Allocating Capacity with Demand Competition: Fixed Factor Allocation*

We consider a supply chain consisting of a supplier and two retailers. The supplier sells a single product to the retailers, who, in turn, retail the product to customers. The supplier has limited production capacity, and the retailers compete for the supplier's capacity and are duopolists engaged in Cournot competition for their customers. When the sum of the retailers' orders exceeds the supplier's capacity, the supplier allocates his capacity according to a preannounced allocation rule. We propose a new capacity allocation rule, fixed factor allocation, which incorporates the ideas of proportional and lexicographic allocations: it prioritizes retailers as in lexicographic allocation, but guarantees only a fixed proportion of the total available capacity to the prioritized retailer. We show that (1) the fixed factor allocation rule incorporates lexicographic and proportional allocations from the perspectives of the supplier and the supply chain; (2) under fixed factor allocation, the supply chain profit is not affected by the allocation factor when it is greater than a threshold; (3) the retailers share the supply chain profit with the supplier depending on the value of the allocation factor; and (4) the fixed factor allocation coordinates the supply chain when the market size is sufficiently large. We also compare fixed factor with proportional and lexicographic allocations, respectively. Furthermore, we demonstrate how the supplier can optimize his capacity level and wholesale price under fixed factor allocation.     

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.     

Channel Strategies and Stocking Policies in Uncapacitated and Capacitated Supply Chains*

A supply chain consisting of a single supplier distributing two independent products through multiple retailers is analyzed in this paper. The supplier needs to incentivize its retailers to adopt stocking policies that are mutually advantageous and that result in the optimal level of market coverage. The focus is on determining the optimal stocking policies for retailers and the resulting distribution strategy given that the supplier has either unlimited or limited capacity. The results provide insights on the optimal distribution strategy and stocking policies for the supply chain. In general, the paper shows that it is optimal for the supplier to use an intensive distribution strategy (i.e., the products are stocked by all retailers). Selective or exclusive strategies are optimal only when retailers are risk averse, stocking synergies exist, and there are differences in demand or supply uncertainties across products. The analysis also shows that retailers hold larger stocks of a product which generates higher supplier margins but only when the supplier has unlimited capacity. If the supplier has limited capacity, then their margins have no effect on retailers' stocking decisions. Contrary to conventional wisdom, retailers hold larger stocks of a product that has less demand uncertainty as compared to one that has more demand uncertainty.     

Managing Downstream Competition via Capacity Allocation

Consider a supply chain with one supplier and multiple retailers. The supplier produces a single product and sells it to the retailers, who in turn sell the product to consumers. The supplier has limited production capacity, and the retailers are engaged in a Cournot competition at the consumer/market level. When the sum of the retailer orders exceeds the capacity, the supplier allocates her capacity according to a pre‐announced allocation mechanism. Two mechanisms are considered: proportional allocation and lexicographic allocation. An extensive study of the two allocation mechanisms shows that the lexicographic mechanism has the ability to dampen the competition at the retail level, increasing the profits for both the supplier and the supply chain.     

Impact of secondary market on consumer return policies and supply chain coordination

In this paper, we develop a unified model to study the inventory management problem of a product and the coordination of the associated supply chain consisting of a single supplier and considerably many retailers in the presence of a secondary market. Specifically, consumer returns are allowed in the initial sales. Then, we introduce a secondary market to salvage the returns and the leftovers from the initial sales. In this secondary market, a discount price will be offered to the consumers but no returns are accepted. Moreover, between the primary and the secondary market, there is an internal market where retailers can trade among themselves so that they are able to adjust their inventory levels to prepare for the sales in the secondary market. We study the retailers' and the supply chain's inventory decision in this case and highlight the impact of the secondary market on the sales as well as on the supply chain coordination contracts. We conclude that the secondary market helps us to increase the total wholesale volume. Numerical examples show that the total sales profit is also increased. However, the secondary market aggravates the incentive conflict between the retailers and the supply chain on deciding the optimal inventory levels and hence requires the supplier to offer more generous buyback or sales rebate contracts for coordination of the supply chain. Finally, we extend our analysis to more general cases and also show that our results are robust to some of the modeling assumptions.     

Decision Bias in Capacity Allocation Games with Uncertain Demand

Existing studies on capacity allocation games have demonstrated that the standard Nash theory exaggerates retailers' tendency of ordering more than they need in the situation of supply shortage. Adding to the results in the literature, our experimental study with consideration of demand uncertainty demonstrates that the standard Nash theory also exaggerates retailers' tendency of telling the truth in their ordering strategy. To account for these systematic biases, based on the quantal response equilibrium framework, we develop a behavioral model with different mental weights on the underage and overage costs to characterize a retailer's perception bias regarding a critical fractile. Based on the parameter estimates, we show that retailers perceive the critical fractile as being closer to 0.5 than it is, and the perceived critical fractile increases over time. Such empirical evidence of retailers' behavior in capacity allocation games can be valuable, for example, in the mechanism design of coordination and in improving supply chain performance.     

Pay‐Back‐Revenue‐Sharing Contract in Coordinating Supply Chains with Random Yield

We consider coordination issues in supply chains where supplier's production process is subject to random yield losses. For a simple supply chain with a single supplier and retailer facing deterministic demand, a pay back contract which has the retailer paying a discount price for the supplier's excess units can provide the right incentive for the supplier to increase his production size and achieve coordination. Building upon this result, we consider coordination issues for two other supply chains: one with competing retailers, the other with stochastic demand. When retailers compete for both demand and supply, they tend to over‐order. We show that a combination of a pay back and revenue sharing mechanism can coordinate the supply chain, with the pay back mechanism correcting the supplier's under‐producing problem and the revenue sharing mechanism correcting the retailers' over‐ordering problem. When demand is stochastic, we consider a modified pay‐back‐revenue‐sharing contract under which the retailer agrees to not only purchase the supplier's excess output (beyond the retailer's order), but also share with the supplier a portion of the revenue made from the sales of the excess output. We show that this contract, by giving the supplier additional incentives in the form of revenue share, can achieve coordination.     

The Impact of Forecast Errors on Early Order Commitment in a Supply Chain*

Supply chain partnership involves mutual commitments among participating firms. One example is early order commitment, wherein a retailer commits to purchase a fixed‐order quantity and delivery time from a supplier before the real need takes place. This paper explores the value of practicing early order commitment in the supply chain. We investigate the complex interactions between early order commitment and forecast errors by simulating a supply chain with one capacitated supplier and multiple retailers under demand uncertainty. We found that practicing early order commitment can generate significant savings in the supply chain, but the benefits are only valid within a range of order commitment periods. Different components of forecast errors have different cost implications to the supplier and the retailers. The presence of trend in the demand increases the total supply chain cost, but makes early order commitment more appealing. The more retailers sharing the same supplier, the more valuable for the supply chain to practice early order commitment. Except in cases where little capacity cushion is available, our findings are relatively consistent in the environments where cost structure, number of retailers, capacity utilization, and capacity policy are varied.     

Push and Pull Contracts in a Local Supply Chain with an Outside Market*

Wholesale price contracts are widely studied in a single supplier‐single retailer supply chain, but without considering an outside market where the supplier may sell if he gets a high enough price and the retailer may buy if the price is low enough. We fill this gap in the literature by studying push and pull contracts in a local supplier–retailer supply chain with the presence of an outside market. Taking the local supplier's maximum production capacity and the outside market barriers into account, we identify the Pareto set of the push and/or pull contracts and draw managerial implications. The main results include the following. First, the most inefficient point of the pull Pareto set cannot always be removed by considering both the push and pull contracts. Second, the supplier's production capacity plays a significant role in the presence of an outside market; it affects the supplier's negotiating power with the retailer and the coordination of the supply chain can be accomplished only with a large enough capacity. Third, the import and export barriers influence the supply chain significantly: (i) an export barrier in the local market and the supplier's production capacity influence the supplier's export strategy; (ii) a low import (resp., export) barrier in the local market can improve the local supply chain's efficiency by use of a push (resp., pull) contract; and (iii) a high import (resp., export) barrier in the local market encourages the supplier (resp., retailer) to bear more inventory risk.     

The Dynamics of Domestic Gray Markets and Its Impact on Supply Chains

Gray markets are created by unauthorized retailers selling manufacturer's branded products. Similar to international gray markets, domestic gray markets are a growing phenomenon whose impact on supply chains is not clear. We consider a supply chain with one manufacturer and several authorized retailers who face a newsvendor problem and a domestic gray market. While a gray market provides an opportunity for retailers to clear their excess inventory (inventory‐correction effect), it also can be a threat to their demand (demand‐cannibalization effect). We first characterize the emerging equilibrium by assuming an MSRP environment. Comparing a decentralized and centralized system, we show that a wholesale pricing contract is quite efficient in a gray market environment; we explain the underlying mechanism and note some of the operational decisions that could hurt that efficiency. We show that the gray market price determines the degree of both the negative effects of demand‐cannibalization and the positive effects of inventory correction, which in turn determines the net impact of gray markets on the retailer's stocking choice and, ultimately, the manufacturer's profit. We then study the authorized retailers' problem as a price‐setting newsvendor. We observe that the gray market creates price competition between the authorized and unauthorized retailers, causing a drop in the primary market price. However, this price competition can be counteracted by the authorized retailers' stocking decision. Finally, we extend our model to consider the cases where the demand can be correlated across retailers.     

Price Incentives and Coordination in a Two‐Product Decentralized Supply Chain

We investigate pricing incentives for competing retailers who distribute two variants of a manufacturer's product in a decentralized supply chain. Under a two‐dimensional Hotelling model, we derive decentralized retailers' prices for the products, and distortions in pricing when compared to centrally optimal prices. We show that price distortions decrease as consumers' travel cost between retailers increases, due to less intense competition. However, price distortions do not change monotonically in consumers' switching cost between products within stores. To fix decentralized retailers' price distortions, we construct a two‐part pricing contract that coordinates the supply chain. We show that the coordinating contract is Pareto‐improving and analyze increase in the supply chain profit under coordination.     

Discount Pricing Policies and the Coordination of Decentralized Distribution Systems*

A challenge of supply chain management is to align the objectives, and hence coordinate the activities, of independent supply chain members. In this study, we approach this problem in a simple way by extending traditional quantity discounts that are based solely on buyers' individual order size to discount policies that are based on both buyers' individual order size and their annual volume. We show that discount policies are able to achieve nearly optimal system profit and, hence, provide effective coordination, for a decentralized two‐echelon distribution system, whereby a supplier sells a product to a group of heterogeneous and independent retailers each facing a downward‐sloping demand curve of its retail price. When buyers are heterogeneous, a critical issue of coordination is to motivate different customers to increase their demand and lot size according to their potential so as to improve profits. We show that market heterogeneity presents an effective discriminating factor for the supplier to segment customers in the design of a coordination mechanism.     

VERTICAL INFORMATION EXCHANGE IN A SUPPLY CHAIN WITH DUOPOLY RETAILERS

We consider a supply chain with one manufacturer in the upstream and two competing retailers in the downstream. The retailers sell differentiated goods and are endowed with some private demand information. The paper shows that the manufacturer's optimal strategy is independent of the type of downstream competition, Cournot or Bertrand, and that no information will be shared with the manufacturer on a voluntary basis. However, complete information sharing, which benefits all three parties, can be achieved through side payment when the retailers' information is statistically less accurate or when the leakage effect is more beneficial to the retailers.     

Storage constrained vendor managed inventory models with unequal shipment frequencies

We consider a supply chain where a vendor manages its multiple retailers' stocks under a vendor managed inventory (VMI) contract that specifies upper stock limits at the retailers' premises and overstock costs for exceeding those limits. We formulate a mixed integer nonlinear program that minimizes total supply chain costs and allows unequal shipment frequencies to the retailers. We develop an algorithm to solve its relaxed version which provides a lower bound cost solution. We propose a cost efficient heuristic procedure to generate delivery schedules to the retailers. We conduct a sensitivity analysis to provide insights on the performance of the proposed heuristic. Results show that our heuristic finds optimal or near optimal solutions, and it proposes substantial savings compared to the total supply-chain cost in the cases where there is no VMI and where there is VMI but with equal shipment frequencies to retailers.     

Manufacturer's pricing strategy for supply chain with warranty period-dependent demand

This article presents a review of the issues associated with a manufacturer's pricing strategies in a two-echelon supply chain that comprises one manufacturer and two competing retailers, with warranty period-dependent demands. The manufacturer, as a Stackelberg leader, specifies wholesale prices to two competing retailers who face warranty period-dependent demand and have different sales costs. The manufacturer considers three pricing options: (1) setting the same price for both retailers, while disregarding their difference with regard to sales cost; (2) setting a different price to each retailer on the basis of their sales cost; and (3) setting the same price to both retailers according to the average sales cost of the industry. In this article, the retailers' optimal warranty periods and their optimal profit, manufacturer's optimal wholesale price, and his/her optimal profit associated with different pricing strategies have been derived using the game theory. Our analysis shows that the results for retailers are the same with Strategy 1 or Strategy 3. In addition, we compared the effects of different pricing strategies of the manufacturer on supply chain decisions and profit. We conclude from the results that the manufacturer should either adopt Strategy 2 with symmetrical sales cost information or Strategy 3 if retailers' sales costs are asymmetrical.     

Information leakage and supply chain contracts

This paper investigates information leakage under different contract configurations in a supply chain. We consider two competing retailers, one of whom (incumbent) has private information about market demand while the other (entrant) has no access to acquire any market demand information. We assume that the supplier is the leader who may choose a wholesale price contract (WPC) or a revenue-sharing contract (RSC) with each retailer independently. We explore the effect of the supplier's and incumbent's incentives on non-leakage equilibrium and find out that there exists a non-leakage equilibrium only when the incumbent signs an RSC with the supplier under an appropriately given revenue-sharing rate in situations of high demand variation.     

需求信息可部分观察时供应链中的信息汇聚效应

考虑由一个供应商和两个零售商组成的二级供应链,供应链中的上下游企业共享需求信息.假设产品的需求分布未知且需求信息只可部分观察,企业按贝叶斯法则更新自己的先验.由于需求信息在供应商处汇聚,供应商与零售商占有的信息量不同,这就可能扭曲供应商对市场需求的认识,造成供应商认为市场过度膨胀或萎缩,我们把这种现象称为信息汇聚效应.本文将给出信息汇聚效应的定义,并给出在两周期供应链中发生信息汇聚效应的充分条件,进而推出发生信息汇聚效应概率的下界.数值算例表明,在一定情况下,在供应链中发生信息汇聚的概率会很可观.     

水平竞争条件下的供应链信息泄露策略

本文探讨非对称信息下,制造商针对议价能力不同的大型及小型零售商分别采用了收益共享、批发价合约时,大型零售商的市场信息被制造商泄露给竞争对手,从而对供应链产生的影响。通过对比有无信息泄露下各方成员的博弈过程,分析供应链信息泄露的原理;进而在制造商总是会泄露信息的前提下,构建基于信号传递的信息泄露下供应链成员决策模型,分别讨论分离均衡与混同均衡两种情形下,零售商的订货策略及其相应的收益。在此基础上进一步做出扩展,制造商有主动权以选择是否泄露信息的情况,对比分析零售商的策略选择问题。经过分析发现,出于自身利益的角度,制造商总是会泄露信息,从而导致供应链的整体利润下滑。对此,大型零售商的订货策略选择与市场需求的波动程度有关：波动较小则选择混同均衡;波动较大则选择分离均衡。特别地,当市场需求为低时,大型零售商的最优订货量会向下扭曲,即支付一定的“信息租金”作为应对信息泄露的代价。     

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。     

Vertical cost information sharing in a supply chain with value-adding retailers

We consider a supply chain consisting of one supplier and two value-adding heterogeneous retailers. Each retailer has full knowledge about his own value-added cost structure that is unknown to the supplier and the other retailer. Assuming there is no horizontal information sharing between two retailers, we model the supply chain with a three-stage game-theoretic framework. In the first stage each retailer decides if he is willing to vertically disclose his private cost information to the supplier. In the second stage, given the information he has about the retailers, the supplier announces the wholesale price to the retailers. In response to the wholesale price, in the third stage, the retailers optimize their own retail prices and the values added to the product, respectively. Under certain conditions, we prove the existence of equilibrium prices and added values. Furthermore, we obtain the condition under which both retailers are unwilling to vertically share their private information with the supplier, as well as the conditions under which both retailers have incentives to reveal their cost information to the supplier, thus leading to a win–win situation for the whole supply chain.