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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ItemCapacity Games with Supply Function Competition(Institute for Operations Research and Management Sciences, 2021-10-17)We introduce a general model for suppliers competing for a buyer's procurement business. The buyer faces uncertain demand and there is a requirement to reserve capacity in advance of knowing the demand. Each supplier has costs that are two dimensional, with some capacity costs incurred prior to production and some production costs incurred at the time of delivery. These costs are general functions of quantity and this naturally leads us to a supply function competition framework in which each supplier offers a schedule of prices and quantities. We show that there is an equilibrium of a particular form: the buyer makes a reservation choice that maximizes the overall supply chain profit, each supplier makes a profit equal to their marginal contribution to the supply chain, and the buyer takes the remaining profit. This is a natural equilibrium for the suppliers to coordinate on since no supplier can do better in any other equilibrium. These results make use of a submodularity property for the supply chain optimal profits as a function of the suppliers available and build on the assumption that the buyer breaks a tie to favor the solution that gives the largest supply chain profit. We demonstrate the applications of our model in three operations management problems: a newsvendor problem with unreliable suppliers, a portfolio procurement problem with supply options and a spot market, and a bundling problem with non-substitutable products.
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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.
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ItemAchieving Efficiency in Capacity Procurement(Now Publishers, 2020-10-01)This chapter studies a capacity procurement problem in which a buyer meets an uncertain demand using a combination of spot purchases and supply options that are offered by a number of competing suppliers. The specific setting we consider involves the suppliers each owning a block of capacity and the buyer restricted to reserving the entire block or none. For this setting, we are interested in understanding the buyer’s optimal procurement strategy and the suppliers’ competitive bidding behavior in the supply option market. To this end, we first examine the buyer’s optimal decision given a set of supply options, and then study the suppliers’ optimal bidding strategies in equilibrium. We find that it is optimal for suppliers to set execution price at cost and hence make a profit only through the reservation payment. We also prove that when all the blocks have the same size the buyer’s optimal profit as a function of supplier set is submodular. This property allows us to characterize an equilibrium in which the supply chain optimum is achieved, each supplier makes a profit equal to their marginal contribution to the supply chain and the buyer takes the remaining profit. When the blocks have different sizes, we develop a recursive procedure to characterize a class of equilibria in which the supply chain efficiency is achieved.
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ItemCapacity Investment in a New Production Location(WILEY, 2021-12)ABSTRACT Firms proactively search for low‐cost production locations to enjoy cost‐based advantages. In this article, we develop a two‐stage stochastic program to study a firm's capacity investment and production decisions about the exploration of new production locations. In the first stage, the firm determines how much capacity to build at the new location, and in the second stage, after the product demand and the production cost at the new location have been observed, the firm determines the optimal production quantities. We first characterize the firm's optimal decisions and then examine how the optimal capacity level and firm profit are affected by the key parameters. We find that the firm may be better off when either the production cost or the demand is more variable. Using numerical analyses, we also investigate the value of retaining the existing location, and our results demonstrate that retaining the existing location obtains the highest value when the market size is large, the consumers are insensitive to price, the market demand is highly uncertain, or the variability of the production cost at the new location is either sufficiently high or sufficiently low. Finally, we extend our baseline setting in two directions: one in which the firm makes the production decision prior to demand realization, and the other in which there is a finite capacity at the existing location. For both extensions, we demonstrate the robustness of the results obtained for the baseline setting.
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ItemResponsible Sourcing under Asymmetric Information: Price Signaling versus Supplier Disclosure(Wiley, 2020-10-01)Given the growth in socially conscious consumption, firms are increasingly concerned with sourcing from responsible suppliers. However, a firm’s sourcing decisions are not always apparent to consumers. Therefore, we investigate two mechanisms, signaling and disclosure, which a firm can use to communicate its sourcing decisions to consumers in a setting where only some consumers care about the firm’s sourcing practices. We develop a supplier selection model with an embedded game in which the firm signals its supplier choice through price. Then, motivated by the observation that some firms have begun to disclose their supplier information, we consider a model in which the firm may voluntarily disclose information, but at a cost. We find that, under signaling alone, a firm which sources from a more responsible supplier may distort its price upward to signal its responsible sourcing. This leads to reduced profit, implying that the firm may have an incentive to source from a less responsible supplier. However, if supplier disclosure is an option, the firm will choose to source responsibly if the disclosure cost is small and the proportion of socially conscious consumers is large. Our findings highlight the importance of transparency and socially conscious consumption in driving responsible sourcing.
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ItemSourcing Competition under Cost Uncertainty and Information Asymmetry(Wiley, 2020-02-01)Driven by increasing costs in the traditionally regarded low‐cost manufacturing bases (e.g., China), many firms have started to outsource their production to the regions of even lower costs (e.g., Southeast Asia). However, a new environment may involve higher cost uncertainty and severer information asymmetry. Motivated by these observations, we consider a sourcing game where competing firms choose between a supplier with transparent certain cost (type‐C supplier) and a supplier with potentially lower but less transparent, uncertain cost (type‐U supplier). We characterize the equilibrium of the sourcing game and study how different parameters affect the firms’ sourcing strategy and profit performance. First, we find that due to information asymmetry, a large market size can make firms prefer the C‐supplier to the U‐supplier even if the latter has a lower average cost. Second, reducing the cost uncertainty or improving the signal accuracy of the U‐supplier does not necessarily make it more attractive to sourcing firms, which cautions the suppliers when making efforts to mitigate cost uncertainty or improve cost estimation. Third, higher competition intensity makes the diversified sourcing strategy more likely to be adopted under certain conditions. Interestingly, increasing the cost of the C‐supplier (e.g., a cost hike in China) may make both sourcing firms better off because it can lead to a new sourcing equilibrium. Finally, this study shows that the direction of quantity distortion under the optimal competitive mechanism differs from that under the traditional monopolistic setting.