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

Abstract

Make-to-stock suppliers selling to regular buyers must balance the cost of overstocking against the cost of buyers’ reactions when items become 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 and decision support on these trade-offs, we (i) develop a novel newsvendor model of a firm with heterogeneous buyers with service-dependent demand, (ii) provide properties of the optimal ordering and buyer selection decisions of the firm, and (iii) derive a novel Lagrangian Relaxation (LR)-based index policy for selecting buyers and compare it with two other LR-based index policies. The model concerns 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. The firm selects which buyers to serve if the demand exceeds the order quantity (current capacity). For two buyers, we show that a fixed order quantity (FOQ) policy and an index buyer selection policy are optimal. For more buyers, the optimal policy involves overstocking (understocking) when the overall buyer satisfaction is high (low) and selecting buyers that maximize the current revenue (future demand) when the overall buyer satisfaction after the demand is high (low). To tackle the problem, we derive three LR-based index policies: a Lagrangian index policy that uses a uniform capacity price, a Whittle index policy that uses a discriminatory capacity price and is myopically optimal, and a novel “active-constraint” index policy that uses a discriminatory capacity price when the capacity constraint is active. Numerical results indicate that the latter policy is near-optimal and outperforms the other two and that combining it with the right FOQ policy can be very efficient.

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