On a cooperative advertising model for a supply chain with one manufacturer and one retailer

, , ,  and  recently studied a game-theoretic model for cooperative advertising in a supply chain consisting of one manufacturer and one retailer. However, the sales-volume (demand) function considered in this model can become negative for some values of the decision variables, and in fact, this does happen for the proposed Stackelberg and Nash equilibrium solutions. Yue et al. (2006) acknowledge the negativity problem and suggest two constraints to fix it; however, they do not incorporate these constraints into their mathematical analysis. In this paper, we show that the results obtained by analyzing the advertising model under the constraints suggested by Yue et al. can differ significantly from those obtained in the previous papers.     

Retail competition and cooperative advertising

We consider a cooperative advertising channel consisting of a manufacturer selling its product through a retailer in competition with another independent retailer. The manufacturer subsidizes its retailer’s advertising only when a certain threshold is positive. Moreover, the manufacturer’s support for its retailer is higher under competition than in its absence.     

Coordination of supply chains by option contracts: A cooperative game theory approach

Manufacturer–retailer supply chains commonly adopt a wholesale price mechanism. This mechanism, however, has often led manufacturers and retailers to situations of conflicts of interest. For example, due to uncertain market demand, retailers prefer to order flexibly from manufacturers so as to avoid incurring inventory costs and to be able to respond flexibly to market changes. Manufacturers, on the other hand, prefer retailers to place full orders as early as possible so that they can hedge against the risks of over- and under-production. Such conflicts between retailers and manufacturers can result in an inefficient supply chain. Motivated by this problem, we take a cooperative game approach in this paper to consider the coordination issue in a manufacturer–retailer supply chain using option contracts. Using the wholesale price mechanism as a benchmark, we develop an option contract model. Our study demonstrates that, compared with the benchmark based on the wholesale price mechanism, option contracts can coordinate the supply chain and achieve Pareto-improvement. We also discuss scenarios in which option contracts are selected according to individual supply chain members’ risk preferences and negotiating powers.     

A note on channel performance under consignment contract with revenue sharing

Wang et al. [Y. Wang, L. Jiang, Z.J. Shen, Channel performance under consignment contract with revenue sharing. Management Science 50 (2004), 34–47] indicate that a decentralized supply chain cannot be perfectly coordinated. This note provides a cooperative game model that implements profit sharing between the manufacturer and the retailer to achieve their cooperation. When the manufacturer and the retailer are assumed to be risk-neutral, under a very mild restriction on the demand distribution function, the cooperative game model can achieve its unique equilibrium solution in iso-price-elastic or linear demand case. Under the revenue sharing agreement attached with the equilibrium payment scheme, the decentralized supply chain can be perfectly coordinated.     

The impact of consumer returns policies on consignment contracts with inventory control

We consider a consignment contract with consumer non-defective returns behavior. In our model, an upstream vendor contracts with a downstream retailer. The vendor decides his consignment price charged to the retailer for each unit sold and his refund price for each returned item, and then the retailer sets her retail price for selling the product. The vendor gets paid based on net sold units and salvages unsold units as well as returned items in a secondary market. Under the framework, we study and compare two different consignment arrangements: the retailer/vendor manages consignment inventory (RMCI/VMCI) programs. To study the impact of return policy, we discuss a consignment contract without return policy as a benchmark. We show that whether or not the vendor offers a return policy, it is always beneficial for the channel to delegate the inventory decision to the vendor. We find that the vendor’s return policy depends crucially on the salvage value of returns. If the product has no salvage value, the vendor’s optimal decision is not to offer a return policy; otherwise, the vendor can gain more profit by offering a return policy when the salvage value turns out to be positive.     

Delayed effects of cooperative advertising in goodwill dynamics

This paper proposes a tool to control cooperative advertising which increases the goodwill of companies operating in a competitive market. We introduce the lag between advertising exposure and customer reaction in the goodwill dynamics evolved à la Nerlove–Arrow. As a result, we obtain a cooperative differential game with immediate and delayed effects of control variables for which we investigate the optimal solution. We examine the role the pre-coalition programmes and the length of delayed response in generating goodwill.     

Optimal promotion planning—depth and frequency—for a two-stage supply chain under Markov switching demand

In considering the retailer–supplier supply chain, this paper analyzes how a retailer reasonably decides both the depth and frequency of the price discount promotion including or excluding a supplier’s inventory decision. Assuming that the promotion frequency used by the retailer is probabilistic, we model a promotion-inventory decision under an AR(1) demand with a Markov switching promotion regime. After obtaining the optimal promotion plan, our analysis also considers the behavior of the optimal promotion decision; the retailer’s price format selection, either an Every-Day-Low-Price policy (EDLP) or a Promotion policy (HiLo); and the impact of information sharing of promotion status on the system’s performance. Our results suggest that a retailer tends to overpromote if inventory cost is excluded in its promotion decision, that increasing the market share is a preferable action for both the retailer and the supplier, that total margin and price-elasticity play an important role in selecting the price format, and that the profitability for a supplier of sharing promotion information depends on the transition probabilities of the Markov switching regime.     

Markdown money contracts for perishable goods with clearance pricing

It is common in practice that retailers liquidate unsold perishable goods via clearance pricing. Markdown money is frequently used between manufacturers and retailers in such a supply chain setting. It is a form of rebate from a manufacturer to subsidize a retailer’s clearance pricing after the regular season. Two forms of markdown money are percent markdown money, in which the markdown money is limited to only a certain percentage of the retail price markdown, and quantity markdown money, which is essentially a buyback contract or returns policy with a rebate credit paid to the retailer for each unsold unit after the regular season. We show both forms of markdown money contracts can coordinate the supply chain and we discuss their strengths and limitations.     

Inventory systems with stochastic demand and supply: Properties and approximations

We model a retailer whose supplier is subject to complete supply disruptions. We combine discrete-event uncertainty (disruptions) and continuous sources of uncertainty (stochastic demand or supply yield), which have different impacts on optimal inventory settings. This prevents optimal solutions from being found in closed form. We develop a closed-form approximate solution by focusing on a single stochastic period of demand or yield. We show how the familiar newsboy fractile is a critical trade-off in these systems, since the optimal base-stock policies balance inventory holding costs with the risk of shortage costs generated by a disruption.     

An empirical study on the Lanchester model of combat for competitive advertising decisions

This paper presents an empirical study on the Lanchester model of combat for competitive advertising decisions. Three issues are evaluated: (i) the specification of the market share response model; (ii) the effect of inflation on the estimation of the response model; and (iii) the performance of competitive strategies. It is shown that (a) the square root function that is used in previous studies is often inappropriate to characterize the market share response model; (b) market share variations are more responsive to current advertising expenditures; (c) closed-loop Nash equilibrium strategies are better competitive advertising strategies for firms to maximize profits than open-loop Nash equilibrium strategies; and (d), finally, general perfect equilibria Nash equilibrium strategies developed by Case are usually not good competitive advertising strategies for firms to maximize profits.     

Cooperative game theory approach to allocating benefits of horizontal cooperation

Logistics costs in general, and transportation costs in particular, represent a large fraction of the operating costs of many companies. One way to try to reduce these costs is through horizontal cooperation among shippers. Thus, when the transportation needs of two or more companies are merged, their collective transportation requirements can be met at lower cost. The attainable cost savings are due to economies of scale, which translate into cheaper rates due to increased negotiation power, use of larger vehicles and bundling of shipments. In this paper, a linear model is presented and used to study the cost savings that different companies may achieve when they merge their transportation requirements. On the one hand, solving this optimization model for different collaboration scenarios allows testing and quantifying the synergies among different potential partners, thus identifying the most profitable collaboration opportunities. On the other, the problem of allocating the joint cost savings of the cooperation is tackled using cooperative game theory. The proposed approach is illustrated with an example in which different cooperative game solution concepts are compared. Extensive numerical experiments have also been carried out to gain insight into the properties of the corresponding cost savings game and the behavior of the different solution concepts.     

随机需求下供应商管理库存的供应链模型

以一个供应商和一个零售商的两阶段供应链为背景,利用报童模型给出了供应商管理库存(VMI)的供应链模型,在需求服从均匀分布的条件下得出解析解,并与传统的零售商管理库存(RMI)系统作了比较,分析了这两种情况下批发价和订货量的变化.数值结果表明VMI导致了批发价的缩减,但提高了订货量,VMI减轻了双重边际效应,系统利润多于传统的RMI系统.     

A survey of game-theoretic models of cooperative advertising

The paper surveys the literature on cooperative advertising in marketing channels (supply chains) using game theoretic methods. During the last decade, in particular, this literature has expanded considerably and has studied static as well as dynamic settings. The survey is divided into two main parts. The first one deals with simple marketing channels having one supplier and one reseller only. The second one covers marketing channels of a more complex structure, having more than one supplier and/or reseller.     

Long-term and penalty contracts in a two-stage supply chain with stochastic demand

Recent applications of game-theoretic analysis to supply chain efficiency have focused on constructs between a buyer (the retailer or manufacturer) and a seller (the supplier) in successive stages of a supply chain. If demand for the final product is stochastic then the supplier has an incentive to keep its capacity relatively low to avoid creating unneeded capacity. The manufacturer, on the other hand, prefers the supplier’s capacity to be high to ensure that the final demand is satisfied. The manufacturer therefore constructs a contract to induce the supplier to increase its production capacity. Most research examines contracting when final demand is realized after the manufacturer places its order to the supplier. However, if final demand is realized before the manufacturer places its order to the supplier, these types of contracts can be ineffective. This paper examines two contracts under the latter timing scenario: long-term contracts in which the business relationship is repeated, and penalty contracts in which the supplier is penalized for too little capacity. Results indicate long-term contracts increase the profit potential of the supply chain. Furthermore, the penalty contracts can ensure that the supplier chooses a capacity level such that the full profit potential is achieved.     

Coordination of cooperative cost-reduction efforts in a supply chain partnership

We study cooperative cost reduction in a decentralized supply chain with a single manufacturer and multiple suppliers. The manufacturer assembles components that are procured from the suppliers to produce a final product. Both the manufacturer and the suppliers invest in reducing the unit production costs of the components. We see that neither of the two well-known conventional contracts, the wholesale price contract and the cost-plus pricing contract, generally coordinates the supply chain, i.e., under both of these types of contract, the individual optimal cost-reduction efforts of players deviate from the centralized system-optimal solution. However, this result is not surprising because these contracts encourage either only the manufacturer or only the suppliers alone to invest in cost reduction.     

The role of store brand positioning for appropriating supply chain profit under shelf space allocation

We consider a retailer’s decision of developing a store brand (SB) version of a national brand (NB) and the role that its positioning strategy plays in appropriating the supply chain profit. Since the business of the retailer can be regarded as selling to NB manufacturers the shelf space at its disposal, we formulate a game-theoretical model of a single-retailer, single-manufacturer supply chain, where the retailer can decide whether to launch its own SB product and sells scarce shelf-space to a competing NB in a consumer good category. As a result, the most likely equilibrium outcome is that the available selling amount of each brand is constrained by the shelf-space available for its products and both brands coexist in the category. In this paper, we conceptualize the SB positioning that involves both product quality and product features. Our analysis shows that when the NB cross-price effect is not too large, the retailer should position its SB’s quality closer to the NB, more emphasize its SB’s differences in features facing a weaker NB, and less emphasize its SB’s differences in features facing a stronger NB. Our results stress the importance of SB positioning under the shelf-space allocation, in order to maximize the retailer’s value appropriation across the 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.     

Coordination of supply chains with bidirectional option contracts

In this paper we develop a supply contract for a two-echelon manufacturer–retailer supply chain with a bidirectional option, which may be exercised as either a call option or a put option. Under the bidirectional option contract, we derive closed-form expressions for the retailer’s optimal order strategies, including the initial order strategy and the option purchasing strategy, with a general demand distribution. We also analytically examine the feedback effects of the bidirectional option on the retailer’s initial order strategy. In addition, taking a chain-wide perspective, we explore how the bidirectional option contract should be set to attain supply chain coordination.     

The Leitmann-Schmitendorf advertising game with n players and time discounting

The extension of the Leitmann-Schmitendorf advertising game to n players and positive time discounting is investigated. We show that the strong time consistency of the open-loop Nash equilibrium is preserved. As to optimal controls, while the boundary solution is unaffected by the number of firms as well as discounting, the inner solution depends on industry structure. The fully symmetric version of the game allows us to identify the parameter regions wherein both solutions are sustainable.     

Measuring endogenous supply chain volatility: Beyond the bullwhip effect

Most recent research on supply chain volatility has focused on one particular dimension of that volatility, namely the amplification of upstream order variability. While not ignoring this aspect of supply chain volatility, we focus on a different but equally critical aspect of volatility: the cyclical oscillation of on-hand and on-order inventories about their target values. We prove that such cyclicality does not require oscillatory or random retailer demand as a prerequisite; the resulting volatility is therefore endogenous rather than simply an amplification of exogenous demand inputs. We also measure the amount of amplification resulting from a step increase in demand. The order amplification is the product of two factors, each of which is clearly linked to either on-hand or on-order inventory. Our results attest that supply chain volatility can arise in the absence of exogenous oscillatory or random demand and suggest strategies for avoiding or minimizing such volatility.