Pricing policies for substitutable products in a supply chain with Internet and traditional channels

This study considers pricing policies in a supply chain with one manufacturer, who sells a product to an independent retailer and directly to consumers through an Internet channel. In addition to the manufacturer’s product, the retailer sells a substitute product produced by another manufacturer. Given the wholesale prices of the two substitute products, the manufacturer decides the retail price of the Internet channel, and the retailer decides the retail prices of the two substitute products. Both the manufacturer and the retailer choose their own decision variables to maximize their respective profits. This work formulates the price competition, using the settings of Nash and Stackelberg games, and derives the corresponding existence and uniqueness conditions for equilibrium solutions. A sensitivity analysis of an equilibrium solution is then conducted for the model parameters, and the profits are compared for two game settings. The findings show that improving brand loyalty is profitable for both of the manufacturer and retailer, and that an increased service value may alleviate the threat of the Internet channel for the retailer and increase the manufacturer’s profit. The study also derives some conditions under which the manufacturer and the retailer mutually prefer the Stackelberg game. Based on these results, this study proposes an appropriate cooperation strategy for the manufacturer and retailer.     

Product variety and channel structure strategy for a retailer-Stackelberg supply chain

Motivated by the observations that the direct sales channel is increasingly used for customized products and that retailers wield leadership, we develop in this paper a retailer-Stackelberg pricing model to investigate the product variety and channel structure strategies of manufacturer in a circular spatial market. To avoid channel conflict, we consider the commonly observed case where the indirect channel sells standard products whereas the direct channel offers custom products. Our analytical results indicate that if the reservation price in the indirect channel is sufficiently low, adding the direct channel raises the unit wholesale price and retail price in the indirect channel due to customization in the direct channel. Despite the fact that dual channels for the retailer may dominate the single indirect channel, we find that the motivation for the manufacturer to use dual channels decreases with the unit production cost, while increases with (i) the marginal cost of variety, (ii) the retailer’s marginal selling cost, and (iii) the customer’s fit cost. Interestingly, our equilibrium analysis demonstrates that it is more likely for the manufacturer to use dual channels under the retailer Stackelberg channel leadership scenario than under the manufacturer Stackelberg scenario if offering a greater variety is very expensive. When offering a greater variety is inexpensive, the decentralization of the indirect channel may invert the manufacturer’s channel structure decision. Furthermore, endogenization of product variety will also invert the channel structure decision if the standard product’s reservation price is sufficiently low.     

The role of retailer’s performance in optimal wholesale price discount policies

The main goal of this paper is to model the effects of wholesale price control on manufacturer’s profit, taking explicitly into account the retailer’s sales motivation and performance. We consider a stylized distribution channel where a manufacturer sells a single kind of good to a single retailer. Wholesale price discounts are assumed to increase the retailer’s motivation thus improving sales. We study the manufacturer’s profit maximization problem as an optimal control model where the manufacturer’s control is the discount on wholesale price and retailer’s motivation is one of the state variables. In particular in the paper we prove that an increasing discount policy is optimal for the manufacturer when the retailer is not efficient while efficient retailers may require to decrease the trade discounts at the end of the selling period. Computational experiments point out how the discount on wholesale price passed by the retailer to the market (pass-through) influences the optimal profit of the manufacturer.     

A Stackelberg game and its improvement in a VMI system with a manufacturing vendor

Vendor managed inventory (VMI) is an inventory management strategy to let a vendor manage his retailers’ inventories, which makes the vendor have the opportunity to obtain some inventory and market-related information of his retailers. This paper discusses how the vendor can take advantage of this information for increasing his own profit by using a Stackelberg game in a VMI system. The vendor here is a manufacturer who procures raw materials to produce a finished product and supplies it at the same wholesale price to multiple retailers. The retailers then sell the product in independent markets at retail prices. Solution procedures are developed to find the Stackelberg game equilibrium that each enterprise is not willing to deviate from for maximizing his own profit. The equilibrium makes the manufacturer benefited, and the retailers’ profits maximized. The equilibrium can then be improved for further benefiting the manufacturer and his retailers if the retailers are willing to cooperate with the manufacturer by using a cooperative contract. Finally, a numerical example and the corresponding sensitivity analysis are given to illustrate that: (1) the manufacturer can benefit from his leadership, and monopolize the added profit of the VMI system in some cases; (2) The manufacturer can further improve his own profit, and then the retailers’ profits by the cooperative contract, as compared to the Stackelberg equilibrium; (3) market and raw material related parameters have significant influence on every enterprise’s net profit.     

Pricing and advertisement in a manufacturer–retailer supply chain

We use a game theoretical approach to study pricing and advertisement decisions in a manufacturer–retailer supply chain when price discounts are offered by both the manufacturer and retailer. When the manufacturer is the leader of the game, we obtained Stackelberg equilibrium with manufacturer’s local allowance, national brand name investment, manufacturer’s preferred price discount, retailer’s price discount, and local advertising expense. For the special case of two-stage equilibrium when the manufacturer’s price discount is exogenous, we found that the retailer is willing to increase local advertising expense if the manufacturer increases local advertising allowance and provides deeper price discount, or if the manufacturer decreases its brand name investment. When both the manufacturer and retailer have power, Nash equilibrium in a competition game is obtained. The comparison between the Nash equilibrium and Stackelberg equilibrium shows that the manufacturer always prefers Stackelberg equilibrium, but there is no definitive conclusion for the retailer. The bargaining power can be used to determine the profit sharing between the manufacturer and the retailer. Once the profit sharing is determined, we suggest a simple contract to help the manufacturer and retailer obtain their desired profit sharing.     

Optimal selection of retailers for a manufacturing vendor in a vendor managed inventory system

A Vendor Managed Inventory (VMI) system consists of a manufacturing vendor and a number of retailers. In such a system, it is essential for the vendor to optimally determine retailer selection and other related decisions, such as the product’s replenishment cycle time and the wholesale price, in order to maximize his profit. Meanwhile, each retailer’s decisions on her willingness to enter the system and retail price are simultaneously considered in the retailer selection process. However, the above interactive decision making is complex and the available studies on interactive retailer selection are scarce. In this study, we formulate the retailer selection problem as a Stackelberg game model to help the manufacturer, as a vendor, optimally select his retailers to form a VMI system. This model is non-linear, mixed-integer, game-theoretic, and analytically intractable. Therefore, we further develop a hybrid algorithm for effectively and efficiently solving the developed model. The hybrid algorithm combines dynamic programming (DP), genetic algorithm (GA) and analytical methods. As demonstrated by our numerical studies, the optimal retailer selection can increase the manufacturer’s profit by up to 90% and the selected retailers’ profits significantly compared to non-selection strategy. The proposed hybrid algorithm can solve the model within a minute for a problem with 100 candidate retailers, whereas a pure GA has to take more than 1 h to solve a small sized problem of 20 candidate retailers achieving an objective value no worse than that obtained by the hybrid algorithm.     

Price and lead time decisions in dual-channel supply chains

Manufacturers today are increasingly adopting a dual channel to sell their products, i.e., the traditional retail channel and an online direct channel. Empirical studies have shown that service quality (we focus on the delivery lead time of the direct channel) even goes beyond product price as one of the major factors influencing consumer acceptance of the direct channel. Delivery lead time has significant effects on demand, profit, and pricing strategy. However, there is scant literature addressing the decision on the promised delivery lead time of a direct channel and its impact on the manufacturer’s and retailer’s pricing decisions. To fill this gap, we examine the optimal decisions of delivery lead time and prices in a centralized and a decentralized dual-channel supply chain using the two-stage optimization technique and Stackelberg game, and analyze the impacts of delivery lead time and customer acceptance of a direct channel on the manufacturer’s and retailer’s pricing behaviours. We analytically show that delivery lead time strongly influences the manufacturer’s and the retailer’s pricing strategies and profits. Our numerical studies reveal that the difference between the demand transfer ratios in the two channels with respect to delivery lead time and direct sale price, customer acceptance of the direct channel, and product type have great effects on the lead time and pricing decisions.     

基于批发价契约的多零售商横向转载的供应链协调

研究了多零售商横向转载的供应链批发价契约协调问题。以包含一个制造商和多个零售商的供应链系统为研究对象,基于批发价契约研究了零售商转载下的供应链协调问题,获取了批发价契约可以协调零售商存在横向转载的供应链的理论证据,并给出了相应的产生供应链协调的条件,详细分析了协调情形下供应链系统最优订货量与多零售商无转载及单报童等情形下的最优订货量之间的关系。进一步研究了制造商与零售商在Stackelberg博弈下,零售商横向转载对制造商收益的影响,并提出了在Stackelberg博弈模型中,批发价契约也有可能促使制造商选择供应链系统最优订货量所对应的批发价格,使得供应链协调,且给出了此种协调产生的具体条件。数值算例则对两种供应链协调情形下的订货量、批发价格及期望收益进行了计算与仿真。研究表明,批发价契约可能会使得多零售商存在转载的供应链实现协调,传统的双重边际化效应将会由于制造商和零售商的理性而被弱化。     

不同权力结构对制造商双渠道供应链的影响研究

在一个制造商和一个零售商组成的供应链中, 制造商拥有线下传统渠道及线上直销双渠道。首先根据消费者剩余理论, 构建了制造商双渠道需求函数;接着分别构建了两类Stackelberg博弈及Nash博弈三种权力结构下制造商和零售商的利润模型并对模型进行了求解;最后分析了三种不同权力结构对制造商双渠道供应链的影响。研究发现:制造商线上直销渠道价格不受三种博弈权力结构的影响;线下传统渠道零售价格、需求, 线上直销渠道需求及制造商双渠道供应链总利润不受两类Stackelberg博弈权力结构的影响;线下传统渠道零售价格及线上直销渠道需求在Nash博弈权力结构下最小, 而线下传统渠道需求及供应链总利润在Nash博弈权力结构下最大;制造商批发价格、利润及零售商利润对三种博弈权力结构较敏感, 随供应链成员自身博弈权力地位的下降而逐渐降低。     

价格竞争下风险规避对闭环供应链决策的影响研究

基于零售商销售价格与回收价格竞争情形,构建了一个可持续的闭环供应链.考虑决策者风险规避行为,研究了闭环供应链成员的定价决策问题.利用博弈论,在风险中性与风险规避特性下分别探讨了批发价格,零售价格和回收价格的最优决策,并建立了它们的表达式.研究结论表明,仅当零售商具有风险规避时,制造商决策不受零售商的影响,而仅当制造商具有风险规避时,零售商决策会受制造商的影响.同时,当二者都具有风险规避特性时,他们之间的决策会相互影响.     

Pricing and two-tier advertising with one manufacturer and one retailer

This paper considers the pricing decisions and two-tier advertising levels between one manufacturer and one retailer where customer demand depends on the retail price and advertisement by a manufacturer and a retailer. We solve a Stackelberg game with the manufacturer as the leader and the retailer as the follower. With price sensitive customer demand and a linear wholesale contract, we obtain the optimal decisions by the manufacturer and the optimal responses by the retailer. Our results show that cost sharing of local advertising does not work well, it is better for the manufacturer to advertise nationally and offer the retailer a lower wholesale price.     

Selling to the “Newsvendor” with a forecast update: Analysis of a dual purchase contract

We consider a supply chain in which a manufacturer sells to a procure-to-stock retailer facing a newsvendor problem with a forecast update. Under a wholesale price contract, the retailer waits as long as she can and optimally places her order after observing the forecast update. We show that the retailer’s wait-and-decide strategy, induced by the wholesale price contract, hinders the manufacturer’s ability to (1) set the wholesale price and maximize his profit, (2) hedge against excess inventory risk, and (3) reduce his profit uncertainty. To mitigate the adverse effect of wholesale price contract, we propose the dual purchase contract, through which the manufacturer provides a discount for orders placed before the forecast update. We characterize how and when a dual purchase contract creates strict Pareto improvement over a wholesale price contract. To do so, we establish the retailer’s optimal ordering policy and the manufacturer’s optimal pricing and production policies. We show how the dual purchase contract reduces profit variability and how it can be used as a risk hedging tool for a risk averse manufacturer. Through a numerical study, we provide additional managerial insights and show, for example, that market uncertainty is a key factor that defines when the dual purchase contract provides strict Pareto improvement over the wholesale price contract.     

具有价格粘性的供应链动态模型及其协调策略

本文针对由一个制造商和一个零售商构成的供应链系统,在市场价格具有粘性的情况下,利用动态博弈理论分析了制造商和零售商如何确定其最优的批发价格和产品订购量以实现自身长期利润的最大化。本文首先利用汉密尔顿-雅可比-贝尔曼方程分别求解了供应链系统在Stackelberg博弈下的最优批发价格和最优产品订购数量。然后,利用数值算例说明了该供应链系统协调的必要性。最后,利用数量折扣契约协调了该供应链系统,并证明了协调的有效性。     

Using MSRP to enhance the ability of rebates to control distribution channels

Manufacturers have increasingly instituted widespread mail-in rebate programs in recent years. Two primary purposes for rebates are to: (1) more directly impact consumer demand by reducing net retail price, and (2) capitalize on consumers’ slippage behavior because not all consumers who intend to redeem the rebate at purchase time end up actually redeeming it. However, retailers can counteract the power of rebates to impact demand by simply raising the retail price by the amount of the manufacturer’s rebate. We show that by combining a manufacturer’s suggested retail price (MSRP) along with a rebate, the manufacturer can better control the channel by inhibiting the retailer’s ability to raise price, particularly when consumers exhibit loss aversion. As a result, incorporating MSRP with a rebate promotion plan increases the manufacturer’s profit. More surprisingly, the profit of the supply chain as a whole also increases, and the channel efficiency increases as well. In fact, contrary to results from the existing rebate literature suggesting that rebates should always be offered whenever slippage exists, we demonstrate that MSRP can actually be a more effective tool than rebates in managing retailer and consumer behavior when consumers do not have sufficient loss aversion and the slippage rate is low enough.     

“Bricks vs. Clicks”: The impact of manufacturer encroachment with a dealer leasing and selling of durable goods

In durable goods markets, many brand name manufacturers, including IBM, HP, Epson, and Lenovo, have adopted dual-channel supply chains to market their products. There is scant literature, however, addressing the product durability and its impact on players’ optimal strategies in a dual-channel supply chain. To fill this void, we consider a two-period dual-channel model in which a manufacturer sells a durable product directly through both a manufacturer-owned e-channel and an independent dealer who adopts a mix of selling and leasing to consumers. Our results show that the manufacturer begins encroaching into the market in Period 1, but the dealer starts withdrawing from the retail channel in Period 2. Moreover, as the direct selling cost decreases, the equilibrium quantities and wholesale prices become quite angular and often nonmonotonic. Among other results, we find that both the dealer and the supply chain may benefit from the manufacturer’s encroachment. Our results also indicate that both the market structure and the nature of competition have an important impact on the player’s (dealer’s) optimal choice of leasing and selling.     

Optimal Advertising and Pricing in a Dynamic Durable Goods Supply Chain

Cooperative advertising is an incentive offered by a manufacturer to influence retailers’ promotional decisions. We study a dynamic durable goods duopoly with a manufacturer and two independent and competing retailers. The manufacturer, as a Stackelberg leader, announces his wholesale prices and his shares of retailers’ advertising costs, and the retailers in response play a Nash differential game in choosing their optimal retail prices and advertising efforts over time. We obtain the feedback equilibrium policies for the manufacturer and the retailers in explicit form for a linear demand formulation. We investigate issues, like channel coordination and antidiscriminatory legislation, and also study a case, when the manufacturer sells through only one retailer and the second retailer sells a competing brand.     

Contracting with demand uncertainty under supply chain competition

We examine supply chain contracts for two competing supply chains selling a substitutable product, each consisting of one manufacturer and one retailer. Both manufacturers are Stackelberg leaders and the retailers are followers. Manufacturers in two competing supply chains may choose different contracts, either a wholesale price contract in which the retailer??s demand forecasting information is not shared, or a revenue-sharing contract in which the retailer??s demand forecasting information is shared. Under supply chain competition and demand uncertainty, we identify which contract is more advantageous for each supply chain, and under what circumstances.     

Wholesale pricing and evolutionarily stable strategies of retailers with imperfectly observable objective

This paper develops a one-population (indirect) evolutionary game model of a supply chain with one manufacturer/supplier and many (a sufficiently large number of) retailers to study how the retailer’s marketing objective depends on the wholesale price, its observability, the error probability of the observed result on the rival’s preference, the market scale and the retailer’s bargaining power. This paper also presents an algorithm for computing the optimal wholesale price of the manufacturer. We find that the profit (revenue) maximization behavior is an evolutionarily stable marketing strategy if the wholesale price is sufficiently high (low). Given an appropriate wholesale price, the revenue maximization behavior coexists with the profit maximization behavior in the retailers’ population. The larger the market scale, the stronger the motivation of the retailer to take profit maximization behavior due to a higher wholesale price. The cross effects of the retailer’s reservation payoff and the other factors should be considered in the decision process.     

基于风险偏好的供应链企业社会责任投入与定价策略研究

本文研究制造商承担企业社会责任时,竞争市场下供应链的均衡价格策略。通过Stackelberg博弈模型,探讨供应链成员的风险规避程度、竞争市场的需求波动性和竞争市场的需求相关性以及制造商企业社会责任水平对供应链均衡策略的影响。研究表明,在制造商承担企业社会责任时,风险规避程度对价格策略的影响依赖于制造商企业社会责任水平的高低;竞争市场的需求波动性较大或竞争市场需求相关性较高时,制造商向下游风险规避型零售商提供较低的批发价格合约, 此时产品的市场价格降低,消费者福利增加;当制造商的生产成本较低时,承担越高的企业社会责任导致消费者福利增加;反之,当制造商的生产成本较高时,消费者福利总是减少。     

Nash game model for optimizing market strategies,configuration of platform products in a Vendor Managed Inventory (VMI) supply chain for a product family

This paper discusses how a manufacturer and its retailers interact with each other to optimize their product marketing strategies, platform product configuration and inventory policies in a VMI (Vendor Managed Inventory) supply chain. The manufacturer procures raw materials from multiple suppliers to produce a family of products sold to multiple retailers. Multiple types of products are substitutable each other to end customers. The manufacturer makes its decision on raw materials’ procurement, platform product configuration, product replenishment policies to retailers with VMI, price discount rate, and advertising investment to maximize its profit. Retailers in turn consider the optimal local advertising investments and retail prices to maximize their profits. This problem is modeled as a dual simultaneous non-cooperative game (as a dual Nash game) model with two sub-games. One is between the retailers serving in competing retail markets and the other is between the manufacturer and the retailers. This paper combines analytical, iterative and GA (genetic algorithm) methods to develop a game solution algorithm to find the Nash equilibrium. A numerical example is conducted to test the proposed model and algorithm, and gain managerial implications.