Vertical cooperative advertising and pricing decisions in a manufacturer–retailer supply chain: A game-theoretic approach

Manufacturers can increase the advertising expenditures of their retailers by bearing a fraction of the occurring costs within the framework of a vertical cooperative advertising program. We expand the existing research which deals with advertising and pricing decisions in a manufacturer–retailer supply chain contemporaneously. By means of game theory, four different relationships between the channel members are considered: Firstly, three non-cooperative games with either symmetrical distribution of power or asymmetrical distribution with one player being the leader in each case, and one cooperative game where both players tend to maximize the total profit. The latter is complemented by a bargaining model, which proposes a fair split of profit on the basis of the players’ risk attitude and bargaining power. Our main findings are as follows: (a) In contrast to previous analyses, we do not limit the ratio between manufacturer’s and retailer’s margin, which provides more general insights into the effects of the underlying distribution of power within the channel. (b) The highest total profit is gained when both players cooperate. This behavior puts also the customers in a better position, as it produces the lowest retail price as well as the highest advertising expenditures compared to the other configurations.     

Optimal contracts and the manufacturer’s pricing strategies in a supply chain with an inequity-averse retailer

Studies in the supply chain literature have typically focused on profit or revenue maximization and assumed that agents within the supply chain are self-interested and only care about their own monetary payoffs. Research in these areas, however, rarely considers an important phenomenon called inequity aversion in which the object pursued by agents within the supply chain is not only their own profit maximization but also the equity of profit allocation. In fact, when agents within a supply chain collaborate with each other to serve a market, the scheme of profit allocation between them usually plays a determinate role in cooperation. Taking into account the impact of agents’ behavior of inequity aversion on the coordination of the supply chain, this paper investigates the optimal contracts and the manufacturer’s pricing strategies in a single-manufacturer and single-retailer supply chain. In this way, we obtain two interesting results: (1) the retailer’s equity aversion largely affects the manufacturer’s decision making, which is not always bad for the manufacturer; and (2) the retailer’s inequity aversion as well as the consumer’s price-sensitive coefficient plays a dominant role in the manufacturer’s decision making.     

Coordination of a three-level supply chain (supplier–manufacturer–retailer) with permissible delay in payments and price discounts

Different coordination mechanisms are used to manage supply chains. This paper investigates a coordination of a three-level supply chain (supplier–manufacturer–retailer) by coupling two well-known trade credit mechanisms that are widely used in practice, permissible delay in payments and price discounts, where the length of the delay period and discounts offered along the supply chain are decision variables. The paper investigates nine different cases of delay in payments along with eight cases of price discounts among the three players in the supply chain. A numerical example was presented to compare between the cases considered. Also, extensive sensitivity analyses were performed to study the effect of changing the model parameters on the optimal decisions. In addition, we point out the limitations of each model developed in this paper. The numerical examples and the sensitivity analyses conclude that the coupling of delay in payments and price discounts increases the profit of the supply chain more than using only a single mechanism at a time.     

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.     

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.     

Establishing Nash equilibrium of the manufacturer–supplier game in supply chain management

We study a game model of multi-leader and one-follower in supply chain optimization where n suppliers compete to provide a single product for a manufacturer. We regard the selling price of each supplier as a pre-determined parameter and consider the case that suppliers compete on the basis of delivery frequency to the manufacturer. Each supplier's profit depends not only on its own delivery frequency, but also on other suppliers' frequencies through their impact on manufacturer's purchase allocation to the suppliers. We first solve the follower's (manufacturer's) purchase allocation problem by deducing an explicit formula of its solution. We then formulate the n leaders' (suppliers') game as a generalized Nash game with shared constraints, which is theoretically difficult, but in our case could be solved numerically by converting to a regular variational inequality problem. For the special case that the selling prices of all suppliers are identical, we provide a sufficient and necessary condition for the existence and uniqueness of the Nash equilibrium. An explicit formula of the Nash equilibrium is obtained and its local uniqueness property is proved.     

Principal–agent problem for returns handling in a reverse supply chain with one manufacturer and two competing dealers

Focusing on the principal–agent problem in handling new-products returned by customers in a reverse supply chain with one manufacturer and two competing dealers, we investigate how a manufacturer motivates her dealers to exert their efforts to handle and sell the returned new-products using mathematical modelling. By taking into consideration the dealers’ individual rationalities, we design optimal incentive contracts under both symmetric and asymmetric information and obtain the following insights. In the symmetric information situation, dealers’ effort levels are identical to those maximising the expected overall profit of the supply chain. In the asymmetric information situation, however, the dealers’ effort levels are lower than the supply chain optimum. Further, in the case of intensifying competition between the dealers, their effort levels increase, while each dealer’ revenue share received from the manufacturer decreases and the risk, incentive and total agency costs of the entire supply chain tend to diminish. The revenue share is inversely correlated with return uncertainties. When we introduce another random environmental factor affecting returns into the incentive contract, this revenue share increases with a rise in dealers’ effort levels, while the above-mentioned costs of the entire system decline and this improves the supply chain system coordination. The incorporation of fairness into the principal–agent model promotes a further increase in the dealers’ effort levels, which is proved using the fixed-point theorem. Finally, we provide an example to demonstrate the main results.     

Qualifying for a government’s scrappage program to stimulate consumers’ trade-in transactions? Analysis of an automobile supply chain involving a manufacturer and a retailer

We investigate an automobile supply chain where a manufacturer and a retailer serve a market with a fuel-efficient automobile under a scrappage program by the government. The program awards a subsidy to each consumer who trades in his or her used automobile with a new fuel-efficient automobile, if the manufacturer’s suggested retail price (MSRP) for the new one does not exceed a cutoff level. We derive the conditions assuring that the manufacturer has an incentive to qualify for the program, and find that when the cutoff level is low, the manufacturer may be unwilling to qualify for the program even if the subsidy is high. We also show that when the manufacturer qualifies for the program, increasing the MSRP cutoff level would raise the manufacturer’s expected profit but may decrease the expected sales. A moderate cutoff level can maximize the effectiveness of the program in stimulating the sales of fuel-efficient automobiles, whereas a sufficiently high cutoff level can result in the largest profit for the manufacturer. The retailer’s profit always increases when the manufacturer chooses to qualify for the program. Furthermore, we compute the government’s optimal MSRP cutoff level and subsidy for a given sales target, and find that as the program budget increases, the government should raise the subsidy but reduce the MSRP cutoff level to maximize sales.     

A game theory approach in seller–buyer supply chain

In this paper, several seller–buyer supply chain models are proposed which incorporate both cost factors as well as elements of competition and cooperation between seller and buyer. We assume that unit marketing expenditure and unit price charged by the buyer influence the demand of the product being sold. The relationships between seller and buyer will be modeled by non-cooperative and cooperative games, respectively. The non-cooperative game is based on the Stackelberg strategy solution concept, where we consider separately the case when the seller is the leader (Seller-Stackelberg) and also when the buyer is the leader (Buyer-Stackelberg). Pareto efficient solutions will be provided for the cooperative game model. Numerical examples presented in this paper, including sensitivity analysis of some key parameters, will compare the results between different models considered.     

Value of supplier’s capacity information in a two-echelon supply chain

In traditional supply chain models it is generally assumed that full information is available to all parties involved. Although this seems reasonable, there are cases where chain members are independent agents and possess different levels of information. In this study, we analyze a two-echelon, single supplier-multiple retailers supply chain in a single-period setting where the capacity of the supplier is limited. Embedding the lack of information about the capacity of the supplier in the model, we aim to analyze the reaction of the retailers, compare it with the full-information case, and assess the value of information and the effects of information asymmetry using game theoretic analysis. In our numerical studies, we conclude that the value of information is highly dependent on the capacity conditions and estimates of the retailers, and having information is not necessarily beneficial to the retailers.     

Retailer or e-tailer? Strategic pricing and economic-lot-size decisions in a competitive supply chain with drop-shipping

Drop-shipping is an arrangement whereby an e-tailer, who does not hold inventories, processes orders and requests a manufacturer to ship products directly to the end customers. To explore the economic benefits of adopting drop-shipping distribution strategy in a competitive environment, we investigate the profitability and the efficiency of the drop-shipping channel as compared to the traditional channel. Specifically, we develop Economic Order Quantity (EOQ) games with pricing and lot-sizing decisions to examine the strategic interactions between a manufacturer and its retailer/e-tailer in the traditional/drop-shipping distribution channels. We identify conditions under which the drop-shipping channel profitably outperforms the traditional one. It is found that the economic interests of adopting drop-shipping distribution for the channel members may not always be consistent. There are cases where only the manufacture would favour drop-shipping. In this study, we also reveal that the inefficiency caused by lack of coordination in the traditional channel can be alleviated in the drop-shipping channel where the lot-sizing decision is made by the manufacturer.     

Dynamic conformance and design quality in a supply chain: an assessment of contracts’ coordinating power

We consider a two-echelon supply chain involving one manufacturer and one supplier who collaborate on improving both design and conformance quality. Design quality is supposed to increase product desirability, and therefore market demand, while conformance quality should reduce the proportion of defective items, and therefore increase the manufacturer’s sales revenue. We investigate how the supply chain parties allocate effort between design and conformance quality under both cooperative and non-cooperative settings in an intertemporal framework. Furthermore, we evaluate wholesale price contracts and revenue-sharing contracts in terms of their performance and coordination power. We show that although a revenue-sharing contract enables the manufacturer to effectively involve the supplier in quality improvement, neither contract type allows for perfect coordination resulting in the quality that can be achieved by a cooperative supply chain. We thus suggest a reward-based extension to the revenue-sharing contract, to ensure system-wide optimal quality performance. Importantly, we find that the supplier would be better off adopting a reward-based revenue sharing contract and refusing a standard revenue-sharing contract, while the opposite would be true for the manufacturer.     

Seller’s optimal credit period and replenishment time in a supply chain with up-stream and down-stream trade credits

In practice, a supplier often offers its retailers a permissible delay period M to settle their unpaid accounts. Likewise, a retailer in turn offers another trade credit period N to its customers. The benefits of trade credit are not only to attract new buyers who consider it a type of price reduction, but also to provide a competitive strategy other than introduce permanent price reductions. On the other hand, the policy of granting credit terms adds an additional cost to the seller as well as an additional dimension of default risk. In this paper, we first incorporate the fact that trade credit has a positive impact on demand but negative impacts on costs and default risks to establish an economic order quantity model for the seller in a supply chain with up-stream and down-stream trade credits. Then we derive the necessary and sufficient conditions to obtain the optimal replenishment time and credit period for the seller. Finally, we use some numerical examples to illustrate the theoretical results.     

Subsidizing to disrupt a terrorism supply chain—a four-player game

Terrorism with weapons of mass destruction (WMDs) is an urgent threat to homeland security. The process of counter-WMD terrorism often involves multiple government and terrorist group players, which is under-studied in the literature. In this paper, first we consider two subgames: a proliferation game between two terrorist groups or cells (where one handling the black market for profits proliferates to the other one to attack, and this is modelled as a terrorism supply chain) and a subsidization game between two governments (where one potential WMD victim government subsidizes the other host government, who can interfere with terrorist activities). Then we integrate these two subgames to study how the victim government can use the strategy of subsidization to induce the host government to disrupt the terrorism supply chain. To our knowledge, this is the first game-theoretic study for modelling and optimally disrupting a terrorism supply chain in a complex four-player scenario. We find that in the integrated game, when proliferation payment is high or low, the practical terrorist group will proliferate and not proliferate, respectively, regardless of government decisions. In contrast, in the subsidization subgame between the two governments, the decision of subsidization depends on its cost. When proliferation payment is medium, the decision of subsidization depends on not only its cost but also the preparation cost and the attacking cost. Findings from our results would assist in government policymaking.     

Impurity modes in a curved Fermi–Pasta–Ulam chain

The spatial localization properties of nonlinear excitations/modes supported by a curved Fermi–Pasta–Ulam (FPU) lattice chain in presence of an isolated impurity of mass lighter or heavier than the host mass, is investigated. The impurity modes oscillate locally at and around the impurity site. It is examined that a light-mass impurity mode fulfills non-resonance with the linear (or phonon) spectrum because its frequency is located above the phonon band whereas frequency of a heavy-mass impurity mode drops into the phonon band. The phenomenon of resonance of impurities with plane waves explains the lifetimes of localized impurity modes in the nonlinear system.     

Facility location and supply chain management – A review

Facility location decisions play a critical role in the strategic design of supply chain networks. In this paper, a literature review of facility location models in the context of supply chain management is given. We identify basic features that such models must capture to support decision-making involved in strategic supply chain planning. In particular, the integration of location decisions with other decisions relevant to the design of a supply chain network is discussed. Furthermore, aspects related to the structure of the supply chain network, including those specific to reverse logistics, are also addressed. Significant contributions to the current state-of-the-art are surveyed taking into account numerous factors. Supply chain performance measures and optimization techniques are also reviewed. Applications of facility location models to supply chain network design ranging across various industries are presented. Finally, a list of issues requiring further research are highlighted.     

Pricing industry loss warranties in a Lévy–Frailty framework

We propose a novel risk-neutral pricing approach for industry loss warranties. In doing so, we explicitly take into account the statistical dependence of the losses on individual policies in the underlying insurance portfolio, caused by the occurrence of a natural catastrophe. Inspired by recent advances in the structured credit literature, we model joint claim events in a Lévy–Frailty framework with a stochastic time change. Event time is driven by rare and large jumps of a compound Poisson subordinator and thus elapses more quickly when a natural catastrophe has struck, leading to a clustering of losses. We estimate the model on historical ILW quotes and obtain encouraging fit statistics.     

Modeling the synergy level in a vertical collaborative supply chain through the IMP interaction model and DEA framework

This work develops a mathematical programming model that characterizes the main variables present in the interaction dynamics of each agent in a collaborative vertical logistical system, such as a supply chain, and measures the synergy level of such system. The model is based on the interaction model developed by the IMP (Industrial Marketing and Purchasing) group and also on the DEA (Data Envelopment Analysis) framework. The basics of these two approaches allow modeling of the characteristics of an agent as well as the collaborative relationships with other agents within the chain. The model was validated using information of supply chain of leather and its products, classified by DANE (Departamento Nacional de Estadistica—Colombia) as the sector CIIU323.