Supply Chain Contracting Under Competition: Bilateral Bargaining vs. Stackelberg

We analyze contracting behaviors in a two‐tier supply chain system consisting of competing manufacturers and competing retailers. We contrast the contracting outcome of a Stackelberg game, in which the manufacturers offer take‐it‐or‐leave‐it contracts to the retailers, with that of a bargaining game, in which the firms bilaterally negotiate contract terms via a process of alternating offers. The manufacturers in the Stackelberg game possess a Stackelberg‐leader advantage in that the retailers are not entitled to make counteroffers. Our analysis suggests that whether this advantage would benefit the manufacturers depends on the contractual form. With simple contracts such as wholesale‐price contracts, which generally do not allow one party to fully extract the trade surplus, the Stackelberg game replicates the boundary case of the bargaining game with the manufacturers possessing all the bargaining power. In contrast, with sophisticated contracts such as two‐part tariffs, which enable full surplus extraction, the two games lead to distinct outcomes. We further show that the game structure being Stackelberg or bargaining critically affects firms' preferences over contract types and thus their equilibrium contract choices. These observations suggest that the Stackelberg game may not be a sufficient device to predict contracting behaviors in reality where bargaining is commonly observed.     

The Comparison of Two Vertical Outsourcing Structures under Push and Pull Contracts

In a three‐tier supply chain comprising an original equipment manufacturer (OEM), a contract manufacturer (CM), and a supplier, there exist two typical outsourcing structures: control and delegation. Under the control structure, the OEM contracts with the CM and the supplier respectively. Under the delegation structure, the OEM contracts with the CM only and the CM subcontracts with the supplier. We compare the two outsourcing structures under a push contract (whereby orders are placed before demand is realized) and a pull contract (whereby orders are placed after demand is realized). For all combinations of outsourcing structures and contracts, we derive the corresponding equilibrium wholesale prices, order quantities, and capacities. We find that the equilibrium production quantity is higher under control than under delegation for the push contract whereas the reverse holds for the pull contract. Both the OEM and the CM prefer control over delegation under the push contract. However, under the pull contract, the OEM prefers control over delegation whereas the CM and the supplier prefer delegation over control. We also show that for a given outsourcing structure, the OEM prefers the pull contract over the push contract. In extending our settings to a general two‐wholesale‐price (TWP) contract, we find that when wholesale prices are endogenized decision variables, the TWP contract under our setting degenerates to either a push or a pull contract.     

On the Advantage of Quantity Leadership When Outsourcing Production to a Competitive Contract Manufacturer

This study investigates a supply chain comprising an original equipment manufacturer (OEM) and a contract manufacturer (CM), in which the CM acts as both upstream partner and downstream competitor to the OEM. The two parties can engage in one of three Cournot competition games: a simultaneous game, a sequential game with the OEM as the Stackelberg leader, and a sequential game with the CM as the Stackelberg leader. On the basis of these three basic games, this study investigates the two parties' Stackelberg leadership/followership decisions. When the outsourcing quantity and wholesale price are exogenously given, either party may prefer Stackelberg leadership or followership. For example, when the wholesale price or the proportion of production outsourced to the CM is lower than a threshold value, both parties prefer Stackelberg leadership and, consequently, play a simultaneous game in the consumer market. When the outsourcing quantity and wholesale price are decision variables, the competitive CM sets a wholesale price sufficiently low to allow both parties to coexist in the market, and the OEM outsources its entire production to this CM. This study also examines the impact of the supply chain parties' bargaining power on contract outcomes by considering a wholesale price that is determined via the generalized Nash bargaining scheme, finding a Stackelberg equilibrium to be sustained when the CM's degree of bargaining power is great and the non‐competitive CM's wholesale price is high.     

The Impact of Contracts and Competition on Upstream Innovation in a Supply Chain

We consider a supply chain with an upstream supplier who invests in innovation and a downstream manufacturer who sells to consumers. We study the impact of supply chain contracts with endogenous upstream innovation, focusing on three different contract scenarios: (i) a wholesale price contract, (ii) a quality‐dependent wholesale price contract, and (iii) a revenue‐sharing contract. We confirm that the revenue‐sharing contract can coordinate supply chain decisions including the innovation investment, whereas the other two contracts may result in underinvestment in innovation. However, the downstream manufacturer does not always prefer the revenue‐sharing contract; the manufacturer's profit can be higher with a quality‐dependent wholesale price contract than with a revenue‐sharing contract, specifically when the upstream supplier's innovation cost is low. We then extend our model to incorporate upstream competition between suppliers. By inviting upstream competition, with the wholesale price contract, the manufacturer can increase his profit substantially. Furthermore, under upstream competition, the revenue‐sharing contract coordinates the supply chain, and results in an optimal contract form for the manufacturer when suppliers are symmetric. We also analyze the case of complementary components suppliers, and show that most of our results are robust.     

力量不对等供应链中不同定价权下的契约选择

寄存契约为供应商管理库存运营模式中的一种,零售商偏好寄存契约从而把库存风险转移给供应商,而供应商则偏好传统模式从而不需承担库存风险.从批发价格的定价权出发,探讨力量不对等供应链中成员偏好某种契约的务件.分析在力量不对等的供应链中,当批发价格为外生批发价格,即批发价格由外部市场决定时,供应链中成员在传统模式和寄存契约下的决策问题,并分析外生批发价格的大小如何影响供应链中成员的契约选择;当批发价格为内生批发价格,即批发价格由供应链中强势方(零售商或供应商)决定时,分别分析供应链中成员在传统模式和寄存契约下的决策问题,并横向分析不同力量对比度的供应链中,供应链成员如何选择契约和供应链的最终运行模式,从而为供应链成员的运营模式选择提供一定的科学指导.     

供应链中具有产能限制的竞争企业中的信息共享研究

本文研究由一个供货商和两个制造商组成的二级供应链中，制造商之间的横向信息共享策略和供应商的定价问题。在模型中，上游供应商同时为下游两家制造商提供价格相同的原材料，下游制造商生产具有替代性的商品进行数量竞争，并受到相同的产能限制。以Cournot博弈为研究手段，求解了制造商的均衡订货决策和信息共享策略，分析比较了在不同的信息共享策略下制造商的利润、供应商的利润和批发价格。本文在研究制造商的信息共享策略时考虑了上游供应商的批发价格的影响。研究表明，当均衡解受到产能约束时，制造商的信息共享策略会反向。在某些情况下，完全信息共享和完全信息不共享都可能成为博弈的占优策略。上游供应商通过调整批发价格可以影响制造商的信息共享决策。该模型为上游供应商提供了一种最优定价策略，也为下游制造商提供了求解自身最优订货量和信息共享决策的方法。     

Supplier competition and its impact on firm׳s sourcing strategy

Most research on firms׳ sourcing strategies assumes that wholesale prices and reliability of suppliers are exogenous. It is of our interest to study suppliers׳ competition on both wholesale price and reliability and firms׳ corresponding optimal sourcing strategy under complete information. In particular, we study a problem in which a firm procures a single product from two suppliers, taking into account suppliers׳ price and reliability differences. This motivates the suppliers to compete on these two factors. We investigate the equilibria of this supplier game and the firm׳s corresponding sourcing decisions. Our study shows that suppliers׳ reliability often plays a more important role than wholesale price in supplier competition and that maintaining high reliability and a high wholesale price is the ideal strategy for suppliers if multiple options exist. The conventional wisdom implies that low supply reliability and high demand uncertainty motivate dual-sourcing. We notice that when the suppliers׳ shared market/transportation network is often disrupted and demand uncertainty is high, suppliers׳ competition on both price and reliability may render the sole-sourcing strategy to be optimal in some cases that depend on the format of suppliers׳ cost functions. Moreover, numerical study shows that when the cost or vulnerability (to market disruptions) of one supplier increases, its profit and that of the firm may not necessarily decrease under supplier competition.     

Manufacturer–Retailer Negotiations in the Presence of an Oligopolistic Input Market

When a manufacturer relies solely on its own inputs in making products, the focus of negotiations between the manufacturer and retailer is exclusively on profits in the output (retail) market. In such cases, absent retail competition concerns, standard two‐part tariff negotiations set the per‐unit wholesale price equal to marginal cost, and require fixed transfers from the retailer to the manufacturer. In this article, we recognize that manufacturers often rely on imperfectly competitive markets for at least some inputs. Incorporating this seemingly natural feature has profound implications for manufacturer–retailer negotiations since it shifts their focus from being exclusively on output markets to one that balances strategic concerns in both input and output realms. The article's main result is that the added need to discipline input prices can lead the manufacturer and retailer to write contingent contracts that are cost‐plus and prescribe lump‐sum slotting allowances (i.e., fixed transfer from the manufacturer to the retailer).     

Strategic Outsourcing Decisions for Manufacturers that Produce Partially Substitutable Products in a Quantity‐Setting Duopoly Situation*

This article examines production and outsourcing decisions for two manufacturers that produce partially substitutable products and play a strategic game with quantity competition. When both manufacturers outsource key components to the same upstream supplier, their products become more substitutable due to the increased commonality of the products. In addition, outsourcing may create better consumer perception about the product if the manufacturers choose reputable suppliers with better brand or quality. We explicitly model the substitutability change and the brand/quality effect and provide conditions under which the manufacturers should outsource the components to a supplier. We present the subgame perfect Nash equilibriums for the situation in which there is only one supplier and the case in which two suppliers compete with each other in the upstream supply chain. Numerical examples are presented to illustrate the findings.     

Competition and Coordination in a Two‐Channel Supply Chain

We study competition and coordination in a supply chain in which a single supplier both operates a direct channel and sells its product through multiple differentiated retailers. We study analytically the supply chain with symmetric retailers and find that the supplier prefers to have as many retailers as possible in the market, even if the retailers' equilibrium retail price is lower than that of the supplier, and even if the number of retailers and their cost or market advantage prevent sales through the direct channel. We find that the two‐channel supply chain may be subject to inefficiencies not present in the single‐channel supply chain. We show that several contracts known to coordinate a single‐channel supply chain do not coordinate the two‐channel supply chain; thus we propose a linear quantity discount contract and demonstrate its ability to perfectly coordinate the two‐channel supply chain with symmetric retailers. We provide some analytical results for the supply chain with asymmetric retailers and propose an efficient solution approach for finding the equilibrium. We find numerically that the supplier still benefits from having more retailers in the market and that linear quantity discount contracts can mitigate supply chain inefficiency, though they no longer achieve perfect coordination.     

Supply Chain Coordination in the Presence of Gray Markets and Strategic Consumers

The practice of diverting genuine products to unauthorized gray markets continues to challenge companies in various industries and creates intense competition for authorized channels. Recent industry surveys report that the abuse of channel incentives is a primary reason for the growth of gray market activities. Therefore, it is crucial that companies take the presence of gray markets into consideration when they design contracts to distribute products through authorized retailers. This issue has received little attention in the extensive literature on contracting and supply chain coordination. In this study, we analyze the impacts of gray markets on two classic contracts, wholesale price and quantity discount, in a supply chain with one manufacturer and one retailer when the retailer has the opportunity to sell to a domestic gray market. Our analysis provides interesting and counterintuitive results. First, a classic quantity‐discount contract that normally coordinates the supply chain can perform so poorly in the presence of a gray market that the supply chain would be better off using a wholesale price contract instead. Second, the presence of gray market can also degrade the performance of the wholesale price contract; therefore, a more sophisticated contract is needed for coordinating the supply chain. We show that contracts that solely depend on retailer's order quantity cannot coordinate the supply chain, and provide the conditions for coordinating the supply chain with price‐dependent quantity discount contracts. We also provide comparative statics and show that when there is a gray market, coordinating the supply chain enhances total consumer welfare.     

Stable and Coordinating Contracts for a Supply Chain with Multiple Risk‐Averse Suppliers

We analyze a decentralized supply chain with a single risk‐averse retailer and multiple risk‐averse suppliers under a Conditional Value at Risk objective. We define coordinating contracts and show that the supply chain is coordinated only when the least risk‐averse agent bears the entire risk and the lowest‐cost supplier handles all production. However, due to competition, not all coordinating contracts are stable. Thus, we introduce the notion of contract core, which reflects the agents' “bargaining power” and restricts the set of coordinating contracts to a subset which is “credible.” We also study the concept of contract equilibrium, which helps to characterize contracts that are immune to opportunistic renegotiation. We show that, the concept of contract core imposes conditions on the share of profit among different agents, while the concept of contract equilibrium provide conditions on how the payment changes with the order quantity.     

Role of Random Capacity Risk and the Retailer in Decentralized Supply Chains with Competing Suppliers

This research considers a supply chain under the following conditions: (i) two heterogeneous suppliers are in competition, (ii) supply capacity is random and pricing is endogenous, (iii) consumer demand, with and without an intermediate retailer, is price dependent. Specifically, we examine how uncertainty in supply capacity affects optimal ordering and pricing decisions, supplier and retailer profits, and the incentives to reduce such uncertainty. When two suppliers sell through a monopolistic retailer, supply uncertainty not only affects the retailer's diversification strategy for replenishment, but also changes the suppliers’ wholesale price competition and the incentive for reducing capacity uncertainty. In this dual‐sourcing model, we show that the benefit of reducing capacity uncertainty depends on the cost heterogeneity between the suppliers. In addition, we show that a supplier does not necessarily benefit from capacity variability reduction. We contrast this incentive misalignment with findings from the single‐supplier case and a supplier‐duopoly case where both suppliers sell directly to market without the monopolistic retailer. In the latter single‐supplier and duopoly cases, we prove that the unreliable supplier always benefits from reducing capacity variability. These results highlight the role of the retailer's diversification strategy in distorting a supplier's incentive for reducing capacity uncertainty under supplier price competition.     

The Effect of Learning and Integration Investment on Manufacturing Outsourcing Decisions: A Game Theoretic Approach

We introduce a two‐period Stackelberg game of a supplier and buyer. We recognize that learning from manufacturing experience has many advantages. Consistent with the literature, we assume both the buyer and supplier realize reductions in their respective production costs in period 2 due to volume‐based learning from period 1 production. In addition, we introduce another learning concept, the future value, to capture the buyer's benefits of transferring current manufacturing experience for the design and development of future products and technologies. In contrast to the literature, we allow the supplier two mechanisms to impact the buyer's outsourcing decision: price and the investment in integration process improvement (IPI) that reduces the buyer's unit cost of integration. IPI may include the investment in new materials, specialized technology, or the re‐design of the integration process. Conditions are given whereby the buyer partially outsources component demand as opposed to fully outsourcing or fully producing in‐house. Furthermore, conditions are given characterizing when the supplier's price and investment in IPI are substitute strategies versus complements. Both analytic and numerical results are presented.     

Requirement or Promise? An Analysis of the First‐Mover Advantage in Quality Contracting

Quality contracting is critical and challenging due to the many unique issues related to quality. In this study, we analyze the first‐mover right in quality contracting by considering two different strategies for the buyer: the quality requirement strategy (QR) where buyer moves first by posting quality requirement to suppliers and quality promise strategy (QP) where buyer voluntarily gives up the first‐mover right to suppliers to ask them to promise quality. We study which strategy (1) better encourages suppliers' quality improvement efforts and (2) leads to a higher expected profit for the buyer. To analyze the drivers behind the buyer's choice between QR and QP, we start with the basic model where buyer faces only one supplier who has the opportunity to make quality improvements. We then gradually add other business features such as information asymmetry and supplier competition, analyzing how each feature adds/changes the driving forces and how they interact in the buyer's decision between QR and QP. We consider both the case where the wholesale price is fixed (when the buyer has the power to dictate price or price is set by the market) and the case where the wholesale price is included as a variable (when price is part of the negotiation). We find that QP always leads to the first‐best quality efforts from the supplier(s) while QR limits their efforts. However, this does not guarantee higher expected profit for the buyer under QP. We provide insightful guidelines in buyer's choice between QP and QR. This research enriches the limited literature on quality contracting with quality improvement opportunity and asymmetric information.     

Complexity as a Contract Design Factor: A Human‐to‐Human Experimental Study

Despite being theoretically suboptimal, simpler contracts (such as price‐only contracts and quantity discount contracts with limited number of price blocks) are commonly preferred in practice. Thus, exploring the tension between theory and practice regarding complexity and performance in contract design is especially relevant. Using human subject experiments, Kalkancı et al. (2011) showed that such simpler contracts perform effectively for a supplier interacting with a computerized buyer under asymmetric demand information. We use a similar set of experiments with the modification that a human supplier interacts with a human buyer. We show that human interactions strengthen the supplier's preference for simpler contracts. We find that suppliers have fairness concerns even when they interact with computerized buyers. These fairness concerns tend to be even stronger when suppliers interact with human buyers, particularly when the complexity of the contract is low. We also find that suppliers are more prone to random decision errors (i.e., bounded rationality) when interacting with human buyers. In the absence of social preferences, Kalkancı et al. identified reinforcement and bounded rationality as key biases that impact suppliers' decisions. In human‐to‐human experiments, we find evidence for social preference effects. However, these effects may be secondary to bounded rationality.     

Coordination in a Single‐Supplier,Multi‐Retailer Distribution System: Supplier‐Facilitated Transshipments

We consider supplier‐facilitated transshipments for achieving supply chain coordination in a single supplier, multi‐retailer distribution system with non‐cooperative retailers. The previous transshipment literature has focused on coordination through retailer‐negotiated transshipments and thus does not consider the supplier's decision‐making. In contrast, in this study, we assume the supplier is an active participant in the system and we seek to understand how the supplier can facilitate the implementation of coordinating transshipments. We study a two‐period model with wholesale orders at the start of the first period and preventive transshipments performed at the start of the second period. Inspired by a supplier‐facilitated transshipment scheme observed in practice, we assume the supplier implements transshipments through a bi‐directional adjustment contract. Under this contract, each retailer can either buy additional inventory from, or sell back excess inventory to, the supplier. We show that coordination can be achieved through carefully designed contracts with state‐dependent adjustment prices and a wholesale price menu. We demonstrate that the supplier's role in facilitating coordinating transshipments is critical. In addition, we use our understanding of the coordinating contract form to derive some simpler and easier‐to‐implement heuristic contracts. We use a numerical study to demonstrate the value, to the supplier, of using the coordinating adjustment and wholesale prices, and to evaluate the heuristics’ performance.     

The Impact of Manufacturers' Wholesale Prices on a Retailer's Shelf‐Space and Pricing Decisions*

This article examines shelf‐space allocation and pricing decisions in the marketing channel as the results of a static game played à la Stackelberg between two manufacturers of competing brands and one retailer. The competing manufacturers act as leaders that play a simultaneous and noncooperative game. They fix their transfer prices by taking into account the shelf‐space allocation and price‐markup decisions of their common exclusive dealer. The results indicate that the wholesale prices of brands are strongly linked to their share of the shelf. The main results of our numerical simulations may be summarized as follows: first, the lower the unit cost and/or the greater the price elasticity, the greater the shelf space allocated to that brand. Second, the higher the shelf‐space elasticity, the lower are the wholesale prices and the profits of all channel members.     

Supply Diversification with Responsive Pricing

We study sourcing and pricing decisions of a firm with correlated suppliers and a price‐dependent demand. With two suppliers, the insight—cost is the order qualifier while reliability is the order winner—derived in the literature for the case of exogenously determined price and independent suppliers, continues to hold when the suppliers' capacities are correlated. Moreover, a firm orders only from one supplier if the effective purchase cost from him, which includes the imputed cost of his unreliability, is lower than the wholesale price charged by his rival. Otherwise, the firm orders from both. Furthermore, the firm's diversification decision does not depend on the correlation between the two suppliers' random capacities. However, its order quantities do depend on the capacity correlation, and, if the firm's objective function is unimodal, the total order quantity decreases as the capacity correlation increases in the sense of the supermodular order. With more than two suppliers, the insight no longer holds. That is, when ordering from two or more suppliers, one is the lowest‐cost supplier and the others are not selected on the basis of their costs. We conclude the paper by developing a solution algorithm for the firm's optimal diversification problem.     

Benchmark Schedules for Subcontracted Operations: Decentralization Inefficiencies that Arise from Competition and First‐Come‐First‐Served Processing*

Subcontracting has become a prominent business practice across many industries. Subcontracting of industrial production is generally based on short‐term need for additional processing capacity, and is frequently employed by manufacturers to process customer orders more quickly than using only in‐house production. In this article, we study a popular business model where multiple manufacturers, each capable of processing his entire workload in‐house, have the option to subcontract some of their operations to a single third party with a flexible resource. Each manufacturer can deliver customer orders only after his entire batch of jobs, processed in‐house and at the third party, is completed. The third party facility is available to several manufacturers who compete for its use. Current business practice of First‐Come‐First‐Served (FCFS) processing of the subcontracted workloads as well as the competitive Nash equilibrium schedules developed in earlier studies result in two types of inefficiencies; the third party capacity is not maximally utilized, and the manufacturers incur decentralization cost. In this article, we develop models to assess the value created by coordinating the manufacturers' subcontracting decisions by comparing two types of centralized control against FCFS and Nash equilibrium schedules. We present optimal and/or approximate algorithms to quantify the third party underutilization and the manufacturers' decentralization cost. We find that both inefficiencies are more severe with competition than they are when the third party allocates capacity in an FCFS manner. However, in a decentralized setting, a larger percentage of the players prefer Nash equilibrium schedules to FCFS schedules. We extend our analysis to incomplete information scenarios where manufacturers reveal limited demand information, and find that more information dramatically benefits the third party and the manufacturers, however, the marginal benefit of additional information is decreasing. Finally, we discuss an extension wherein each manufacturer's objective takes into account asymmetries in subcontracting, in‐house processing, and delay costs.