Dynamic Ordering and Buyer Selection Policies in a Newsvendor Setting with Service-Dependent Demand

Make-to-stock suppliers with regular buyers must balance the cost of overstocking against the cost arising from the buyers' reactions when items are unavailable. In selecting which buyers to satisfy when shortages occur, they must weigh the current revenue from the satisfied buyers against the loss in future demand from the dissatisfied buyers. To provide insight into these trade-offs, we study a newsvendor model of a firm that orders items for a group of repeat buyers who generate different revenues and visit the firm with different average rates that depend on whether they are satisfied or dissatisfied with their last visit. If the demand exceeds the order quantity (current capacity), the firm must select which buyers to serve. For two buyers, we show that a fixed order quantity (FOQ) policy and an index buyer selection policy are optimal, where the index of each buyer depends on her revenue rate, the loss in her future demand if she is not served, and the type-I service level of the other buyer if she is served. For more buyers, the optimal policy is not an index policy and cannot be obtained in closed form. It depends on the buyer satisfaction level before (ex-ante) and after the demand (ex-post), with overstocking (understocking) when the ex-ante satisfaction is high (low) and selecting buyers that maximize the current revenue (future demand) when the ex-post state is high (low). To tackle the problem, we derive three Lagrangian relaxation-based index policies: a (revenue-greedy) Whittle index policy, which is myopically optimal, a Lagrangian index policy, which sets a uniform price for violating the capacity constraint, and an active-constraint index policy, which sets a discriminatory price whenever the capacity constraint is active. Numerical results indicate that the latter policy is near-optimal and outperforms the other two and that FOQ policies can be very efficient