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.     

Channel Coordination with Cooperative Advertising Considering Effect of Advertising on Willingness to Pay

In this paper, cooperative advertising in a manufacturer–retailer supply chain is studied. Advertising can enhance willingness to pay (WTP) of customers. This trade-off between the benefits of increasing WTP of customers and the advertising expenditure is a key to understanding the retailers optimal advertising decision. On the other hand, it is interesting to understand in which condition supporting the retailer for his advertising expenditure is beneficial for the manufacturer. In this study, in order to capture pricing and advertising strategies of the channel member, three non-cooperative games including Nash, Stackelberg retailer and Stackelberg manufacturer game-theoretic models are established. In spite of the related studies which restrict price in order to prevent negative demand, the proposed model allows channel members to increase their prices by enhancing WTP of customers. In this study, contrary to similar additive form demand functions applied in the co-op ad literature which limits their studies for cases that profit function is concave with respect to variables, optimal prices and advertising strategies are obtained for all the solution space. Surprisingly for the very high values of the advertising effect coefficient, a finite optimal advertising expenditure is achieved.     

Trade credit competition between two retailers in a supply chain under credit-linked retail price and market demand

The paper considers a supply chain system in which the sole manufacturer supplies the same product to two retailers who compete in offering trade credit period to customers. Both the market demand and retail prices vary with the trade credit periods offered by the retailers. The manufacturer also provides a trade credit period to both the retailers to settle down their accounts. The net profit function of the supply chain is derived considering possible relationships among the trade credit periods offered by the manufacturer and the retailers and the time when each retailer receives the last payment from his customer. An algorithm is developed to find the optimal solution of the proposed model. From the numerical study, it is observed that a two-level trade credit financing can increase profits not only for the manufacturer and the retailers but also for the whole supply chain.     

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.     

交货期差异下的双渠道订货与协调优化策略

由于顾客往往具有不同交货期的期望,从而导致线上与线下渠道冲突加剧,同时也为其进行合作提供了基础。因此针对该问题,以一个开辟线上渠道的制造商和一个线下零售商组成的双渠道供应链系统为研究对象,分别建立了考虑交货期差异下二者合作时的利润优化模型。在此基础上,首先采用不动点定理证明了制造商开辟的线上渠道与线下零售商订货纳什均衡的存在性与唯一性,并探讨了二者均衡订货量与交货期差异率的关系;其次,证明了仅仅采用批发价格与服务费用契约无法协调制造商与线下零售商组成的供应链系统,进一步优化设计了两部定价协调机制,并实现二者的双赢。最后通过算例证明了纳什均衡的存在性以及订货均衡与交货期差异率的关系。     

On channel coordination through revenue-sharing contracts with price and shelf-space dependent demand

This paper deals with the problem of coordinating a vertically separated channel under a consignment contract with revenue sharing. We consider the demand of the downstream player, e.g., the retailer, being price and shelf-space sensitive. Under such a setting, the retailer decides on the revenue-sharing percentage and the slotting fee. And the upstream player, e.g., the manufacturer, decides on the retail price and the size of shelf-space. For each item sold, the retailer deducts an agreed-upon percentage from the selling price and remits the balance to the manufacturer. We model the decision-making of the two firms as a Stackelberg game, and carry out equilibrium analysis for both the centralized and decentralized regimes of the channel, with and without cooperation. In addition, a profit sharing scheme through a two-part slotting allowance is proposed, which leads to Pareto improvements among channel participants. Our analysis reveals that the non-cooperative game tends to set a higher revenue-sharing percentage and lower slotting fee by the retailer, and a higher retail price and less display space by the manufacturer, which leads to a lower channel profit. The consistent bias can be perfectly rectified by the cooperative game through the proposed two-part contractual agreement.     

Launching new products through exclusive sales channels

When launching a new product, a manufacturer usually sells it through competing retailers under non-exclusive arrangements. Recently, many new products (cellphones, electronics, toys, etc.) are sold through a single sales channel via an exclusive arrangement. In this paper we present two separate models that examine these two arrangements. Each model is based on a Stackelberg game in which the manufacturer acts as the leader by setting the wholesale price and the retailers act as the followers by choosing their retail prices. For each model, we solve the Stackelberg game by determining the manufacturer’s optimal wholesale price and each retailer’s optimal retail price in equilibrium. Then we examine the conditions under which the manufacturer should sell the new product through an exclusive retailer. In addition, we examine the impact of postponing the wholesale price decision and the impact of demand uncertainty on the manufacturer’s optimal profit under both arrangements.     

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.     

Coordination of cooperative advertising in a two-level supply chain when manufacturer offers discount

We studied the coordination of cooperative advertisement in a manufacturer–retailer supply chain when the manufacturer offers price deductions to customers. With a price sensitive market, the expected demand with cooperative advertising and price deduction is demonstrated. When the manufacturer is a leader, we obtained the optimal national brand name investment, local advertisement and associated manufacturer’s allowance with any given price deduction. When the manufacturer offers more price deduction to customers, the retailer will increase local advertisement if the manufacturer provides the same portion of the local advertising allowance. We obtained the necessary and sufficient condition for the price deduction to ensure an increase of manufacturer’s profit, and a search procedure for determining such an optimal price deduction is provided as well. When the manufacturer and retailer are partners, we obtained the optimal national brand name investment and local advertisement. For any given price deduction, the total profit for the supply chain with cooperative scheme is always higher than that with the non-cooperative scheme. When price elasticity of demand is larger than one, the resulting closed form optimal price deduction with partnership is also obtained. To increase profits for both parties in a supply chain, we recommend that coordination in local and national cooperative advertising with a partnership relationship between manufacturer and retailer is the best solution. The bargaining results show how to share the profit gain between the manufacturer and the retailer, and determine the associated pricing and advertising policies for both parties.     

A game theoretic approach to coordinate pricing and vertical co-op advertising in manufacturer-retailer supply chains

Vertical cooperative (co-op) advertising is a marketing strategy in which the retailer runs local advertising and the manufacturer pays for a portion of its entire costs. This paper considers vertical co-op advertising along with pricing decisions in a supply chain; this consists of one manufacturer and one retailer where demand is influenced by both price and advertisement. Four game-theoretic models are established in order to study the effect of supply chain power balance on the optimal decisions of supply chain members. Comparisons and insights are developed. These embrace three non-cooperative games including Nash, Stackelberg-manufacturer and Stackelberg-retailer, and one cooperative game. In the latter case, both the manufacturer and the retailer reach the highest profit level; subsequently, the feasibility of bargaining game is discussed in a bid to determine a scheme to share the extra joint profit.     

Stackelberg game models between two competitive retailers in fuzzy decision environment

In this paper, we study the pricing problem in a fuzzy supply chain that consists of a manufacturer and two competitive retailers. There is a single product produced by a manufacturer and then sold by two competitive retailers to the consumers. The manufacturer acting as a leader determines the wholesale price, and the retailers acting as the followers set their sale prices independently. Both the manufacturing cost and the demand for product are characterized as fuzzy variables, we analyze how the manufacturer and the retailers make their pricing decisions with the duopolistic retailers’ different behaviors: competition strategy and collusion strategy, and develop the expected value models in this paper. Finally, numerical examples illustrate the effectiveness of the proposed two-echelon models using fuzzy set theory.     

Coordinating advertising and pricing in a manufacturer–retailer channel

Cooperative advertising is a practice that a manufacturer pays retailers a portion of the local advertising cost in order to induce sales. Cooperative advertising plays a significant role in marketing programs of channel members. Nevertheless, most studies to date on cooperative advertising have assumed that the market demand is only influenced by advertising expenditures but not by retail price. This paper addresses channel coordination by seeking optimal cooperative advertising strategies and equilibrium pricing in a two-member distribution channel. We establish and compare two models: a non-cooperative, leader–follower game and a cooperative game. We develop propositions and insights from the comparison of these models. The cooperative model achieves better coordination by generating higher channel-wide profits than the non-cooperative model with these features: (a) the retailer price is lower to consumers; and (b) the advertising efforts are higher for all channel members. We identify the feasible solutions to a bargaining problem where the channel members can determine how to divide the extra profits.     

碳交易规制下信息不对称供应链的减排和低碳推广博弈研究

论文在碳交易规制下,研究单一制造商和双零售商组成的供应链减排与低碳推广决策以及零售商对制造商的成本信息分享问题,分析了零售商对制造商分享成本信息的条件,及不同情形下的制造商减排和零售商低碳推广策略。研究发现:零售商的最优低碳推广水平只与自身相关参数有关,零售商只有在自身低碳推广效率足够高时才会与制造商分享信息;制造商最优减排量随消费者低碳意识、碳交易价格、零售商低碳推广效率及其不确定性增大而提高,随零售商之间竞争程度提高而降低;无论零售商是否对制造商分享成本信息,供应链成员的最优利润随零售商之间竞争程度提高而增加,随消费者低碳意识、碳交易价格提高而提高;零售商低碳推广效率的不确定性越大则制造商的最优利润越低,零售商的最优利润越高;仅一家零售商分享成本信息时,制造商无法通过转移支付使另一家零售商与其分享信息。     

Supply chain coordination through integration of innovation effort and advertising support

This study integrates firms’ innovation and advertising decisions in a two-echelon supply chain, where a monopoly manufacturer sells products to ultimate consumers through an autonomous retailer. Considering that both innovation and advertising contribute to the product demand, we first investigate the optimal equilibriums of channel members under two different game structures: the non-cooperative and cooperative. In the non-cooperative structure, the manufacturer controls the innovation effort and wholesale price while the retailer controls the advertising rate and retail pricing. In the cooperative structure, the manufacturer agrees to share part of retailer’s advertising expenditure. We find that both the optimal operation and marketing decisions are sensitive to effects of innovation and advertising on demand as well as the manufacturer’s cost reduction coefficient due to innovation. Further, we find that the manufacturer always prefers cooperation. Meanwhile, only when the firms’ investments significantly contribute to the market mechanism, does the retailer have incentive to implement a cooperative program. In addition, we further propose a new two-way subsidy policy to coordinate channel members’ business functions.     

考虑互惠偏好的闭环供应链系统合作机制研究

将互惠偏好引入到闭环供应链系统合作机制中,研究了由一个制造商,一个零售商和一个再制造商组成的三层闭环供应链,运用Stackelberg博弈理论分析了闭环供应链整体及各成员的最优决策问题,并对5种情形(决策模式)下的均衡结果进行比较分析.研究发现在考虑互惠偏好行为下,分散决策模式和局部联盟决策模式下的系统利润低于集中决策模式下的收益;新产品和再制造产品的销售量(零售价格)与制造商对零售商的互惠偏好系数呈正(负)相关,与零售商对制造商的互惠偏好系数呈负(正)相关;5种决策模式的供应链系统利润与制造商对零售商的互惠偏好系数呈正相关,与零售商对制造商的互惠偏好系数呈负相关.     

Manufacturer’s revenue-sharing contract and retail competition

This paper investigates a revenue-sharing contract for coordinating a supply chain comprising one manufacturer and two competing retailers. The manufacturer, as a Stackelberg leader, offers a revenue-sharing contract to two competing retailers who face stochastic demand before the selling season. Under the offered contract terms, the competing retailers are to determine the quantities to be ordered from the manufacturer, prior to the season, and the retail price at which to sell the items during the season. The process of pricing and ordering is expected to result in an equilibrium as in the Bayesian Nash game. On the basis of anticipated responses and actions of the retailers, the manufacturer designs the revenue-sharing contract. Adopting the classic newsvendor problem model framework and using numerical methods, the study finds that the provision of revenue-sharing in the contract can obtain better performance than a price-only contract. However, the benefits earned under the revenue-sharing contract by different supply chain partners differ because of the impact of demand variability and price-sensitivity factors. The paper also analyses the impact of demand variability on decisions about optimal retail price, order quantity and profit sharing between the manufacturer and the retailers. Lastly, it investigates how the competition (between retailers) factor influences the decision-making of supply chain members in response to uncertain demand and profit variability.     

Co-op advertising models in manufacturer–retailer supply chains: A game theory approach

In the literature of cooperative (co-op) advertising, the focus of research is on a relationship in which a manufacturer is the leader and retailers are followers. This relationship implies the dominance of the manufacturer over retailers. Recent market structure reviews have shown a shift of retailing power from manufacturers to retailers. Retailers have equal or even greater power than a manufacturer when it comes to retailing. Based on this new market phenomenon, we intend to explore the role of vertical co-op advertising efficiency with respect to transactions between a manufacturer and a retailer through brand name investments, local advertising expenditures, and sharing rules of advertising expenses. Three co-op advertising models are discussed which are based on two noncooperative games and one cooperative game. In a leader–follower noncooperative game, the manufacturer is assumed to be a leader who first specifies the brand name investment and the co-op subsidization policy. The retailer, as a follower, then decides on the local advertising level. In a noncooperative simultaneous move game, the manufacturer and the retailer are assumed to act simultaneously and independently. In a cooperative game, the system profit is maximized for every Pareto efficient co-op advertising scheme, but not for any other schemes. All Pareto efficient co-op advertising schemes are associated with a single local advertising level and a single brand name investment level, but with variable sharing policies of advertising expenses. The best Pareto efficient advertising scheme is obtained taking members' risk attitudes into account. Utilizing the Nash bargaining model, we discuss two situations that (a) both members are risk averse, and (b) both members are risk neutral. Our results are consistent with the bargaining literature.     

供应中断下最优分配和应急采购策略的比较

最优分配采购策略和应急采购策略被广泛应用于供应中断风险管理中,基于最优分配采购策略和应急采购策略,研究了由两个制造商与两个零售商组成的两级供应链在供应中断下的订购和生产决策问题,给出了最优订购和最优生产策略.通过数值例子就可靠性如何影响制造商的最优价格和利润进行了比较.结果表明:随着可靠性的增加,两个制造商的最优价格呈递减态势,且制造商A的递减幅度小于制造商B的递减幅度;当可靠性低于0.3时,制造商A的最优价格低于制造商B的最优价格,当可靠性高于0.3时,制造商A的最优价格高于制造商B的最优价格.随着可靠性的增加,制造商A的利润呈递减态势,制造商B的利润呈递增态势;当可靠性低于0.8时,制造商A的利润高于制造商B的利润,当可靠性低高于0.8时,制造商A利润低于制造商B的利润.     

Resale price maintenance in supply chains with general multiplicative demand

We analyze a supply chain with a Resale Price Maintenance (RPM) contract in which the manufacturer sets the retail price with a general multiplicative price–demand function and prove the existence/uniqueness of an equilibrium. We also compare the equilibrium prices and quantities, consumer surplus and total system welfare for the RPM and wholesale price contracts. We conclude that a manufacturer may capture a smaller share of the total supply chain profit despite her ability to set the retail price.     

A collaborative decentralized distribution system with demand forecast updates

In this paper, we study inventory pooling coalitions within a decentralized distribution system consisting of a manufacturer, a warehouse (or an integration center), and n retailers. At the time their orders are placed, the retailers know their demand distribution but do not know the exact value of the demand. After certain production and transportation lead time elapses, the orders arrive at the warehouse. During this time, the retailers can update their demand forecasts.We first focus on cooperation among the retailers - the retailers coordinate their initial orders and can reallocate their orders in the warehouse after they receive more information about their demand and update their demand forecasts. We study two types of cooperation: forecast sharing and joint forecasting. By using an example, we illustrate how forecast sharing collaboration might worsen performance, and asymmetric forecasting capabilities of the retailers might harm the cooperation. However, this does not happen if the retailers possess symmetric forecasting capabilities or they cooperate by joint forecasting, and the associated cooperative games have non-empty cores.Finally, we analyze the impact that cooperation and non-cooperation of the retailers has on the manufacturer’s profit. We focus on coordination of the entire supply chain through a three-parameter buyback contract. We show that our three-parameter contract can coordinate the system if the retailers have symmetric margins. Moreover, under such a contract the manufacturer benefits from retailers’ cooperation since he can get a share of improved performance.