Supply quality management with wholesale price and revenue-sharing contracts under horizontal competition

In a number of industries (e.g., the airplane industry, aerospace industry, auto industry, or computer industry), certain suppliers essentially have a monopoly on the production technology for key components, and inevitably manufacturers in these industries have common suppliers. A key part of manufacturers’ work with suppliers concerns improving the quality of their respective products, which gives rise to a collaborative activity usually termed as “supply quality management”. When the manufacturers are competitors, they do not wish to see a common supplier dividing his involvement in quality improvement unequally between themselves and their rivals. However, as the suppliers collaborate with several manufacturers, it is highly questionable whether their efforts will be strictly equivalent for each manufacturer. In this paper, a non-cooperative dynamic game is formulated in which a single supplier collaborates with two manufacturers on design quality improvements for their respective products. The manufacturers compete for market demand both on price and design quality. The paper analyzes how each party should allocate resources for quality improvement over time. In order to take into account the potential coordinating power of the compensation scheme adopted in this type of decentralized setting, we compare the possible outcomes under a wholesale price contract and a revenue-sharing contract.     

Flexible supply contracts under price uncertainty

This article develops supply contracts covering environments with changing prices. We investigate characterization properties of the price processes, while considering costs and discount factors. We determine expressions of the contract’s expected low price and its second moment for a given horizon. We then employ these expected price and second moment values to identify an expected optimum time before the contract expires at which the lowest price occurs. Simulation experiments verify our analysis, and they illustrate how the optimum purchase time decreases as the drift term increases.     

Revenue-sharing versus wholesale price mechanisms under different channel power structures

We consider a supply chain channel with two manufacturers and one retailer. Each manufacturer can choose either a wholesale price contract or a revenue-sharing contract with the retailer. We discuss and compare the results of two different types of contracts under different channel power structures, to check whether it is beneficial for manufacturers to use revenue-sharing contracts under different scenarios. Then we consider a supply chain channel with one manufacturer and two retailers. Each retailer can choose either a wholesale price contract or a revenue-sharing contract with the manufacturer. We analyze the likely outcomes under different scenarios to discover whether it is beneficial to use revenue-sharing contracts.     

Marketing-driven channel coordination with revenue-sharing contracts under price promotion to end-customers

This paper explores the equilibrium behavior of a basic supplier-retailer distribution channel with and without revenue-sharing contracts under price promotion to end-customers. Three types of promotional demand patterns characterized by different features of dynamic price sensitivity are considered to rationalize price promotional effects on end-customer demands. Under such a retail price promotion scheme, this work develops a basic model to investigate decentralized channel members’ equilibrium decisions in pricing and logistics operations using a two-stage Stackelberg game approach. Extending from the basic model, this work further derives the equilibrium solutions of the dyadic members under channel coordination with revenue-sharing contracts. Analytical results show that under certain conditions both the supplier and retailer can gain more profits through revenue-sharing contracts by means of appropriate promotional pricing strategies. Moreover, the supplier should provide additional economic incentives to the retailer. Furthermore, a counter-profit revenue-sharing chain effect is found in the illustrative examples. Such a phenomenon infers that the more the retailer requests to share from a unit of sale the more it may lose under the revenue-sharing supply chain coordination scheme.     

Side-payment contracts in two-person nonzero-sum supply chain games: Review,discussion and applications

This paper investigates supply chain coordination with side-payment contracts. We first summarize specific side-payment contracts and present our review on the literature that developed general side-payment schemes to coordinate supply chains. Following our review, we discuss two criteria that a proper side-payment contract must satisfy, and accordingly introduce a decision-dependent transfer payment function and a constant transfer term. We present the condition that the transfer function must satisfy, and use Nash arbitration scheme and Shapley value to compute the constant transfer term and derive its closed-form solution. Next, we provide a five-step procedure for the development of side-payment contract, and apply it to four supply chain games: Cournot and Bertrand games, a two-retailer supply chain game with substitutable products and a one-supplier, one-retailer supply chain. More specifically, for the Cournot game, we construct a linear transfer function and a constant side-payment to coordinate two producers. For the Bertrand game, we build a nonlinear transfer function which is equivalent to a revenue-sharing contract, and show that the constant term is zero and two firms in the game equally share the system-wide profit. For a supply chain with substitutable products, we present a side-payment contract to coordinate two retailers. For a two-echelon supply chain, we develop a proper side-payment scheme that can coordinate the supply chain and also help reduce the impact of forward buying on supply chain performance.     

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.     

Consignment contracts with retail competition

Consignment contracts have been widely employed in many industries. Under such contracts, items are sold at a retailer’s but the supplier retains the full ownership of the inventory until purchased by consumers; the supplier collects payment from the retailer based on actual units sold. We investigate how competition among retailers influences the supply chain decisions and profits under different consignment arrangements, namely a consignment price contract and a consignment contract with revenue share. First, we investigate how these two consignment contracts and a price only contract compare from the perspective of each supply chain partner. We find that the retailers benefit more from a consignment price contract than from a consignment contract with revenue share or a price only contract, regardless of the level of retailer differentiation. The supplier’s most beneficial contact, however, critically depends upon the level of retailer differentiation: a consignment contract with revenue share is preferable for the supplier if retailer differentiation is strong; otherwise a consignment price contract is preferable. Second, we study how retailer differentiation affects the profits of all supply chain partners. We find that less retailer differentiation improves the supplier’s profit for both types of consignment contract. Moreover, less retailer differentiation improves profits of the retailers in a consignment price contract, but not necessarily in a consignment contract with revenue share.     

The coordinating contracts for a fuzzy supply chain with effort and price dependent demand

This paper investigates the coordination of a two-echelon supply chain with fuzzy demand that is dependent on both retail price and sales effort. In contrast with the centralized and decentralized decision models, two coordinating models based on symmetric information and asymmetric information about retailer’s scale parameter are developed by game theory, and the corresponding analytical solutions are obtained. Theoretical analysis and numerical examples yield the maximal supply chain profits in two coordination situations are equal to that in the centralized situation and greater than that in the decentralized situation. Furthermore, under asymmetric information contract, the maximal expected profit obtained by the low-scale-level retailer is higher than that under symmetric information contract.     

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.     

On the role of revenue-sharing contracts in supply chains

The supply chain coordinating role of revenue-sharing has, to date, been examined only in static models. With downstream competition, the central conclusion in these models is negative: revenue-sharing cannot, except in degenerate form, achieve coordination. Incorporating dynamics, by allowing inventory carryover in discrete time, this paper establishes a foundation for revenue-sharing contracts in aligning incentives.     

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.     

Transshipment incentive contracts in a multi-level supply chain

Transshipments within a supply chain can be difficult to implement as the costs and benefits are often incurred by different parties. This difficulty becomes even more problematic when the costs and benefits are not completely known by all parties. The primary purpose of this paper is to introduce the role of asymmetric information into the design of supply chain transshipment contracts. Using a representative supply chain from within the soft drink industry as an example, a multi-level contracting framework is developed that aligns incentives to encourage transshipments and improve performance in the absence of all parties having full information. Analysis of the proposed framework suggests that, even if a transshipment is likely to be unprofitable to the transshipping dyad, it may still be best for the entire supply chain. Moreover, overall supply chain inventories with transshipments do not necessarily increase relative to the no-transshipment case.     

Profit criteria involving risk in price setting of virtual products

This work deals with pricing of “virtual” products, i.e., products that a retailer can supply after demand has been realized. Such products allow the retailer to avoid holding costs and ensure timely fulfillment of demand with no risk of shortage. Demand is commonly price-dependent and uncertain, and we seek to maximize each of three criteria: expected profit, the likelihood of achieving a profit target, and the profit for a given percentile. Simultaneous multiple criteria are also explored. Two forms of demand uncertainty are considered in the analysis: the multiplicative form, where, due to stochastic dominance, all the investigated profit criteria—and, in fact, any utility function of the profit—can be optimized simultaneously; and the additive form, where stochastic dominance cannot occur. Under the multiplicative form of demand, the property of stochastic dominance is shown to hold in a two-echelon supply chain (comprising both the supplier and the retailer) and in a centralized system.     

Retail price markup commitment in decentralized supply chains

We investigate the operational decisions and resulting profits for a supply chain facing price-dependent demand under a policy where there is an ex-ante commitment made on the retail price markup. We obtain closed-form solutions for this policy under the assumption of a multiplicative demand function and we analytically compare its performance with that of a traditional price-only policy. We compare these results to results obtained when demand follows a linear additive form. These formulations are shown to be qualitatively different as the manufacturer’s wholesale pricing decision is independent of the retail price markup commitment in the multiplicative case, but not when demand is linear additive. We demonstrate that the ex-ante commitment can lead to Pareto-improving solutions under linear additive demand, but not under the multiplicative demand function. We also consider the effect of pricing power in the supply chain by varying who determines the retail price markup.     

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.     

Effects of constrained supply and price contracts on agricultural cooperatives

Planning strategies depend in part on the supply flow structure of a supply chain. In food supply chains, many firms are constrained by raw material supply (e.g. vegetables and milk). This paper first examines the economic consequences of constrained supply in agricultural cooperatives. Secondly, it deals with the effects of adding price contracts to the current cooperative contract. This model combines an inventory policy approach and a Monte-Carlo simulation, to take into account price uncertainty. We illustrate our results using the case of a dairy cooperative.     

Vendor Management Inventory with consignment contracts and the benefits of cooperative advertising

Most of the cooperative advertising literature has focused on studying the effects of such programs considering marketing variables. This paper integrates production and inventory management with pricing and advertising considerations to assess the effects of cooperative advertising programs in bilateral monopolies. We consider a supply chain where a Vendor Managed Inventory (VMI) along with a consignment contract is implemented to coordinate the chain. We develop and solve a differential model for two games. The first one is a benchmark scenario where no cooperative advertising is offered, while the manufacturer offers the cooperative program in the second game. The main results show that cooperative advertising programs, usually considered as successful marketing initiatives, can be very difficult to implement in a supply chain undertaking a VMI policy with a consignment contract, in which operations and marketing interface is taken into account. A cooperative program mainly hurts the manufacturer’s profits, and can be profit-Pareto-improving only in a few cases. Although the retailer is generally willing to receive a support from the manufacturer, she can opt for a non-cooperative program when the largest part of the supply chain profits goes to the manufacturer. We developed several special cases to strengthen our findings.     

Sustaining long-term supply chain partnerships using price-only contracts

In this paper, we study how an informal, long-term relationship between a manufacturer and a retailer performs in turbulent market environments characterized by uncertain demand. We show that the long-term partnership based on repeated interaction is sustainable under price-only contracts when the supply chain partners are sufficiently patient. That is, the channel can be coordinated over a long time horizon when the factor whereby the members discount the future value of this trusting relationship is sufficiently high. Second, above the minimum discount factor, a range of wholesale prices exists that can sustain the long-term partnership, and there are different possible profit divisions between the two players. Third, when the market is turbulent, i.e., either the expected demand or the demand variance changes from period to period according to a probabilistic law, it is typically less possible to sustain the long-term partnership in a booming market or in a market with low demand variability. Finally, obtaining more information about future market fluctuation may not help the supply chain to sustain the long-term partnership, due to partners’ strategic considerations. With the availability of the market signal, total supply chain profits increase, but the retailer may even be worse-off.     

Strategic wholesale pricing in a supply chain with a potential entrant

This paper develops an adverse selection model for a two-stage supply chain with one supplier, one retailer, and a potential outside entrant supplier who makes a partially substitutable product. The work is different from most research on entry deterrence that only considers a single-stage model. Our main interest is to investigate how the incumbent supplier can strategically maximize her profit by a wholesale pricing policy when facing the potential entrant. We focus on a model where the entrant supplier will sell her product through the same incumbent retailer. We derive the optimal decisions for each player and study the comparative statics of the equilibrium. To investigate how the supply chain structure may affect the deterrence strategy of the incumbent supplier, we also consider three alternative models with different channel structures, when both suppliers sell their products directly, when the entrant has another independent retailer, and when the entrant sells her product directly. Through the comparison, we find that the existence of the common downstream retailer often enhances the deterring motivation of the incumbent supplier.     

Multi-period modeling of two-way price commitment under price-dependent demand

This paper examines the use of price-commitment policies in dynamic contracting in multiple-period, finite-time horizons. Two specific forms of price commitment are considered: one on the part of the retailer through a retail-fixed-markup contract and one on the part of the manufacturer through a price-protection contract. Optimal policies for each form of price commitment are analytically derived, as are optimal policies for the traditional price-only and centralized supply chain scenarios that we use as comparisons. We prove that optimal retail price and order size solutions exist in each period under the assumption of non-increasing price-dependent demand. We show that the existence of retailer inventory between periods causes the optimal policies to differ from a static single-period model. Further, we show that a supplier offers a price-protection policy as a signal to the retailer to resolve the gaming that naturally occurs under price-only; this effectively decouples the multi-period dynamic contracting setting into repeated single-period scenarios. However, the resulting behavior can actually inhibit supply chain performance. On the retail commitment side, we find that retail-fixed-markup policies are quite effective in improving supply chain efficiency. We show that such policies can lead to Pareto-improvement over price-only contracts and can even coordinate the supply chain in some situations.