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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.

The author considers a model of a decentralized distribution system consisting of n retailers selling an identical product. Retailers face a stochastic demand and must order their initial inventory before this demand is realized. After demand realization, retailers decide how much of their unsold inventory or unsatisfied demand they want to share with other retailers. This is followed by a transshipment of leftover inventories and distribution of the additional profit generated through inventory sharing. The author addresses the following issue: Suppose that the retailers distribute the profit from inventory sharing according to an allocation rule that induces retailers to share their residuals in a way that maximizes the additional profit, such as the Shapley value, but may not belong to the core. Is it likely that, in this framework, all retailers will jointly share their residuals and not form subcoalitions? Previous research has looked at this problem from a myopic viewpoint and concluded that the grand coalition is not stable. Unlike the prior work, the author looks at stability in a farsighted sense. That is, retailers do not consider only their immediate payoffs but are also concerned with reactions of other retailers to their actions. In a symmetric setting, with identical additional unit revenues from transshipments generated by all retailers, farsighted retailers always maximize their allocations by not defecting from the grand coalition. The author also provides conditions when the same is true for nonidentical additional unit revenues.inventory sharing, cooperation and competition, farsighted stability, coalitions

In this paper, we examine a supply chain in which a single supplier sells to a downstream retailer. We consider a multiperiod model with the following sequence of events. In period t the supplier offers a contract to the retailer, and the retailer makes her purchasing decision in anticipation of the random demand. The demand then unravels, and the retailer carries over any excess inventory to the next period (unmet demand is lost). In period t+1 the supplier designs a new contract based on his belief of the retailer's inventory, and the game is played dynamically. We assume that short-term contracts are used, i.e., the contracting is dynamically conducted at the beginning of each period. We also assume that the retailer's inventory before ordering is not observed by the supplier. This setting describes scenarios in which the downstream retailer does not share inventory/sales information with the supplier. For instance, it captures the phenomenon of retailers distorting past sales information to secure better contracting terms from their suppliers. We cast our problem as a dynamic adverse-selection problem and show that, given relatively high production and holding costs, the optimal contract can take the form of a batch-order contract, which minimizes the retailer's information advantage. We then analyze the performance of this type of contract with respect to some useful benchmarks and quantify the value of prudent contract design and the value of inventory information to the supply chain. Markovian adverse-selection models, in which the state and action in a period affect the state in the subsequent period, are recognized as theoretically challenging and are relatively less understood. We take a nontrivial step towards a better understanding of such models under short-term contracting.

In this paper, we study dynamic alliance formation among agents in competitive markets. We look at n agents selling substitutable products competing in a market. In this setting, we examine models with deterministic and stochastic demand, and we use a two-stage approach. In Stage 1, agents form alliances (coalitions), and in Stage 2, coalitions make decisions (price and inventory) and compete against one another. To analyze the stability of coalition structures in Stage 1, we use two notions from cooperative games--the largest consistent set (LCS) and the equilibrium process of coalition formation (EPCF)--which allow players to be farsighted. Thus, in forming alliances, players consider two key phenomena: First, players trade off the size of the total profit of the system versus their allocation of this total pie, and second, they weigh the possibility that an immediate beneficial defection can trigger further counter defections that in the end may prove to be worse than the status quo. In particular, one such example is that of the grand coalition--which we show to be stable in the farsighted sense--even though players benefit myopically by defecting from it. We also provide conditions under which a situation of a few lone players competing against a large coalition is stable. We examine the impact of the size of the market (n), the degree of competition, the effect of cost parameters, and the variability of the demand process on the prices, inventory levels, and structure of the market. We discuss the possible strategic implications of our results to firms in a competitive market and for new entrants.competition, farsightedness, coalitions, cooperative games

In this paper, we study dynamic supplier alliances in a decentralized assembly system. We examine a supply chain in which n suppliers sell complementary components to a downstream assembler, who faces a price-sensitive deterministic demand. We analyze alliance/coalition formation between suppliers, using a two stage approach. In Stage 1, suppliers form coalitions that each agree to sell a kit of components to the assembler. In Stage 2, coalitions make wholesale price decisions, while the assembler buys the components (kits) from the coalitions and sets the selling price of the product. Stage 2 is modeled as a competitive game, in which the primary competition is vertical (i.e., supplier coalitions compete against the downstream assembler), and the secondary competition is horizontal, in that coalitions compete against each other. Here, we consider three modes of competition-Supplier Stackelberg, Vertical Nash, and Assembler Stackelberg modelswhich correspond to different power structures in the market. In Stage 1, we analyze the stability of coalition structures. We assume that suppliers are farsighted, that is, each coalition considers the possibility that once it acts, another coalition may react, and a third coalition might in turn react, and so on. Using this framework, we predict the structure of possible supplier alliances, as a function of the power structure in the market, the number of suppliers, and the structure of the demand.

Because greenhouse-gas (GHG) emissions from the supply chains of just the 2,500 largest global corporations account for more than 20% of global emissions, rationalizing emissions in supply chains could make an important contribution toward meeting the global CO2 emission-reduction targets agreed upon in the 2015 Paris Climate Agreement. Accordingly, in this paper, we consider supply chains with joint production of GHG emissions, operating under either a carbon-tax regime, wherein a regulator levies a penalty on the emissions generated by the firms in the supply chain, or an internal carbon-pricing scheme. Supply chain leaders, such as Walmart, are assumed to be environmentally motivated to induce their suppliers to abate their emissions. We adopt a cooperative game-theory methodology to derive a footprint-balanced scheme for reapportioning the total carbon emissions amongst the firms in the supply chain. This emission responsibility-allocation scheme, which is the Shapley value of an associated cooperative game, is shown to have several desirable characteristics. In particular, (i) it is transparent and easy to compute; (ii) when the abatement-cost functions of the firms are private information, it incentivizes suppliers to exert pollution-abatement efforts that, among all footprint-balanced allocation schemes, minimize the maximum deviation from the socially optimal pollution level; and (iii) the Shapley value is the unique allocation mechanism satisfying certain contextually desirable properties. This paper was accepted by Jayashankar Swaminathan, operations management.