorithm is supported by the fact that continuous relaxation of the D-EOQ-Max problem provides a solution that can be up to 50% worse than the optimal solution, and this worst-case error bound is tight. Applications of the D-EOQ-Max problem include supply and inventory management, logistics and scheduling.