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We present and study a three-stage model of a decentralized distribution system consisting of n retailers, each of whom faces a stochastic demand for an identical product. In the first stage, before the demand is realized, each retailer independently orders her initial inventory. In the second stage, after the demand is realized, each retailer decides how much of her residual supply/demand she wants to share with the other retailers. In the third stage, residual inventories are transshipped to meet residual demands, and an additional profit is allocated. Our model is an extension of the two-stage model of Anupindi et al. (ABZ) (2001), which implicitly assumes that all residuals enter the transshipment stage. We show, however, that allocation rules in the third stage based on dual solutions, which were used in the ABZ model, may induce the retailers to hold back some of their residual supply/demand. In general, we study the effect of implementing various allocations rules in the third stage on the values of the residual supply/demand the retailers are willing to share with others in the second stage, and the trade-off involved in achieving an optimal solution for the corresponding centralized system.

We analyze the effect of price and order postponement in a decentralized newsvendor model with multiplicative and price-dependent demand, wherein the manufacturer sets the wholesale price, and possibly offers a buyback rate, and the retailer determines the order quantity and retail price. Such postponement strategies can be used by the retailer by delaying his operational decisions (order quantity and retail price) until after demand uncertainty is observed. We show how the equilibrium values of the contract parameters and profits are affected by (i) vertical competition, (ii) type of contract (wholesale price-only or buyback), (iii) demand distribution, (iv) form of the expected demand function, and (v) the timing of the retailer's operational decisions. Although in most cases postponement is quite beneficial for the channel members, we show that for some model parameters, due to vertical competition, the expected value of perfect information about demand for price postponement and order postponement may be negative for the channel and even, surprisingly, for both members. We also show that when a buyback option is offered, neither order postponement nor price postponement has an effect on the equilibrium wholesale price, profit allocation ratio between the manufacturer and the retailer, and channel efficiency, and that the equilibrium wholesale price, expected retail price, profit allocation ratio between the manufacturer and the retailer, and channel efficiency in the model with buyback options under either order or price postponement further coincide with their counterparts in the corresponding deterministic model.

In this paper, we study a decentralized assembly system consisting of a single assembler who buys complementary components from independent suppliers under two contracting schemes: push and pull. In both schemes, the component suppliers are allowed to freely form coalitions (or alliances) among themselves to better coordinate their pricing or production decisions. We show that the sole driver of the inefficiency in a push system, which is due to horizontal decentralization of suppliers, is the number of alliances that were formed. Specifically, it is shown that in a push system, the assembler's profit, the total profit of all suppliers and the consumers' surplus are all decreasing in the number of coalitions, and are thus maximized when the grand coalition is formed. We further carry out a stability analysis of coalition structures to verify to what extent suppliers can reduce or eliminate the inefficiency due to their decentralization by forming alliances. We show that in a push system with more than two suppliers and a power demand distribution, myopic suppliers would act independently, resulting with a least efficient channel, which makes all channel members, as well as the end consumers, worse off. On the other hand, we prove that farsighted suppliers would form the grand coalition and thus be able to completely eliminate the inefficiency stemming from their decentralization. Finally, it is shown that, in contrast to a push system, in a pull system the suppliers can easily coordinate their production quantities to eliminate the inefficiency due to their decentralization.alliance formation, newsvendor model, stable coalitions, push and pull models

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