Ordering policy and coordination of a supply chain with two-period demand uncertainty

We develop a two-period game model of a one-manufacturer and one-retailer supply chain to investigate the optimal decisions of the players, where stock-out and holding costs are incorporated into the model. The demand at each period is stochastic and price sharply drops in mid-life. We assume the retailer has a single order opportunity, and decides how much inventory to keep in the middle of selling season. We show that both the price-protection mid-life and end-of-life returns (PME) scheme and the only mid-life and end-of-life returns (ME) scheme may achieve channel coordination and access a ‘win-win’ situation under some conditions. The larger the lowest expected profit of the retailer, the lower the possibility of ‘win-win’ situation will be. Combined with the analysis of feasible regions for coordination policies, we find that PME scheme is not always better than ME scheme from the perspective of implementable mechanism. Finally, we find that adopting the dispose-down-to (DDT) policy can bring a larger improvement of the expected channel profit in the centralized setting, and it is interesting that by using DDT policy, double marginalization occurs only at Period 1, and however, does not plague the retailer in Period 2.     

Wholesale-price contract of supply chain with information gathering

This paper investigates a wholesale-price contract of supply chain under the endogenous information structure. This supply chain consists of one supplier and one retailer during the selling season. The retailer does not know his selling cost but can spend resources to acquire information. The supplier offers a contract, which induces the retailer to gather information and generate more production orders with beta costs. We find that there exists an upper bound of the information gathering cost such that the supplier induces the retailer to gather information. The increasing cost of information gathering may decrease the order quantity and wholesale price. Moreover, the cost beta has an impact on the expected profits of the two parties. With the increasing cost of information gathering, the supplier’s expected profit is reduced, while that of the retailer becomes ambiguous in terms of the distribution function and the interval of selling cost information. Finally, a numerical example is presented to explain the main results.     

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.     

A two-period supply contract model for a decentralized assembly system

Supply contract helps in coordinating the supply of quantities from different suppliers in order to meet the demand for a product. In this paper, supply contract models are developed by considering an assembly system operated under a centralized and a decentralized control modes. The centralized control mode considers a single decision maker and offers a global optimal solution. However, the decentralized control mode considers each player in the contract as a decision maker and offers local optimal solutions based on the production and cost characteristics of each player. Such local optimal solutions are adjusted through coordinating parameters to obtain global optimal solutions. If a contract developed for a decentralized control mode achieves the global optimal solution, then the supply chain (or channel) is said to be coordinated.     

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.     

Bargaining in competing supply chains with uncertainty

Substantial literature has been devoted to supply chain coordination. The majority of this literature ignores competition between supply chains. Moreover, a significant part of this literature focuses on coordination that induce the supply chain members to follow strategies that produce the equilibria chosen by a vertically integrated supply chain. This paper investigates the equilibrium behavior of two competing supply chains in the presence of demand uncertainty. We consider joint pricing and quantity decisions and competition under three possible supply chain strategies: Vertical Integration (VI), Manufacturer’s Stackelberg (MS), and Bargaining on the Wholesale price (BW(α), α is the bargaining parameter) over a single or infinitely many periods. We show that, in contrast to earlier literature, using VIVI (VI in both chains) is the unique Nash Equilibrium over one period decision, while using MSMS or BW(α)BW(α) may be Nash Equilibrium over infinitely many periods.     

Strategic commitment to price to stimulate downstream innovation in a supply chain

It is generally in a firm’s interest for its supply chain partners to invest in innovations. To the extent that these innovations either reduce the partners’ variable costs or stimulate demand for the end product, they will tend to lead to higher levels of output for all of the firms in the chain. However, in response to the innovations of its partners, a firm may have an incentive to opportunistically increase its own prices. The possibility of such opportunistic behavior creates a hold-up problem that leads supply chain partners to underinvest in innovation. Clearly, this hold-up problem could be eliminated by a pre-commitment to price. However, by making an advance commitment to price, a firm sacrifices an important means of responding to demand uncertainty. In this paper we examine the trade-off that is faced when a firm’s channel partner has opportunities to invest in either cost reduction or quality improvement, i.e. demand enhancement. Should it commit to a price in order to encourage innovation, or should it remain flexible in order to respond to demand uncertainty. We discuss several simple wholesale pricing mechanisms with respect to this trade-off.     

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.     

Scalable methodology for supply chain inventory coordination with private information

This paper considers the problems of coordinating serial and assembly inventory systems with private information where end-item demands are known over a finite horizon. In a private information environment, the objective function and cost parameters of each facility are regarded as private information that no other facilities in the system have access to. The solution approach decomposes the problem into separable subproblems such that the private information is partitioned as required. Global optimality is sought with an iterative procedure in which the subproblems negotiate the level of material flows between facilities. At the core of the solution procedure is a supplier–buyer link model that can be used as a building block to form other supply chain configurations. Experimental results show that the proposed methodology provides promising results when compared to competing methodologies that disregard information privacy.     

Random yield supply chain with a yield dependent secondary market

This paper considers a simple supply chain with one supplier and one retailer where the supplier’s production is subject to random yield and the retailer faces uncertain demand. There exists a secondary market for acquiring or disposing products by the supplier. We study both the centralized and decentralized systems. In the decentralized system, a no risk sharing contract and a risk sharing minimum commitment contract are analyzed. The supply chain with the risk sharing contract is further analyzed with a constant secondary market price and a yield dependent secondary market price. We present both the supplier’s and the retailer’s optimal strategies and provide insights for managers when making decisions under random yield risk and demand uncertainty. We find that the secondary market generally has a positive impact on supply chain performance and the actual effect of random yield risk on the supply chain performance depends on cost parameters and supply chain contract settings. Under certain conditions, reducing yield randomness may weaken the double marginalization effect and improve the chain performance. From the numerical study, we also show that there exists an optimal commitment level for the supply chain.     

Coordinating a supply chain with effort and price dependent stochastic demand

This paper investigates the issue of channel coordination for a supply chain facing stochastic demand that is sensitive to both sales effort and retail price. In the standard newsvendor setting, the returns policy and the revenue sharing contract have been shown to be able to align incentives of the supply chain’s members so that the decentralized supply chain behaves as well as the integrated one. When the demand is influenced by both retail price and retailer sales effort, none of the above traditional contracts can coordinate the supply chain. To resolve this issue, we explore a variety of other contract types including joint return policy with revenue sharing contract, return policy with sales rebate and penalty (SRP) contract, and revenue sharing contract with SRP. We find that only the properly designed returns policy with SRP contract is able to achieve channel coordination and lead to a Pareto improving win–win situation for supply chain members. We then provide analytical method to determine the contract parameters and finally we use a numerical example to illustrate the findings and gain more insights.     

Coordination in a two-stage capacitated supply chain with multiple suppliers

The aim of this paper is to coordinate the inventory policies in a decentralized supply chain with stochastic demand by means of contracts. The system considered is a decentralized two-stage supply chain consisting of multiple independent suppliers and a manufacturer with limited production capacities. The suppliers operate on a make-to-stock basis and apply base stock policy to manage their inventories. On the other hand, the manufacturer employs a make-to-order strategy. Under the necessary assumptions, each supplier is modeled as an M/M/1 make-to-stock queue; and the manufacturer is modeled as a GI/M/1 queue after deriving an approximate distribution for the interarrival times of the manufacturer. Once the supply chain is modeled as a queuing system, centralized and decentralized models are developed. Comparison of the optimal solutions to these models reveals that the supply chain needs coordination. Three different transfer payment contracts are examined in this paper. These are the backorder and holding cost subsidy contracts, the transfer payment contract based on Pareto improvement, and the cost sharing contract. Each contract is evaluated according to its coordination ability and whether it is Pareto improving or not. The results indicate that all three contracts can coordinate the supply chain. However, when the Pareto improvement is taken into account, the cost sharing contract seems to be the one that will be preferred by all parties.     

Trade credit for supply chain coordination

Trade-credit is a seller’s short-term loan to the buyer, allowing the buyer to delay payment of an invoice. It has been the largest source of working capital for a majority of business-to-business firms in the United States. Numerous theories have been proposed to explain trade-credit, mainly from finance perspectives. It has also been an important issue in supply chain management. Surprisingly, most literature in supply chain management has examined the retailer’s stocking policies given a supplier’s trade-credit. This paper attempts to shed light on trade-credit from a supplier’s perspective, and presents it as a tool for supply chain coordination. Specifically, we explicitly assume firms’ financial needs for inventory. Following a Newsvendor framework, we assume that the supplier grants trade-credit and markdown allowance. Given the supplier’s offer, the retailer determines order quantity and the financing option for the inventory, either trade-credit or direct financing from a financial institution. Our result shows that the supplier’s markdown allowance alone cannot fully coordinate the supply chain if the retailer employs direct financing. Positive financing costs call for trade-credit in order to subsidize the retailer’s costs of inventory financing. Using trade-credit in addition to markdown allowance, the supplier fully coordinates the retailer’s decisions for the largest joint profit, and extracts a greater portion of the maximized joint profit.     

Analysis of supply chains with quantity based fixed incentives

This paper examines the use of quantity based fixed incentives to coordinate inventory decisions in a decentralized supply chain. We consider a two stage supply chain of autonomous supplier and distributor and prove that the optimal ordering policy for the newsvendor distributor under fixed incentives is an (s,S)$(s\text{,}S)$ type policy. We further show that external and internal quantity based incentives can restore channel coordination in single period and channel members can benefit through arbitrary splitting of the resulting additional chain profit. The single period results are extended to multiple periods and the impact of fixed incentives on the distributor’s optimal stocking policy and channel efficiency are examined under three different multi-period supplier strategies. Numerical examples are used to compare the multi-period strategies and to provide additional managerial insights. The results show that contrary to common belief, incentive plans developed and maintained based only on current inventory data perform poorly in long term and that such incentive plans must be periodically updated to enhance their efficiency. Furthermore, we show that high level of incentives designed to push too much inventory downstream of the supply chain can actually reduce the chain’s efficiency.     

均值-CVaR零售商的供应链服务决策及协调契约

研究零售商具有风险偏好行为下,同时考虑价格、质量和服务水平的供应链联合决策问题。运用均值-CVaR准则来刻画零售商风险偏好行为,它包括风险厌恶、风险中性和风险追求,同时具有损失规避的特性。首先得到供应链集中系统、制造商提供服务（模型$\mbox{I}$）和零售商提供服务（模型$\mbox{II}$）下的最优决策和最优利润（期望效用）。其次,证明了成本共担契约在零售商风险厌恶时可以实现供应链协调.第三,对模型$\mbox{I}$和模型$\mbox{II}$协调后的最优利润（期望效用）进行比较,证明两种模型下制造商利润相同,而与模型$\mbox{I}$相比,模型$\mbox{II}$下零售商获得更多的期望效用。最后,数值例子证明了得到的研究结果。     

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.     

A quantity discount approach to supply chain coordination

Quantity discounts provide a practical foundation for inventory coordination in supply chains. However, typical supply chain participants may encounter difficulties in implementing the coordination policy simply because (1) specified lot size adjustments may deviate from the economic lot sizes and (2) the buying firm may face amplified overstocking risks related to increased order quantities. The main objective of this study is to develop a quantity discount model that resolves the practical challenges associated with implementing quantity discount policies for supply chain coordination between a supplier and a buyer. The proposed Buyer’s Risk Adjustment (B-RA) model allows the supplier to offer discounts that capitalize on the original economic lot sizes and share the buyer’s risk of temporary overstocking under uncertain demand. The analytical results suggest that the proposed B-RA discount approach is a feasible alternative for supply chain coordination under uncertain demand conditions.     

Distributed supply chain management using ant colony optimization

Successful supply chain management requires a cooperative integration between all the partners in the network. At the operational level, the partners individual behavior should be optimal and therefore their activities have to be planned using sophisticated optimization tools. However, these tools should take into account the planning of the remaining partners, through the exchange of information, in order to allow some kind of cooperation between the elements of the chain. This paper introduces a new supply chain management technique, based on modeling a generic supply chain with suppliers, logistics and distributers, as a distributed optimization problem. The different operational activities are solved by the optimization meta-heuristic called ant colony optimization, which allows the exchange of information between different optimization problems by means of a pheromone matrix. The simulation results show that the new methodology is more efficient than a simple decentralized methodology for different instances of a supply chain.     

Towards integration: a revenue-sharing contract in a supply chain

Email: zhaoqiong.qin{at}erau.edu Received on 31 May 2006. Accepted on 11 December 2006. This paper deals with the problem of a revenue-sharing contractadopted in a supply chain involving one supplier and one retailerwith short life-cycle products. Under this contract, the retailercan obtain the product from the supplier at a discounted pricewhile as a compensation, the retailer must share his revenuewith the supplier at a certain revenue-sharing rate, say r (0 r 1), where r represents the portion of the revenue to bekept by the retailer. We use a two-stage (Stackelberg) gameto model the problem, where one player is the game's leaderand the other the game's follower. Our ultimate objective isto maximize the overall supply chain's total profit, and toshow the effects of salvage revenue and the revenue-sharingrate on transfer cost rate, profit of the supplier and retailerand the overall supply chain's total profit while upholdingthe individual components’ incentives. Our analysis exhibitsthat the case in which salvage revenue is not shared is preferredand the computational results to explore the effects of therevenue-sharing rate lead to many managerial insights regardingthe leader of the game.     

Revenue management for a supply chain with two streams of customers

In this paper, we consider revenue management for a service supply chain with one supplier and one retailer. The supplier has a limited capacity of a perishable product and both the supplier and the retailer face customers. Each customer may choose to buy a product from either the supplier or the retailer by considering prices and the cost associated with switching. For the centralized model, the supplier determines the selling prices for both herself and the retailer, and the retailer simply collects a commission fee for each product sold. We derive monotone properties for the revenue functions and pricing strategies. Further, we show that the commission fee increases the retailer’s price while decreasing the supplier’s and leads to efficiency loss of the chain. For the decentralized decision-making model, the supplier and the retailer compete in price over time. Two models are considered. In the first, the retailer buys products from the supplier before the selling season and in the second the retailer shares products with the supplier in retailing. For both models, we discuss the existence of the equilibrium and characterize the optimal decisions. Numerical results are presented to illustrate properties of the models and to compare the supply chain performance between the centralized and the decentralized models.