Implementation of the Newsvendor Model with Clearance Pricing: How to (and How Not to) Estimate a Salvage Value

The newsvendor model is designed to decide how much of a product to order when the product is to be sold over a short selling season with stochastic demand and there are no additional opportunities to replenish inventory. There are many practical situations that reasonably conform to those assumptions, but the traditional newsvendor model also assumes a fixed salvage value: all inventory left over at the end of the season is sold off at a fixed per-unit price. The fixed salvage value assumption is questionable when a clearance price is rationally chosen in response to the events observed during the selling season: a deep discount should be taken if there is plenty of inventory remaining at the end of the season, whereas a shallow discount is appropriate for a product with higher than expected demand. This paper solves for the optimal order quantity in the newsvendor model, assuming rational clearance pricing. We then study the performance of the traditional newsvendor model. The key to effective implementation of the traditional newsvendor model is choosing an appropriate fixed salvage value. (We show that an optimal order quantity cannot be generally achieved by merely enhancing the traditional newsvendor model to include a nonlinear salvage value function.) We demonstrate that several intuitive methods for estimating the salvage value can lead to an excessively large order quantity and a substantial profit loss. Even though the traditional model can result in poor performance, the model seems as if it is working correctly: the order quantity chosen is optimal given the salvage value inputted to the model, and the observed salvage value given the chosen order quantity equals the inputted one. We discuss how to estimate a salvage value that leads the traditional newsvendor model to the optimal or near-optimal order quantity. Our results highlight the importance of understanding how a model can interact with its own inputs: when inputs to a model are influenced by the decisions of the model, care is needed to appreciate how that interaction influences the decisions recommended by the model and how the model’s inputs should be estimated

Competition in the Supply Option Market

This paper develops a multiattribute competition model for procurement of short life-cycle products. In such an environment, the buyer installs dedicated production capacity at the suppliers before demand is realized. Final production orders are decided after demand materializes. Of course, the buyer is reluctant to bear all the capacity and inventory risk, and thus signs flexible contracts with several suppliers. We model the suppliers' offers as option contracts, where each supplier charges a reservation price per unit of capacity and an execution price per unit of delivered supply. These two parameters illustrate the trade-off between total price and flexibility of a contract, which are both important to the buyer. We model the interaction between suppliers and the buyer as a game in which the suppliers are the leaders and the buyer is the follower. Specifically, suppliers compete to provide supply capacity to the buyer, and the buyer optimizes its expected profit by selecting one or more suppliers. We characterize the suppliers' equilibria in pure strategies for a class of customer demand distributions. In particular, we show that this type of interaction gives rise to cluster competition. That is, in equilibrium suppliers tend to be clustered in small groups of two or three suppliers each, such that within the same group all suppliers use similar technologies and offer the same type of contract. Finally, we show that in equilibrium, supply chain inefficiencies—i.e., the loss of profit due to competition—are at most 25% of the profit of a centralized supply chain.United States. Office of Naval Research (contract N00014-95-1-0232)United States. Office of Naval Research (contract N00014-01-1-0146)National Science Foundation (U.S.) (contract DMI-0085683)National Science Foundation (U.S.) (DMI-0245352)National Science Foundation (U.S.) (CMMI-0758069)Massachusetts Institute of Technology. Center for Digital BusinessUniversity of Navarra. IESE Business School (CIIL International Center for Logistics Research

Coordination in closed-loop supply chain with price-dependent returns

This paper proposes two Closed-loop Supply Chain (CLSC) games in which a manufacturer sets some green activity programs efforts and a retailer sets the selling price. Both strategies influence the return rate, which is a state variable. The pricing strategy plays a key role in the identification of the best contract to achieve coordination as well as in achieving environmental objectives. The pricing strategy influences the return rate negatively, as consumers delay the return of their goods when the purchasing (and repurchasing) price is high. We then compare a wholesale price contract (WPC) and a revenue sharing contract (RSC) mechanism as both have interesting pricing policy implications. Our result shows that firms coordinate the CLSC through a (WPC) when the sharing parameter is too low while the negative effect of pricing on returns is too severe. In that case, the low sharing parameter deters the manufacturer to accept any sharing agreements. Further, firms coordinate the CLSC when the sharing parameter is medium independent of the negative impact of pricing on returns. When the sharing parameter is too high the retailer never opts for an RSC. We find that the magnitude of pricing effect on returns determines the contract to be adopted: For certain sharing parameter, firms prefer an RSC when the price effect on return is low and a WPC when this effect is high. In all other cases, firms do not have a consensus on the contract to be adopted and coordination is then not achieved