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.     

两级供应链中供应中断情形下零售商转运策略

考虑由两个供应商和两个零售商组成的两级供应链系统,且两个供应商以一定概率发生供货中断,基于供应商供货发生中断的四种情形,分别对零售商实施相互转运策略、单向转运策略和不转运策略下建立最优订货决策模型。从理论上比较了三种策略下零售商期望利润和订货量高低,并分析相互转运和单向转运策略下零售商期望利润和订货量与转运价格、转运成本之间的关系,最后运用算例进行验证,同时分析了三种策略下,供应中断概率和其它主要参数的变化对零售商期望利润和最优订货量的影响。     

Balancing Inventory and Stockout Risk in Retail Supply Chains Using Fast‐Ship

In this study, we consider a two‐retailer, one‐supplier supply chain in which retailers satisfy excess demand by offering to directly ship out‐of‐stock items on an expedited basis at no extra cost to customers. This practice is referred to as the fast‐ship option. We consider two scenarios along with the fast‐ship option. In the first scenario, retailers transship when out of stock, whereas in the second scenario, they do not. If they do not transship, some customers may perform the search on their own. In each scenario, the wholesale prices are either exogenous, or chosen endogenously by the supplier. For both cases, we determine the supplier's and the retailers’ optimal decisions. The key research question we ask and answer is the following: which of the two scenarios is preferred by either player when all decisions are made optimally? We show that when fewer customers are willing to search on their own and wholesale prices are exogenous, both the supplier and the retailers prefer to transship. In addition, the decision maker in a centralized chain will have the exact same preference as that of players in a decentralized setting when the retailers’ and the supplier's preferences coincide and wholesale prices are exogenous. This preference concordance does not hold if wholesale prices are endogenous.     

Retailer Transshipment versus Central Depot Allocation for Supply Network Design

We consider a supply chain structure with shipments from an external warehouse directly to retailers and compare two enhancement options: costly transshipment among retailers after demand has been realized vs. cost‐free allocation to the retailers from the development of a centralized depot. Stochastic programming models are developed for both the transshipment and allocation structures. We study the impact of cost parameters and demand coefficient of variation on both system structures. Our results show an increasing convex relationship between average costs and demand coefficient of variation, and furthermore that this increase is more pronounced for the allocation structure. We employ simulation and nonlinear search techniques to computationally compare the cost performance of allocation and transshipment structures under a wide range of system parameters such as demand uncertainty and correlation; lead times from the external warehouse to retailers, from warehouse to central depot, and from depot to retailers; and transshipment, holding, and penalty costs. The transshipment approach is found to outperform allocation for a broad range of parameter inputs including many situations for which transshipment is not an economically sound decision for a single period. The insights provided enable the manager to choose whether to invest in reducing lead times or demand uncertainty and assist in the selection of investments across identical and nonidentical retailers.     

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.     

两层级分散决策供应链库存转运问题研究

本文考虑一个由制造商及分散决策零售商构成的两层级供应链,研究了库存转运对供应链各方利润的影响。通过构建博弈模型并推导子博弈完美纳什均衡,确定了制造商及零售商的最优决策水平,并确定供应链各方在库存转运下利润提高和降低的条件。理论分析显示,制造商及零售商利润增减均由转运价格决定,转运价格阈值则受临界分位点水平影响。最后给出了零售商进行库存转运的供应链协调契约。     

The Retail Space‐Exchange Problem with Pricing and Space Allocation Decisions

We consider retail space‐exchange problems where two retailers exchange shelf space to increase accessibility to more of their consumers in more locations without opening new stores. Using the Hotelling model, we find two retailers’ optimal prices, given their host and guest space in two stores under the space‐exchange strategy. Next, using the optimal space‐dependent prices, we analyze a non‐cooperative game, where each retailer makes a space allocation decision for the retailer's own store. We show that the two retailers will implement such a strategy in the game, if and only if their stores are large enough to serve more than one‐half of their consumers. Nash equilibrium for the game exists, and its value depends on consumers’ utilities and trip costs as well as the total available space in each retailer's store. Moreover, as a result of the space‐exchange strategy, each retailer's prices in two stores are both higher than the retailer's price before the space exchange, but they may or may not be identical.     

Impact of Retailers with Knowledge of Supplier's Inventory on Supply Chain Performance

We model a supply chain consisting of a supplier and multiple retailers facing deterministic demand. We denote some retailers as strategic in the sense that given the supplier inventory information, they will implement the optimal stocking policy by incorporating such information. On the other hand, some retailers are denoted as naïve in the sense that they ignore supply information and resort to a simplistic ordering policy. Naïve retailers learn the optimal policy over time and adjust their orders accordingly. We study the dynamics of this game and investigate the impact of such strategic and naïve retailers on the cost, ordering pattern and stocking policies of all parties. We analyze the supply chain under two scenarios: the centralized supply chain where the objective is to minimize the total supply chain cost, and the decentralized supply chain where each self‐interested player minimizes its own cost in a Stackelberg game setting. We fully characterize the optimal policies under both centralized and decentralized scenarios and show that, surprisingly, the supply chain might be better off by virtue of naïve retailers. The result is driven by the fact that strategic and naïve players’ decisions shift the positioning of inventory in the supply chain with its final impact being determined by the relative costs of different retailer‐types. Our results also offer managerial insights into how access to supply information can improve supply chain performance.     

Product Assortment and Price Competition under Multinomial Logit Demand

The role of assortment planning and pricing in shaping sales and profits of retailers is well documented and studied in monopolistic settings. However, such a role remains relatively unexplored in competitive environments. In this study, we study equilibrium behavior of competing retailers in two settings: (i) when prices are exogenously fixed, and retailers compete in assortments only; and (ii) when retailers compete jointly in assortment and prices. For this, we model consumer choice using a multinomial Logit, and assume that each retailer selects products from a predefined set, and faces a display constraint. We show that when the sets of products available to retailers do not overlap, there always exists one equilibrium that Pareto‐dominates all others, and that such an outcome can be reached through an iterative process of best responses. A direct corollary of our results is that competition leads a firm to offer a broader set of products compared to when it is operating as a monopolist, and to broader offerings in the market compared to a centralized planner. When some products are available to all retailers, that is, assortments might overlap, we show that display constraints drive equilibrium existence properties.     

Price and Service Competition in an Outsourced Supply Chain

We consider a buyer who outsources the manufacturing of a product to multiple symmetric make‐to‐stock suppliers who compete on price and service (fill rate). The buyer allocates demand to the suppliers using a score function with an exponential form, which specifies the relative importance of price vs. service, in order to minimize his costs, while the suppliers choose their prices and fill rates to maximize their profits. For the case of dual‐sourcing, we characterize the optimal parameter of the exponential score function, considering the impact of the buyer's decisions on the suppliers, and considering how the suppliers compete against each other to earn a portion of the buyer's demand. We prove the existence of a unique equilibrium and characterize the equilibrium behavior of the system. We then consider a general number of suppliers and show that the equilibrium prices and fill rates, and the buyer's cost, are increasing in the number of suppliers. We compare these results to a model of single‐sourcing, in which the buyer is the Stackelberg leader and extracts all profits from the supplier. We find that the buyer always prefers single‐sourcing to multisourcing. Finally, we study a centralized system and use the results to develop a coordinating contract for the decentralized system.     

需求与回收确定下闭环供应链的竞争与链内协调研究

针对两条分别由单生产商和单零售商组成、零售商负责废品回收的闭环供应链,运用博弈论和均衡理论建立了对应两条闭环供应链均为分散式供应链、均为集中式供应链、一条为分散式供应链一条为集中式供应链的带均衡约束的均衡（EPEC）模型、纳什（Nash）均衡模型和带均衡约束的优化（MPEC）模型,并进行了模型求解。对比三种模式表明：集中式控制是供应链竞争下的占优策略。随后,给出了两条供应链竞争下可协调分散式供应链达到集中式供应链效果的批发价加回收补贴契约。最后的数值算例和敏感性分析表明了模型的合理性、协调契约的有效性、以及相关参数的影响。     

Multiple In‐Cycle Transshipments with Positive Delivery Times

We study a centralized inventory sharing system of two retailers that are replenished periodically. Between two replenishments, a unit can be transshipped to a stocked‐out retailer from the other. It arrives a transshipment time later, during which the stocked‐out retailer incurs backorder cost. Without transshipment, backorder cost is incurred until the next replenishment. Since the transshipment time is shorter than the time between two replenishments, transshipments can reduce the backorder cost at the stocked‐out retailer and the holding costs at the other retailer. The system is directed by a centralized inventory manager, who minimizes the long‐run average cost consisting of replenishment, holding, backorder, and transshipment costs. The transshipment policy is characterized by hold‐back inventory levels, which are nonincreasing in the remaining time until the next replenishment. The transshipment policy differs from those in the literature because we allow for multiple transshipments between replenishments, positive transshipment times, and backorder costs. We also discuss the challenges associated with positive replenishment time and develop upper and lower bounds of average cost in this case. Bounds are numerically shown to have an average gap of 1.1%. A heuristic solution is based on the upper bound and differs from the optimal cost by at most this gap.     

协调多零售商横向转载的收益共享契约

本文研究了协调多零售商横向转载的收益共享契约。该契约包含批发价格和收益共享比例两个参数,由独立于零售商的第三方转载公司制定并实施。在建立多零售商转载博弈模型的基础上,给出了该契约协调零售商转载的充分必要条件;然后以包含两个零售商的转载系统为例,分别给出了协调情形下转载价格和收益共享比例需满足的条件及其解析表达形式,并设计了一类启发式算法来计算零售商的最优订货量、转载价格和期望利润。最后,通过一个算例对文中的相关研究结论进行了验证,并就相关参数对零售商期望收益的影响进行了分析。研究发现,收益共享是对称性零售商的占优选择;非对称情形下,较高的转载成本将导致协调情形下零售商的期望利润降低;较高的产品残值将要求选择较低的转载价格,确保协调契约对于零售商期望利润的帕累托改进;当产品的边际价值较高时,提高转载价格可改善零售商的期望利润;另外,灵敏度分析显示契约参数将显著影响非对称性零售商的期望利润。     

Cooperative sales promotion with a point-sharing policy: Advantages and limitations

Consumption-point programs have been commonly implemented in retail industries in efforts to promote sales and improve customer loyalty. In Korea, many retailers from different industries use a point-sharing policy to augment the conventional consumption-point program of each retailer. In a multi-retailer coalition under such a cooperative sales promotion policy, by purchasing from one coalition retailer, customers earn points that they can redeem points at other retailers in the coalition. On one hand, the introduction of this policy gives customers great flexibility for redeeming earned points, which can increase the demand at all retailers who promote the policy. On the other hand, the additional product costs associated with the points created by one retailer may spill over and be partly borne by other retailers, possibly distorting the coalition members’ equilibrium decisions under decentralized control. Under the general assumptions about the demand functions, we developed a model consisting of two retailers with fixed retail prices and addressed the retailers’ equilibrium decisions under a pure point-sharing policy. The findings suggest that the policy resulted in a cost spillover phenomenon. Then, we revealed that a pure point-sharing policy may fail to maximize the total profit of the coalition. Moreover, we showed that a pure point-sharing policy does not dominate the individual point scheme, which may explain the reason that point sharing is useful but not ubiquitously used in the real world. Our numerical examples also illustrate the way a pure point-sharing policy influences retailers’ profits when retail prices are decision variables. To improve the overall profit under the point-sharing policy further, we propose a target rebate contract to coordinate a pair of retailers. This contract can maximize the total profit and arbitrarily split the profit between retailers.     

Multiperiod Models with Capacities in Competitive Supply Chain

This paper considers a supply chain setting where several capacitated suppliers compete for orders from a single retailer in a multiperiod environment. At each period, the retailer places orders to the suppliers in response to the prices they announce. Each supplier has a fixed capacity. We consider a make‐to‐stock setting where the retailer can carry inventory. The retailer faces exogenous, price‐dependent demand. We study the problem using ideas from fluid models. In particular, we (i) analyze when there are pure equilibrium policies in this setting and characterize the structure of these policies; (ii) consider coordination mechanisms; and (iii) present some preliminary computational results. We also consider a modified model that uses option contracts to coordinate the supply chain.     

中小制造企业在线直销与传统分销双渠道定价决策研究

针对传统渠道中处于非主导地位的中小制造企业开展双渠道销售时存在的价格冲突问题,考虑产品数字属性对渠道需求的影响,构建了制造商与零售商独立决策和制造商占非主导地位两种情况下的双渠道定价决策模型,给出了两种情况下的双渠道最优定价,并分别考察了产品数字属性变化以及决策权利结构不同对最优定价的影响。研究结果表明,处于非主导地位的中小制造企业应采用依从强势零售商的定价策略,该策略有利于制造商和零售商以及渠道整体收益的增加;随着产品数字属性的增大,制造商的最优定价相应地提高,而零售商的最优定价则相应地降低;制造商占非主导地位时的双渠道最优定价高于制造商与零售商独立决策时的双渠道最优定价。     

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.     

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.     

考虑产品绿色度的绿色供应链博弈模型及收益共享契约

本文以一个制造商和一个零售商组成的二级绿色供应链为背景,建立了考虑产品绿色度的四种绿色供应链博弈模型:以制造商为主导的Stackelberg博弈模型、以零售商为主导的Stackelberg博弈模型、制造商和零售商的Nash均衡博弈模型以及集中控制模型。对四种博弈模型在产品绿色度、产品价格以及批发价格等方面进行了比较分析,并进一步建立了收益共享契约下的博弈模型。通过数值仿真探讨了收益共享系数对产品绿色度、制造商利润和零售商利润的影响。     

Managing Clearance Sales in the Presence of Strategic Customers

We study the effect of strategic customer behavior on pricing and rationing decisions of a firm selling a single product over two periods. The seller may limit the availability of the product (that is, ration) in the second (clearance) period. Some customers are strategic and respond to the firm's decisions by timing their purchases. When capacity is nonconstraining and the seller has pricing flexibility, we show that rationing in the clearance period cannot improve revenue. However, when prices are fixed in advance, rationing can improve revenue. In the latter case, we conduct a detailed analysis for linear and exponential demand curves and derive explicit expressions for optimal rationing levels. We find that the policy of doing the better of not restricting availability at the clearance price or not offering the product at the clearance price is typically near optimal. Our analysis also suggests that rationing—although sometimes offering considerable benefit over allowing unrestricted availability in the clearance period—may allow the seller to obtain only a small fraction of the optimal revenue when the prices are chosen optimally without rationing. We extend the analysis to cases where the capacity is constraining and obtain similar results.