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

Analyzing the proposed reconfiguration of accident-and-emergency facilities in England

The Keogh Report of 2013 proposed a major reconfiguration of the accident and emergency (A&E) system under National Health Service (NHS) England to improve service. The proposed reconfiguration includes centralized facilities with multiple specialties as well as small local minor-injury facilities. We use stylized queuing models to analyze cost and service implications of the proposed reconfiguration. We find that increasing numbers of specialty patients that require admission to hospital makes splitting off specialty A&Es from general ones more attractive. The same applies for patients with minor injuries. Our work generally supports the reconfiguration recommended in the Keogh report but with some fine-tuning: For instance, a merger of A&Es (pooling) does not always make sense even though it increases patient numbers when the patients in the two A&Es are of different types. We provide simple quantitative rules to indicate whether the proposed reconfiguration could lower costs in any particular region of the country. The results here are consistent with some NHS England providers attempting specialty A&Es for geriatric patients and mobile drunkenness treatment centers on weekends. Our rules and approach can be useful for identifying candidate reconfiguration opportunities not only for NHS England but also for any other context where pooling and arrival heterogeneity are important considerations

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

Sourcing Flexibility, Spot Trading, and Procurement Contract Structure

We analyze the structure and pricing of option contracts for an industrial good in the presence of spot trading. We combine the analysis of spot trading and buyers' disparate private valuations for different suppliers' products, and we jointly endogenize the determination of three major dimensions in contract design: (i) sales contracts versus options contracts, (ii) flat-price versus volume-dependent contracts, and (iii) volume discounts versus volume premia. We build a model in which a supplier of an industrial good transacts with a manufacturer who uses the supplier's product to produce an end good with an uncertain demand. We show that, consistent with industry observations, volume-dependent optimal sales contracts always demonstrate volume discounts (i.e., involve concave pricing). However, options are more complex agreements, and optimal option contracts can involve both volume discounts and volume premia. Three major contract structures commonly emerge in optimality. First, if the seller has a high discount rate relative to the buyer and the seller's production costs or the production capacity is low, the optimal contracts tend to be flat-price sales contracts. Second, when the seller has a relatively high discount rate compared to the buyer but production costs or production capacity are high, the optimal contracts are sales contracts with volume discounts. Third, if the buyer's discount rate is high relative to the seller's, then the optimal contracts tend to be volume-dependent options contracts and can involve both volume discounts and volume premia. However, when the seller's production capacity is sufficiently low, it is possible to observe flat-price option contracts. Furthermore, we provide links between production and spot market characteristics, contract design, and efficiency.National Science Foundation (U.S.) (contract CMMI-0758069)National Science Foundation (U.S.) (contract DMI-0245352

Establishing Nash equilibrium of the manufacturer-supplier game in supply chain management

We study a game model of multi-leader and one-follower in supply chain optimization where n suppliers compete to provide a single product for a manufacturer. We regard the selling price of each supplier as a pre-determined parameter and consider the case that suppliers compete on the basis of delivery frequency to the manufacturer. Each supplier’s profit depends not only on its own delivery frequency, but also on other suppliers’ frequencies through their impact on manufacturer’s purchase allocation to the suppliers. We first solve the follower’s (manufacturer’s) purchase allocation problem by deducing an explicit formula of its solution. We then formulate the n leaders’ (suppliers’) game as a generalized Nash game with shared constraints, which is theoretically difficult, but in our case could be solved numerically by converting to a regular variational inequality problem. For the special case that the selling prices of all suppliers are identical, we provide a sufficient and necessary condition for the existence and uniqueness of the Nash equilibrium. An explicit formula of the Nash equilibrium is obtained and its local uniqueness property is proved

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