Flexibility or Cost Saving? Sourcing Decisions with Two Suppliers

This article studies a decentralized supply chain in which there are two suppliers and a single buyer. One supplier offers the quantity flexibility (QF) contract to the buyer, while the other offers the cheaper price. Under the QF contract, the buyer does not assume full responsibility for the forecast, yet the supplier guarantees the availability of the forecasted quantity with additional buffer inventory. On the other hand, the price‐only contract places full inventory burden on the buyer, but with a cheaper price. We study this problem from the buyer's perspective and solve for the buyer's optimal procurement and forecasting decisions. We identify areas where flexibility and cheaper price have an advantage, one over the other. Our results indicate that the buyer significantly benefits from having multiple sources of supply. We also find that, from the system's standpoint, a multisupplier system may outperform a single‐supplier supply chain under certain conditions. Interestingly, we observe that providing too much flexibility may benefit the low‐price supplier rather than benefiting the QF supplier. We discuss the managerial implications and provide directions for future research opportunities.     

Coordinating Supply Chains via Advance‐Order Discounts,Minimum Order Quantities,and Delegations

To avoid inventory risks, manufacturers often place rush orders with suppliers only after they receive firm orders from their customers (retailers). Rush orders are costly to both parties because the supplier incurs higher production costs. We consider a situation where the supplier's production cost is reduced if the manufacturer can place some of its order in advance. In addition to the rush order contract with a pre‐established price, we examine whether the supplier should offer advance‐order discounts to encourage the manufacturer to place a portion of its order in advance, even though the manufacturer incurs some inventory risk. While the advance‐order discount contract is Pareto‐improving, our analysis shows that the discount contract cannot coordinate the supply chain. However, if the supplier imposes a pre‐specified minimum order quantity requirement as a qualifier for the manufacturer to receive the advance‐order discount, then such a combined contract can coordinate the supply chain. Furthermore, the combined contract enables the supplier to attain the first‐best solution. We also explore a delegation contract that either party could propose. Under this contract, the manufacturer delegates the ordering and salvaging activities to the supplier in return for a discounted price on all units procured. We find the delegation contract coordinates the supply chain and is Pareto‐improving. We extend our analysis to a setting where the suppliers capacity is limited for advance production but unlimited for rush orders. Our structural results obtained for the one‐supplier‐one‐manufacturer case continue to hold when we have two manufacturers.     

Optimal Quantity Discount Design with Limited Information Sharing*

In this article we address the optimal quantity discount design problem of a supplier in a two‐stage supply chain where the supplier and the buyer share annual demand information only. The supply chain faces a constant deterministic demand that is not price sensitive and operates with fixed setup costs in both stages. We show that the supplier can actually moderate a cost‐minimizing buyer to order in quantities different than the buyer's optimal order quantity in the traditional setting and develop a multi‐breakpoint quantity discount scheme that maximizes supplier's expected net savings. The proposed multi‐breakpoint discount scheme can be easily computed from the available information and, while also maximizing the supplier's net savings, is very effective in achieving high levels of supply chain coordination efficiency in the presence of limited information.     

Quantity Discount‐Based Inventory Coordination: Effectiveness and Critical Environmental Factors

It is understood that quantity discounts provide a practical foundation for coordinating inventory decisions in supply chains. The primary objective of this research is to test, under a variety of environmental conditions, the effectiveness of quantity discounts as an inventory coordination mechanism between a buyer and a supplier. A comprehensive simulation experiment with anova has been designed to investigate the impacts of (1) choice of quantity discount‐based inventory coordination policies, (2) magnitude of demand variation, (3) buyer's and supplier's relative inventory cost structure, and (4) buyer's economic time‐between‐orders on the effectiveness of supply chain inventory coordination. The analytical results confirm that the quantity discount policies have managerial properties as a mediator for inventory coordination. The results also show that the performance of quantity discount‐based inventory coordination policies is influenced significantly by environmental factors, such as the magnitude of demand variation, the buyer's and the supplier's inventory cost structure, and the buyer's economic time‐between‐orders.     

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.     

Coordinating a Supply Chain System with Retailers Under Both Price and Inventory Competition

We investigate a supply chain system with a common supplier selling to downstream retailers who are engaged in both price and inventory competition. We establish the existence and uniqueness of the pure‐strategy Nash equilibrium for the retailer game and study how a supplier can coordinate the system to achieve the best performance. Our main conclusions are as follows: First, a buyback contract can be used to coordinate retailers competing on both price and inventory in a sense that optimal retail prices and inventory levels arise as the Pareto‐dominant equilibrium. With symmetric retailers, the system optimum arises as the unique symmetric equilibrium. Second, the particular type of competition experienced by retailers (price versus inventory competition) affects the characteristics of the contract. Specifically, strong price competition leads to a coordination mechanism with a positive buyback rate, where the supplier subsidizes retailers for leftover inventories; however, strong inventory competition leads to a negative buyback rate, where retailers are punished for overstocking. Using a linear expected demand function, we further explore the impact of system parameters on the coordination contract and the competitive equilibrium. We also find that the performance of the supplier's optimal contract is asymptotic to the system optimal coordination contract as competition becomes fierce.     

两零售商竞争下多因素同时扰动的供应链协调研究

本文研究了由一个制造商两个竞争零售商组成的供应链在百川德博弈下,生产成本、市场需求和价格敏感系数同时扰动的协调机制,考虑了线性数量折扣契约对供应链的协调作用。研究表明,当三因素同时发生扰动后, 集权式供应链中线性数量折扣契约可以协调供应链,而在分散式供应链中,原来的协调契约不具有鲁棒性,制造商只有采用新的线性数量折扣契约,分散式供应链才能实现协调。 最后用一个算例验证了结论。     

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.     

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.     

Unsold Versus Unbought Commitment: Minimum Total Commitment Contracts with Nonzero Setup Costs

We study a minimum total commitment (MTC) contract embedded in a finite‐horizon periodic‐review inventory system. Under this contract, the buyer commits to purchase a minimum quantity of a single product from the supplier over the entire planning horizon. We consider nonstationary demand and per‐unit cost, discount factor, and nonzero setup cost. Because the formulations used in existing literature are unable to handle our setting, we develop a new formulation based on a state transformation technique using unsold commitment instead of unbought commitment as state variable. We first revisit the zero setup cost case and show that the optimal ordering policy is an unsold‐commitment‐dependent base‐stock policy. We also provide a simpler proof of the optimality of the dual base‐stock policy. We then study the nonzero setup cost case and prove a new result, that the optimal solution is an unsold‐commitment‐dependent (s, S) policy. We further propose two heuristic policies, which numerical tests show to perform very well. We also discuss two extensions to show the generality of our method's effectiveness. Finally, we use our results to examine the effect of different contract terms such as duration, lead time, and commitment on buyer's cost. We also compare total supply chain profits under periodic commitment, MTC, and no commitment.     

零售商退出风险的供应链冲击与协调契约分析

零售商退出会导致供应链合作关系的终止,冲击供应链合作运营的基础,供应链企业需要合作应对吗?本文以数量折扣契约下的协调供应链为研究框架,研究存在零售商退出风险时传统数量折扣契约的供应链运作,并构建改进契约下的供应链协调模型。通过理论推演与仿真分析发现,零售商退出风险对供应链运作可能造成巨大的冲击,同时也惊讶地发现,虽然数量折扣契约在冲击下不能协调运作,但运作效率非常高。建议契约调整成本不高的供应链可选择我们改进后的协调数量折扣契约。     

Coordinating contracts for a financially constrained supply chain

We consider a financially constrained supply chain in which a supplier (leader) sells products to a retailer (follower) who has no access to bank financing due to her low credit rating. However, the supplier can borrow from a bank and offer trade credit to the retailer to alleviate her financial constraint. Failure to pay off a bank loan or trade credit incurs a variable default cost. We analyze the centralized version of the supply chain to obtain new coordination requirements. We then examine whether revenue-sharing, buyback, and all-unit quantity discount contracts can coordinate our supply chain. We show that the all-unit quantity discount contract fails to coordinate. However, the revenue-sharing and buyback contracts can coordinate the supply chain, but only when the supply chain has a sufficient total working capital. Moreover, they cannot allocate profit flexibly unless the supplier has a large enough working capital. Finally, we design a generalized revenue-sharing contract that coordinates the supply chain with flexible profit allocation, and also show by numerical examples its superiority over the revenue-sharing and buyback contracts.     

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 Role of Revenue‐Focused Managerial Performance Measures in Supply Chain Coordination

Many firms employ revenue‐focused managerial performance measures (RF‐MPMs) that cause managers to worry more about revenues than about costs. Although this can seemingly misalign the interests of a manager, we show that the use of such measures can help supply chain partners to overcome hold‐up issues with respect to capacity and promotion investments. We develop a game theoretic model in which two supply chain partners engage in repeated interactions in which the supplier invests in capacity and the buyer invests in demand promotion. Following the realization of demand in each period, the two firms negotiate over the output quantity and wholesale price. The novelty of our model is that we allow the owners of each firm to delegate decision‐making power and negotiating responsibility to a free‐agent manager. We characterize the conditions under which the owners of both firms employ RF‐MPMs in equilibrium and benefit from doing so. For a special case of our model, we show that for the owners of the buyer, an RF‐MPM is equivalent to a price only relational contract, and that it complements a price and quantity relational contract as a mechanism for mitigating hold‐up issues.     

在弹性需求和物品易变质条件下数量折扣定价模型

研究在弹性需求和易变质物品条件下,当供应商和零售商独自决策时,供应商如何确定最优数量折扣问题。基于Stackelberg博奕建立了数学模型,证明了零售商的出售价格随供应商出售价格的降低而降低,从而需求量增大。当供应商给予价格折扣时,零售商的利润是增加的。在此基础上,给出了最优数量折扣的计算方法。对供应商和零售商单独决策时,供应商利用数量折扣对供应链进行协调产生的系统利润与供应商和零售商联合决策时的系统利润做了数值分析和比较。结果表明,供应商采用数量折扣的方法使供应链协调是有效的;价格折扣随价格敏感系数的增大而增大,随变质率的增大而减小。     

Long‐Term Contracting: The Role of Private Information in Dynamic Supply Risk Management

We examine the critical role of evolving private information in managing supply risk. The problem features a dyadic channel where a dominant buyer operates a multiperiod inventory system with lost sales and fixed cost. He replenishes from a supplier, whose private state of production is vulnerable to random shocks and evolves dynamically over time. We characterize the optimal inventory policy with a simple semi‐stationary structure; it distorts order quantity for limiting information rent only in the initial period; the optimal payment compensates for production cost in every period but concedes real information rent only in the initial period. These properties allow us to derive an easy‐to‐implement revenue‐sharing contract that facilitates ex ante strategic planning and ex post dynamic execution. This work advances our understanding on when and how to use private information in dynamic risk management.     

Managing High‐Tech Capacity Expansion via Reservation Contracts

We study capacity reservation contracts between a high‐tech manufacturer (supplier) and her OEM customer (buyer). The supplier and the buyer are partners who enter a ‘design‐win” agreement to develop the product, and who share the stochastic demand information. To encourage the supplier for more aggressive capacity expansion, the buyer reserves capacity upfront by paying a deductible fee. As capacity expansion demonstrates diseconomy of scale in this context, we assume convex capacity costs. We show that as the buyer's revenue margin decreases, the supplier faces a sequence of four profit scenarios with decreasing desirability. We examine the effects of market size and demand variability to the contract conditions. We propose two channel coordination contracts, and discuss how such contracts can be tailored for situations where the supplier has the option of not complying with the contract, and when the buyer's demand information is only partially updated during the supplier's capacity lead‐time.     

不公平厌恶下VMI供应链的批发价格契约与协调

供应链契约是影响VMI供应链整体绩效的重要因素,这是近年来关注的重要研究课题。本文着重研究了由供应商与零售商组成的二级VMI供应链协调问题,在供应商存在不公平厌恶的假设下,依据Cui等提出的不公平厌恶模型刻画了供应商的不利与有利不公平厌恶,通过分析得到了分散VMI供应链情形下供应商的最优策略,同时分析了二级VMI供应链在批发价格契约下的协调情况。通过分析得到的主要结论是:在供应商存在不利不公平厌恶的情形下,供应商存在唯一的最优产品生产量,其不高于传统供应商的最优产品生产量且为不利不公平厌恶系数或零售商势力外生参数的严格减函数或减函数,批发价格契约无法使二级VMI供应链达到协调;在供应商存在有利不公平厌恶的情形下,供应商存在唯一的最优产品生产量,其不低于传统供应商的最优产品生产量且为有利不公平厌恶系数或零售商势力外生参数的严格增函数或增函数,批发价格契约在一定条件下可使二级VMI供应链达到协调。最后,通过数值实验分析验证了本文得出的结论。     

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.     

需求和零售商购买成本同时扰动的供应链应急协调

供应链的契约协调机制是供应链管理的重要内容,突发事件下的供应链协调机制是近年来的研究热点。 研究了在单制造商单零售商组成的供应链中,假设生产成本是其生产数量的凸函数下,当市场需求为零售价格的非线性函数,突发事件造成需求和零售商购买成本同时发生扰动时,集权、分权供应链应对突发事件的最优策略。 首先证明了稳定环境下的数量折扣契约可以实现该供应链的协调,在集权式决策下,供应链的原有生产计划对突发事件具有一定的鲁棒性,但是当突发事件造成的扰动超过一定幅度时,供应链的协调将会被打破,供应链系统必须改变生产计划才能实现其利润最大化。 在分权式决策下,供应链的原数量折扣契约不能使扰动后的供应链达到协调,因此,设计了新的数量折扣契约来使扰动后的供应链达到协调。最后给出一个算例验证了相关结论。