Yigal Gerchak

The structure of periodic review policies in the presence of random yield

This work provides a comprehensive analysis of a general periodic review production/inventory model with random (variable) yield. Existence of an order point whose value does not depend on yield being random is proved in the single period case without specifying the yield model and using a very general cost structure. When yield is a random multiple of lot size, the nonorder-up-to optimal policy is characterized for a finite-horizon model. The finite-horizon value functions are shown to converge to the solution of an infinite-horizon functional equation, and the infinite-horizon order point is shown to be no smaller than when yield is certain.

Multiple Lotsizing in Production to Order with Random Yields: Review of Recent Advances

This article provides a review of models, analytical results and insights pertaining to multiple lotsizing in production to order, with emphasis on recent work on multistage systems and inspection issues. The basic setting consists of an order of fixed size that has to be met in its entirety. Production is in lots and is imperfect, and inspection can take place only when lot has completed a stage. Processing each lot at each stage entails fixed and variable costs. The tradeoff is between running large lots, entailing potentially costly overproduction, and small lots, which may necessitate multiple production runs and their associated setups. Variations of this problem have been explored since the 1950s, but only recently has there been significant progress in solving exactly problems of realistic complexity. We first review single-stage models, including those which compute the variance of costs, those dealing with inspections, those with multiple grades and situations with uncertain demand. We then review multi-stage systems, starting with those with no bottlenecks, and progressing to one, and two bottlenecks. The implications of rework capability in the various systems are then explored.

Coordination in decentralized assembly systems with uncertain component yields

Abstract The literature on assembly systems with random component yields has focused on centralized systems, where a single decision maker chooses all components’ production quantities and incurs all the costs. We consider a decentralized setting where the component suppliers choose their production quantities based solely on their own cost/reward structure, and the assembly firm makes ordering decisions based on its own cost/reward structure. When the suppliers control their inputs but the outputs exhibit random yields, coordination in such systems becomes quite complex. In such situations, incentive alignment control mechanisms are needed so that the suppliers will choose production quantities as in the centralized system case. One such mechanism is to penalize the supplier with the worse delivery performance. We analyze the conditions under which system coordination is achieved while respecting participation constraints. Further, we determine the optimal component ordering policy for the assembly firm and derive the optimal coordinating penalties.

Quantifying Operational Synergies in a Merger/Acquisition

Merger and acquisition activity has increased sharply in the last decade. It seems useful to have models that can help senior managers of bidder firms make informed decisions about the amount of premium, over the targets share prices prevailing prior to merger announcement, that can be justified on the basis ofoperational synergies. The goal of this article is to capture important parameters from the production side that have a bearing on the valuation of the targets shares. We show that the production characteristics of both the bidder and the target matter in a significant way. For example, if the bidder and target operate in independent markets, the bidder has flexible production facilities but the targets production facilities are inflexible, then an increase in the bidders demand can make the target less attractive and lower the value of operational synergy.

On the Relation Between the Benefits of Risk Pooling and the Variability of Demand

The benefits of pooling risks, manifested in inventory management by consolidating multiple random demands in one location, are well known. What is less well understood are the determinants of the magnitude of the savings. Recently there has been speculation about the impact of demand variabilities on the benefits of risk pooling. We provide an example where increased variability of the individual demands actually reduces the benefits of risk pooling. We prove, however, that if we restrict increased variability to a common linear transformation, the greater the demand variabilities the larger the benefits of consolidating them, in agreement with intuition. We also provide bounds on the benefits of the consolidation of demands. Our results do not require independence of the demands, apply to any number of pooled demands, and are obtained in a pure cost-driven model.

Coordination of Quantity and Shelf-Retention Timing in the Video Movie Rental Industry

How should a video rental chain replenish its stock of new movies over time? Any such policy should consist of two key dimensions: (i) the number of copies purchased; and (ii) when to remove a movie from the front shelves and replace it by a newly released one. We first analyze this bi-variate problem for an integrated chain. As for decentralized chains, we show that a (wholesale) price-only contract cannot coordinate such a chain. We then consider a price-and-revenue-sharing contract. Such a contract can achieve coordination, but the unique price and share which are needed may not provide one of the parties with its desired profit (i.e., it will violate individual rationality). This situation has been reported in the case of Blockbuster Video and has led to litigation between Blockbuster and Disney Studios. We thus propose adding a third lever: a license fee (or subsidy) associated with each new movie. Such a contract can coordinate the channel and satisfy the individual rationality requirements. In fact, all our results hold true irrespective of whether or not the rental store is allowed to sell surplus copies of movies. We are able to compare the optimal decision variable and coordinating lever values, as well as the optimal profits, for the “rental only” and “sales + rental” models. Our numerical examples, which utilize empirical demand data have significant managerial implications in terms of increasing the effectiveness of the video rental industry.

Supply chain coordination with downstream operating costs: Coordination and investment to improve downstream operating efficiency☆

Abstract We endow the downstream firm in a supply chain with operating costs in addition to the traditional overage and underage costs. We reanalyze Lariviere and Porteuss “Selling to a Newsvendor” model (2001), allowing for non-linear production costs, and provide comparative statics. We then explore investment in reducing downstream operating costs. To overcome the fact that investment is lower in a decentralized chain than in an integrated one, we propose several coordination mechanisms––buybacks, revenue sharing and operating subsidy with a license fee.

OPTIMAL INSPECTION ORDER WHEN PROCESS’ FAILURE RATE IS CONSTANT

Suppose that a lot has been produced by a process with a constant failure rate. So either the entire lot is good, or all units up to some point are good and from that point on are all defective. We wish to determine the order in which units in such lot should be inspected so as to minimize the expected number of inspections needed to identify all defectives. Unlike previous work in this area, we do not a priori assume that the last unit in the lot is defective, and that key difference turns out to dramatically influence the nature of the optimal inspection policy and the expected number of units inspected. After analyzing the optimal policy, we suggest a very simple and intuitive heuristic, which turns out to perform extremely well. Numerical results are provided.

A consignment system where suppliers cannot verify retailer's sales reports

Abstract Newspapers are often sold through stores via consignment arrangements, which involve vendor (publisher) managed inventory and revenue sharing. Since retailers are not required to actually return unsold copies, it is said that some of them occasionally under-report sales. That hurts the publisher on the short run and could also interfere with his rational stocking decisions as these are based, to some extent, on previous sales reports. We construct a discounted dynamic framework for the retailers optimal reporting as a function of the publishers delivery–response function to these reports, and a similar average-cost model. It turns out the optimal report does not depend on actual sales. We then show that the publishers resulting delivery response function is the same as it would be in an integrated system. Thus the retailers untruthful behavior actually causes the system to behave optimally. Had the retailer been verifiably truthful, the system would not be coordinated.

The Effectiveness of Investment in Lead Time Reduction for a Make-to-Stock Product

This paper focuses on a firm selling a make-to-stock product with a constant customer demand rate. The firm follows an exact (Q, r) policy for raw material inventory control and faces a random replenishment lead time. Through this research, we wish to gain a better understanding of the impact of investing in reducing supply lead time when the investment costs have to be borne, partly or fully, by the firm. This work is motivated by the recognition that lead time reduction is now of strategic importance in the successful operation of a firm. We examine different types of investment schemes in replenishment lead time reduction and the different cost models they generate. We present analytical and numerical results and insights for each type of model, compute the optimal (Q, r) policy and the associated investment levels. The work presents new results, and sheds light on some apparently counter-intuitive observations.