Minimum Order Quantity (MOQ) is widely used in many industries, e.g., apparel, pharmaceutical and consumer packaged products. When customers (e.g., distributors or retailers) make order decisions, they can either order none from their suppliers or order at least a minimum quantity, namely, the MOQ. MOQ poses a substantial challenge to managing supply chains efficiently because it requires the customers to order either none or many. Thus it reduces the customers' flexibility of responding to demand, and leads to higher inventory cost and lower service level.

There is little previous work on stochastic inventory systems with MOQ. In order to provide tools and principles for companies that can guide their managerial actions in controlling inventory when they face MOQ from their suppliers, we consider a single-item periodic-review inventory system where the demand is random and the ordering cost is linear. At each time period, the system can either order none or order at least as much as the minimum order quantity. We develop the following key results: (1) characterizing the structure of the optimal inventory policies for the system in a finite time horizon; (2) designing heuristic inventory policies that are easily implementable and have close to optimal performance; (3) developing managerial insights with respect to the impact of MOQ on the system performances.

Joint work with Michael N. Katehakis and Bin Zhou.