We investigate the role of options (contingent claims) in a buyer-supplier system. Specifically using a two-period model with correlated demand, we illustrate how options provide flexibility to a buyer to respond to market changes in the second period. We also study the implications of such arrangements between a buyer and a supplier for coordination of the channel. We show that, in general, channel coordination can be achieved only if we allow the exercise price to be piecewise linear. We develop sufficient conditions on the cost parameters such that linear prices coordinate the channel. We derive the appropriate prices for channel coordination which, however, violate the individual rationality constraint for the supplier. Contrary to popular belief (based on simpler models) we show that credit for returns offered by the supplier does not always coordinate the channel and alleviate the individual rationality constraint. Credit for returns are useful only on a subset of the feasibility region under which channel coordination is achievable with linear prices. Finally, we demonstrate (numerically) the benefits of options in improving channel performance and evaluate the magnitude of loss due to lack of coordination.Supply Contracts, Real Options, Coordination, Flexibility

Classical reasons for carrying inventory include fixed (nonlinear) production or procurement costs, lead times, nonstationary or uncertain supply/demand, and capacity constraints. The last decade has seen active research in supply chain coordination focusing on the role of incentive contracts to achieve first-best levels of inventory. An extensive literature in industrial organization that studies incentives for vertical controls largely ignores the effect of inventories. Does the ability to carry inventory influence the problem of vertical control? Conversely, can inventories arise purely due to incentive effects? This paper explicitly considers both incentives and inventories, and their interplay, in a dynamic model of an upstream firm (supplier) and a downstream firm (buyer) who can carry inventories. In our model, none of the classical reasons for carrying inventory exists. However, as we prove, the buyer's optimal strategy in equilibrium is to carry inventories, and the supplier is unable to prevent this. These inventories arise out of purely strategic considerations not yet identified in the literature, and have a significant impact on the equilibrium solution as well as supplier, buyer, and channel profits. We prove that strategic inventories play a pivotal role under arbitrary contractual structures, general (arbitrary) demand functions and general (finite or infinite) horizon lengths. As one example, two-part tariff contracts do not lead to optimal channel performance, nor can the supplier extract away all of the channel profits, in our dynamic model. Our results imply that firms can and must carry inventories strategically, and that optimal vertical contracts must take the possibility of inventories into account.contracts, inventories, industrial organization, supply chain coordination

We develop a general framework for the analysis of decentralized distribution systems. We carry the analysis in terms of a simplified model which entails N retailers who face stochastic demands and hold stocks locally and/or at one or more central locations. An exogenously specified fraction of any unsatisfied demand (demand greater than locally available stock) at a retailer could be satisfied using excess stocks at other retailers and/or stocks held at a central location. We consider inventory ordering and allocation decisions. The operational decisions of inventory and allocation of stocks and the financial decision of allocation of revenues/costs must be made in a way consistent with the individual incentives of the various independent retailers. We develop a "coopetitive" framework for the sequential decisions of inventory and allocation. We introduce the notion of claims that allows us to separate the ownership (with decision rights) and the location of inventories in the system. For the cooperative shipping and allocation decision, we use the concept of core and develop sufficient conditions for the existence of the core. For the inventory decision, we develop conditions for the existence of a pure strategy Nash Equilibrium. For this decentralized system, we show that there exists an allocation mechanism that achieves the first-best solution for inventory deployment and allocation. We develop conditions under which the first-best equilibrium will be unique. Our model can be easily generalized to include complicated ownership structures such as "super dealers," partnerships, "inventory speculators," and situations in retail e-commerce settings such as "click-through arrangements," separation of "demand generators," and "fulfillment houses," etc. It can also be applied to situations involving capacity allocations and product substitutions.Decentralization, Distribution, Game Theory, Inventory, e-Business

We study a single period multiproduct inventory problem with substitution and proportional costs and revenues. We considerNproducts andNdemand classes with full downward substitution, i.e., excess demand for classican be satisfied using productjfori≥j. We first discuss a two-stage profit maximization formulation for the multiproduct substitution problem. We show that a greedy allocation policy is optimal. We use this to write the expected profits and its first partials explicitly. This in turn enables us to prove additional properties of the profit function and several interesting properties of the optimal solution. In a limited computational study using two products, we illustrate the benefits of solving for the optimal quantities when substitution is considered at the ordering stage over similar computations without considering substitution while ordering. Specifically, we show that the benefits are higher with high demand variability, low substitution cost, low profit margins (or low price to cost ratio), high salvage values, and similarity of products in terms of prices and costs.

We examine a decentralized supply chain in which a single assembler buys complementary components from n suppliers and assembles the final product in anticipation of demand. Players take actions in the following sequence. First (stage 1), the suppliers form coalitions among themselves. Second (stage 2), the coalitions compete for a position in the negotiation sequence. Finally (stage 3), the coalitions negotiate with the assembler on allocations of the supply chain's profit. We model the multilateral negotiations between the suppliers and the assembler sequentially, i.e., the assembler negotiates with one coalition at a time. Each of these negotiations is modeled using the Nash bargaining concept. Further, in forming coalitions we assume that players are farsighted. We then predict at equilibrium the structure of the supply chain as a function of the players' relative negotiation powers. In particular, we show that the assembler always prefers the outcome where suppliers do not form coalitions. However, when the assembler is weak (low negotiation power) the suppliers join forces as a grand coalition, but when the assembler is powerful the suppliers stay independent, which is the preferred outcome to the assembler.decentralized assembly systems, Nash bargaining, negotiation power, commitment tactics, farsighted stable coalitions

A well-known result in inventory theory is that physical centralization of stocks in a system with multiple retailers decreases total costs and increases total profits for the retailers. However, does this centralization also benefit the manufacturer, whose goods the retailers stock, when customers unsatisfied at retailers due to stock-outs are considered lost sales? In this paper we consider a model with two retailers and one manufacturer. We then compare two systems: one in which the retailers hold stocks separately and the other in which they cooperate to centralize stocks at a single location. We show that whether or not centralization of stocks by retailers increases profits for the manufacturer depends on the level of "market search" in the supply chain. Market search is measured as the fraction of customers who, unsatisfied at their "local" retailer due to a stock-out, search for the good at the other retailer before leaving the system. Specifically, we show that there exists a threshold level for market search above which the manufacturer loses. Furthermore, for "very high" search levels, even the system profit (sum of manufacturer and retailer profits) may decrease upon centralization. We then compare the performance of the two systems under optimal pricing/subsidy mechanisms and show that often a manufacturer is better off in a decentralized system with high market search. We conclude with a discussion of the role of information systems in the decentralized systems.inventory, pooling, manufacturer, retailers, competition, cooperation, market search, information system

In this paper, I develop an option valuation framework that explicitly incorporates a product life cycle. I then use the framework to value the real option to change a project's capacity. Standard techniques for valuing real options typically ignore product life cycle models and specify instead a constant expected growth rate for demand or price. I show that this specification can lead to significant error in the valuation of capacity options. In particular, the standard technique tends to undervalue the option to contract capacity and overvalue the option to expand capacity. This result has important implications for capital investment decisions, especially in high-technology industries that feature regular introductions of newly improved products.real option, product life cycle, contingent claim

In this paper we analyze a supply contract for a single product that specifies that the cumulative orders -placed by a buyer, over a finite horizon, be at least as large as a (contracted upon) given quantity. We assume that the demand for the product is uncertain, and the buyer places orders periodically. We derive the optimal purchase policy for the buyer for a given total minimum quantity commitment and a discounted price. We show that the policy is characterized by the order-up-to levels of the corresponding finite horizon and a single-period standard newsboy problem with no commitment but with discounted price. We show that this policy can be computed easily. We can use this to evaluate any discount schedule characterized by a set of (price discount, minimum commitment) pairs.