Performance-based contracting is reshaping service support supply chains in capital intensive industries such as aerospace and defense. Known as Power by the Hour in the private sector and as Performance-Based Logistics (PBL) in defense contracting, it aims to replace traditionally used …xed-price and cost-plus contracts in order to improve product availability and reduce the cost of ownership by tying a supplier's compensation to the output value of the product generated by theTo analyze implications of performance-based relationships, we introduce a multitask principalagent model to support resource allocation and use it to analyze commonly observed contracts. In our model the customer (principal) faces a product availability requirement for the "uptime"of the end product. The customer then o¤ers contracts contingent on availability to n suppliers (agents) of the key subsystems used in the product, who in turn exert cost reduction e¤orts and set spare parts inventory investment levels. We show that the …rst-best solution can be achieved if channel members are risk-neutral. When channel members are risk-averse, we …nd that the second-best contract combines a …xed payment, a cost-sharing incentive, and a performance incentive. Furthermore, we study how these contracts evolve over the product deployment life cycle as uncertainty in support cost changes. Finally, we illustrate the application of our model to a problem based on aircraft maintenance data and show how the allocation of performance requirements and contractual terms change under various environmental assumptions.The authors are grateful to the seminar participants at the Wharton School, Cornell University, University of Texas at Dallas, University of Washington, Columbia University, UC Berkeley, and Naval Postgraduate School for helpful discussions. The authors would also like to acknowledge input from L. Gill, S. Gutierrez, M. Lebeau and M. Mendoza, who provided valuable information concerning current practices. Finally, the authors are grateful for the assistance of Ashish Achlerkar of MCA Solutions, who provided valuable assistance in testing the model and providing access to a real-world data set.

Classical inventory models offer a variety of insights into the optimal way to manage inventories of individual products. However, top managers and industry analysts are often concerned with the aggregate macroscopic view of a firm's inventory rather than with the inventories of individual products. Given that classical inventory models often do not account for many practical considerations that a company's management faces (e.g., competition, industry dynamics, business cycles, the financial state of the company and of the economy, etc.) and that they are derived at the product level and not the firm level, can insights from these models be used to explain the inventory dynamics of entire companies? This exploratory study aims to address this issue using empirical data.We analyze absolute and relative inventories using a quarterly data panel that contains 722 public U.S. companies for the period 1992-2002. We have chosen companies that are not widely diversified and whose business in large part relies on inventory management to concentrate on empirically testing hypotheses derived from a variety of classical inventory models (economic order quantity (EOQ), [Q, r], newsvendor, periodic review, etc.). We find empirical evidence that firms operating with more uncertain demand, longer lead times, and higher gross margins have larger inventories. Furthermore, larger companies appear to benefit from economies of scale and therefore have relatively less inventory than smaller companies. We obtain mixed evidence on the relationship between inventory levels and inventory holding costs. We also analyze the breakdown of data into eight segments-oil and gas, electronics, wholesale, retail, machinery, hardware, food, and chemicals-and find that, with a few notable exceptions, our hypotheses are supported within the segments as well. Overall, our results demonstrate that many of the predictions from classical inventory models extend beyond individual products to the aggregate firm level; hence, these models can help with high-level strategic choices in addition to tactical decisions. Abstract: Classical inventory models offer a variety of insights into the optimal way to manage inventories of individual products. However, top managers and industry analysts are often concerned with the aggregate macroscopic view of a firm's inventory rather than with the inventories of individual products. Given that classical inventory models often do not account for many practical considerations that a company's management faces (e.g., competition, industry dynamics, business cycles, the financial state of the company and of the economy, etc.) and that they are derived at the product and not at the firm level, can insights from these models be used to explain the inventory dynamics of entire companies? This exploratory study aims to address this issue using empirical data.We analyze absolute and relative inventories using a quarterly data panel that contains 722 public US companies for the period 1992 to 2002. We have chosen compani...

A standard problem in operations literature is optimal stocking of substitutable products. We consider a consumer-driven substitution problem with an arbitrary number of products under both centralized inventory management and competition. Substitution is modeled by letting the unsatisfied demand for a product flow to other products in deterministic proportions. We obtain analytically tractable solutions that facilitate comparisons between centralized and competitive inventory management under substitution. For the centralized problem we show that, when demand is multivariate normal, the total profit is decreasing in demand correlation.

This paper studies the impact of competition on a firm's choice of technology (product-flexible or productdedicated) and capacity investment decisions. Specifically, we model two firms competing with each other in two markets characterized by price-dependent and uncertain demand. The firms make three decisions in the following sequence: choice of technology (technology game), capacity investment (capacity game), and production quantities (production game). The technology and capacity games occur while the demand curve is still uncertain, and the production game is postponed until after the demand curve is revealed.We develop best-response functions for each firm in the technology game and compare how a monopolist and a duopolist respond to a given flexibility premium. We show that the firms may respond to competition by adopting a technology which is the same as or different from what the competitor adopts. We conclude that contrary to popular belief, flexibility is not always the best response to competition-flexible and dedicated technologies may coexist in equilibrium. We demonstrate that as the difference between the two market sizes increases, a duopolist is willing to pay less for flexible technology, whereas the decision of a monopolist is not affected. Further, we find that a firm that invests in flexibility benefits from a low correlation between demands for two products, but the extent of this benefit differs depending on the competitor's technology choice. Our results indicate that higher demand substitution may or may not promote the adoption of flexibility under competition, whereas it always facilitates the adoption of flexibility without competition. Finally, we show that contrary to intuition, as the competitor's cost of capacity increases, the premium a flexible firm is willing to pay for flexibility decreases. AbstractThe goal of this paper is to study the impact of competition on a firm's technology choice (productflexible or product-dedicated) and capacity investment decisions. Specifically, we model two firms competing with each other in two markets characterized by price-dependent and uncertain demand. The firms make three decisions in the following sequence: choice of technology (technology game), capacity investment (capacity game) and production quantities (production game). The technology and capacity games occur while the demand curve is still uncertain and the production game is postponed until after the demand curve is revealed.We formally characterize a Markov-perfect Nash equilibrium in the capacity and production games and under suitable assumptions solve the games in closed form. Further, we develop best-response functions for each firm in the technology game and compare how a monopolist and a duopolist respond to a given flexibility premium. We show that the cost premium which the duopolist is willing to accept, when investing in flexbile technology, is higher (smaller) than the premium which the monopolist is willing to accept, if the competitor invests in dedicated (f...

Game theory has become an essential tool in the analysis of supply chains with multiple agents, often with conflicting objectives. This chapter surveys the applications of game theory to supply chain analysis and outlines game-theoretic concepts that have potential for future application. We discuss both noncooperative and cooperative game theory in static and dynamic settings. Careful attention is given to techniques for demonstrating the existence and uniqueness of equilibrium in noncooperative games. A newsvendor game is employed throughout to demonstrate the application of various tools.