Management and Marketing - Research Publications
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ItemCompetitive Multiproduct Contracting Under Multinomial Logit Demand(Wiley, 2022-08-23)Despite the prevalence of multiproduct firms in many industries, the supply chain contracting literature has predominantly focused on problems where an upstream player offers only one product. This paper studies multiproduct contract design for competing manufacturers each with several products to sell via a common retailer. We consider two contracting schemes under multinomial logit demand (MNL): individual contracting, in which the manufacturers set a wholesale price for each of their products separately; and aggregate contracting, in which the manufacturers set the price as a function of the order quantities for their own products. We find that under individual contracting it is optimal for each manufacturer to offer the full range of his products to the retailer and set an equal wholesale margin for these products. This suggests that the classic result of an equal-margin policy for the retailer also holds true for the manufacturers. Further, there is an equilibrium characterized by a system of nonlinear equations that can be solved using the standard bisection search method. Under aggregate contracting, a simple cost-plus contract is optimal for the manufacturers. In equilibrium, each manufacturer charges a markup equal to his marginal contribution to the supply chain, and the supply chain profit is maximized. Comparing these two contracting schemes, we find among other results that the retailer prefers aggregate contracting when there is a large number of products from each manufacturer or when consumer heterogeneity is low, while the opposite is true for the manufacturers. In addition, both the retailer and the manufacturers prefer aggregate contracting when there are few manufacturers in the supply chain. It is also found that as the number of manufacturers or the number of products from each manufacturer increases, the supply chain efficiency loss induced by individual contracting is reduced. Finally, we extend our model to a hybrid setting in which one manufacturer adopts aggregate contracting and the other adopts individual contracting, and demonstrate to the manufacturers the value of aggregate contracting. These results provide useful guidance on optimal contract design for multiproduct firms.
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ItemA Capacity Reservation Game for Suppliers with Multiple Blocks of Capacity(Elsevier, 2022-09-01)This paper studies a supplier competition model in which a buyer reserves capacity from a number of suppliers that each have multiple blocks of capacity (e.g., production or power plants). The suppliers each submit a bid that specifies a reservation price and an execution price for every block, and the buyer determines what blocks to reserve. This game involves both external competition between suppliers and internal competition between blocks from each supplier. We characterize the properties of pure-strategy Nash equilibria for the game. Such equilibria may not always exist, and we provide the conditions under which they do.
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ItemCompetitive Trading in Forward and Spot Markets Under Yield Uncertainty(Wiley, 2022)Many agricultural commodities are traded in both forward and spot markets. This paper studies the interplay of random yield and forward market in a hybrid market with spot and forward transactions. We examine two main questions: (a) How does yield uncertainty (yield risk and yield correlation) affect the equilibrium outcome in this hybrid market? (b) How does the existence of a forward market influence the firms' strategic behaviors and spot price volatility, and how does yield uncertainty mediate the role of the forward market? In our baseline model that considers two firms and no withholding behavior by the firms, it is found that as yield risk increases, firms may sell less in the forward market, and counterintuitively, higher yield risk may benefit firms and make the spot price less volatile. The existence of a forward market leads to greater spot price volatility; that is, a forward market destabilizes spot price. We identify a mitigating effect of yield variability, but an enhancing effect of yield correlation, on the role of the forward market. Finally, we extend our baseline model to the case with more than two firms and the setting where the firms may withhold some products, and demonstrate that some of the key results in the baseline model carry over to these extensions. Nevertheless, the firms' withholding behavior represents a new driving force that changes some results. For example, the decreasing trend of spot price volatility in yield risk disappears in the withholding model.
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ItemContracting Mechanisms for Stable Sourcing Networks(INFORMS, 2022-09-01)Problem definition: We study profit allocation for a sourcing network, in which a buyer sources from a set of differentiated suppliers with limited capacity under uncertain demand for the final product. Whereas the buyer takes the lead in forming the sourcing network and designing the contract mechanism, due to their substantial bargaining power, the suppliers take the lead in determining the terms of the contract. Academic/practical relevance: We identify contracting mechanisms that will ensure the stability of the sourcing network in the long term, where a stable sourcing network requires an effective profit-allocation scheme that motivates all members to join and stay in the network. Methodology: We apply methods from game theory to model the network and analyze the Nash equilibrium of a noncooperative game under a proposed contracting mechanism. We then use a cooperative game model to study the stability of the resulting equilibrium. Results: We show that the optimal network profit, as a set function of the set of suppliers, is submodular, which allows us to demonstrate that the core of the cooperative game is not empty. We also establish a set of conditions that are equivalent to, but much simpler than, the original conditions for the core. We use these results to demonstrate that the proposed fixed-fee contracting mechanism can implement a stable network in the competitive setting by achieving a profit allocation that is in the core of the cooperative game. We also demonstrate that the grand coalition is stable in a farsighted sense under the Shapley value allocation. Managerial implications: Under the fixed-fee mechanism, the buyer’s decisions maximize the network profit, and each supplier earns a profit equal to its marginal contribution. When the aggregate capacity of the supplier network is high relative to demand, or demand is more likely to be small, the fixed-fee mechanism is likely to outperform the Shapley value allocation from the perspective of the buyer.
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ItemService-Level Agreement with Dynamic Inventory Policy: The Effect of the Performance Review Period and the Incentive Structure(WILEY, 2022-10-01)ABSTRACT Performance measures are often outlined in the section of the service‐level agreement (SLA) of the contract between a supplier and a retailer. They are monitored periodically, and penalty and/or bonus payments are imposed in each performance review period, according to the SLA clauses. Previous studies have mostly considered a static inventory policy in analyzing SLAs. However, in practice, the supplier may have an opportunity to adjust the stock level in each inventory review period, according to the observed performance. This study analyzes the dynamic stocking decision for a supplier facing an SLA where the supplier sells a single product to the retailer. The ready rate is used to measure the performance in an SLA. To this end, models for both lump‐sum and linear penalty/bonus structures are developed, and the optimal stocking decisions for a strategic supplier are calculated using the stochastic dynamic programming approach. The results are then compared with the optimal static inventory policy, and new insights are derived to efficiently design an inventory system for the suppliers that are subject to service‐level incentives. In addition, we investigate the impact of SLA parameters—such as the length of the performance review period and incentive structures—on a supplier's performance, with the probability of meeting or exceeding the target service levels and the supplier's cost. We also consider the impact of demand distribution and inventory holding costs. Results show that under lump‐sum incentives, a longer performance review period benefits both the supplier and the buyer, given that the average ready rate increases with less variability as the length of the performance review period increases, leading to decrements in the supplier's total costs. In this scenario, there is a higher chance of gaining bonuses/avoiding penalties for a strategic supplier who adopts a dynamic inventory policy. On the other hand, under linear incentives, the impact of the performance review period on the supplier's cost and the performance measure (i.e., ready rate) is complicated and depends on the magnitude of the holding cost and the bonus and/or penalty structure of the contract. Under this scheme, the performance of a static inventory policy is highly dependent on the holding cost because a high holding cost may lead to failure to meet the contract requirements in terms of the service level.