需求与库存水平相关的供应链量折扣协调模型

考虑由一个供应商和一个零售商构成的供应链系统,零售商的市场需求依赖于该产品的库存水平,研究了利用批量折扣实现供应链完美协调的问题.首先,我们得出了在分散式系统下供应链无法实现完美协调,讨论了供需双方的最优决策.其次,作为stackelberg的主导方,供应商提供批量折扣计划,得出了此折扣计划实现系统完美协调的条件,分别给出了实现完美协调和不能实现完美协调时的批量折扣计划.最后分析了需求函数中的参数和产品的成本对实现供应链系统完美协调的影响.     

考虑最优广告费用及数量折扣的供应链企业间的博弈分析

主要研究由一个制造商和一个销售商组成的二级供应链系统,在随机需求下,考虑广告促销及数量折扣前后,双方如何博弈,如何决策的问题.在制造商Stackelberg策略下,对供应链协调价进行了分析,提供了制造商制定数量折扣策略的思路.     

Integrated inventory model with quantity discount and price-sensitive demand

Quantity discount has been a subject of study for a long time; however, little is known about its effect on integrated inventory models when price-sensitive demand is placed. The objective of this study is to find the optimal pricing and ordering strategies for an integrated inventory system when a quantity discount policy is applied. The pricing strategy discussed here is one in which the vendor offers a quantity discount to the buyer. Then, the buyer will adjust his retail price based on the purchasing cost, which will influence the customer demand as a result. Consequently, an integrated inventory model is established to find the optimal solutions for order quantity, retail price, and the number of shipments from vendor to buyer in one production run, so that the joint total profit incurred has the maximum value. Also, numerical examples and a sensitivity analysis are given to illustrate the results of the model.     

Optimal order lot sizing and pricing with free shipping

Companies, especially those in e-business, are increasingly offering free shipping to buyers whose order sizes exceed the free shipping quantity. In this paper, given that the supplier offers free shipping, we determine the retailer’s optimal order lot size and the optimal retail price. We explicitly incorporate the supplier’s quantity discount, and transportation cost into the model. We analytically and numerically examine the impacts of free shipping, quantity discount and transportation cost on the retailer’s optimal lot sizing and pricing decisions. We find that free shipping can benefit the supplier, the retailer, and the end customers, and can effectively encourage the retailer to order more of the good, to the extent of ordering a few times of the optimal order lot size without free shipping. The order lot size will increase and the retail price will decrease if the supplier offers proper free shipping.     

供应链买卖双方协调订货模型

供需关系贯穿供应链的整个过程;然而,如何促使非一体化供应链协调问题在实践中是非常重要的.因此,供需双方订货批量的研究是供应链管理的一个重要内容之一.本文以订单方式为背景,针对供应链环境下单个供应商和多个订货商在非合作情况下的订货模型进行讨论,并在此基础上给出了一个改进后的线性价格折扣策略,该策略同时考虑了增量折扣和减量折扣两种情况,同时给出了供需上双方订货的S tackelberg博弈模型.数字实验结果表明该折扣模型对于改善供应链运作协调是相当有效的.     

Heuristics for sourcing from multiple suppliers with alternative quantity discounts

In this paper, we analyze the impact of supplier pricing schemes and supplier capacity limitations on the optimal sourcing policy for a single firm. We consider the situation where the total quantity to be procured for a single period is known by the firm and communicated to the supplier set. In response to this communication, each supplier quotes a price and a capacity limit in terms of a maximum quantity that can be supplied to the buyer. Based on this information, the buyer makes a quantity allocation decision among the suppliers and corresponding to this decision is the choice of a subset of suppliers who will receive an order. Based on industry observations, a variety of supplier pricing schemes from the constituent group of suppliers are analyzed, including linear discounts, incremental units discounts, and all units discounts. Given the complexity of the optimization problem for certain types of pricing schemes, heuristic solution methodologies are developed to identify a quantity allocation decision for the firm. Through an extensive computational comparison, we find that these heuristics generate near-optimal solutions very quickly. Data from a major office products retailer is used to illustrate the resulting sourcing strategies given different pricing schemes and capacity limitations of suppliers in this industry. We find for the case of capacity constrained suppliers, the optimal quantity allocations for two complex pricing schemes (linear discount, and incremental units discount) are such that at most one selected supplier will receive an order quantity that is less than its capacity.     

Monotone and bounded interval equilibria in a coordination game with information aggregation

We analyze how private learning in a class of games with common stochastic payoffs affects the form of equilibria, and how properties such as player welfare and the extent of strategic miscoordination relate across monotone and non-monotone equilibria. Researchers typically focus on monotone equilibria. We provide conditions under which non-monotone equilibria also exist, where players attempt to coordinate to obtain the stochastic payoff whenever signals are in a bounded interval. In bounded interval equilibria (BIE), an endogenous fear of miscoordination discourages players from coordinating to obtain the stochastic payoff when their signals suggest coordination is most beneficial. In contrast to monotone equilibria, expected payoffs from successful coordination in BIE are lower than the ex-ante expected payoff from ignoring signals and always trying to coordinate to obtain the stochastic payoff. We show that BIE only exist when, absent private information, the game would be a coordination game.     

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.     

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.     

Optimal business policies for a supplier–transporter–buyer channel with a price-sensitive demand

As the third party logistics partners (carriers) taking a more and more significant role in supply chain practices and customer service performance improvement, there is an emerging need for the studies on optimal channel coordination policies for business processes involving not only supplier and buyer (retailer), but also transportation partners. In this paper, we explicitly add a transportation partner with concave cost functions into the analysis for supplier–buyer channel coordination policies, and analyse the impact of coordination and pricing policies on supply chain profitability. The market demand is assumed to be a decreasing convex function of buyer's selling price (x), D(x)=d/x². Under this assumption, we quantify the improvement on total supply chain profitability when moving from a non-cooperative environment to a fully cooperative environment, and show that the joint annual profit of three partners in a cooperative environment can be at least twice of what may be achieved by three independently operated companies in a leader–follower business game. While in a real-world business environment, a perfect collaboration is hard to achieve, this result can be used to provide a quick estimation on the upper bound on the budget for profit sharing or discount offers among the supply chain partners.     

Impacts of two-stage deterioration on an integrated inventory model under trade credit and variable capacity utilization

The joint economic lot sizing problem (JELP) model provides a global view to facilitate the development of a production-inventory policy for an integrated system. However, when a deteriorating item is involved, previous studies have neglected the following two important issues: (1) the deterioration quantity increases the demand for the supplier's capacity, which consequently requires the supplier to recalculate the corresponding average cost and reevaluate the capacity utilization, and (2) given the supplier's production rate, in-transit deterioration imposes restrictions on the delivery distance or in-transit time. Therefore, the existing integrated policies may lead to infeasible solutions for the distribution channel when a deterioration item is included. In view of these two issues, a generalized JELP model under delay in payments is formulated to investigate the integrated production-inventory policy for an item with two-stage deterioration (in-transit and retail deterioration) while incorporating both transportation time and capacity utilization. By developing the average cost functions of the supply chain members and employing several new definitions (e.g., variable capacity utilization), this paper provides a mechanism for measuring the influence of two-stage deterioration on the supplier's capacity utilization for the JELP. Three algorithms are proposed to obtain optimal decisions based on the theoretical results. This paper demonstrates that the supplier's variable capacity utilization is relevant to transportation time and two-stage deterioration, which can be applied to evaluate the feasibility of the integrated production-inventory policy for the deteriorating item. Furthermore, there is a maximum allowable value for the retailer's order cycle.     

二级供应链上不完美互补产品的定价决策

建立一个由两个制造商和一个零售商组成供应链模型,以求解制造商和零售商的最优定价决策,其中两个制造商向零售商批发的产品是不完美互补的,且零售商采取混合捆绑策略销售这两种产品。考虑三种情形下的决策:(1)完全非合作博弈;(2)局部合作博弈;(3)合作博弈。通过比较前两种情形下的决策,利用Nash协商模型求解得到消除水平和垂直供应链冲突的最优定价决策。与完全非合作博弈决策相比,局部合作博弈决策对制造商是有利的,在一定的条件下也可以实现对零售商收益的帕累托改进;而合作博弈决策在任何情况下都要明显地优于完全非合作博弈决策以及局部合作博弈决策,同时合作博弈决策下的最优产品需求量相比局部合作博弈决策下的最优产品需求量提高了一倍。最后,通过数值试验验证了文章所得结论。     

Playing off-line games with bounded rationality

We study a two-person zero-sum game where players simultaneously choose sequences of actions, and the overall payoff is the average of a one-shot payoff over the joint sequence. We consider the maxmin value of the game played in pure strategies by boundedly rational players and model bounded rationality by introducing complexity limitations. First we define the complexity of a sequence by its smallest period (a nonperiodic sequence being of infinite complexity) and study the maxmin of the game where player 1 is restricted to strategies with complexity at most n and player 2 is restricted to strategies with complexity at most m. We study the asymptotics of this value and a complete characterization in the matching pennies case. We extend the analysis of matching pennies to strategies with bounded recall.     

Cooperative Markov decision processes: time consistency, greedy players satisfaction, and cooperation maintenance

We deal with multi-agent Markov decision processes (MDPs) in which cooperation among players is allowed. We find a cooperative payoff distribution procedure (MDP-CPDP) that distributes in the course of the game the payoff that players would earn in the long run game. We show under which conditions such a MDP-CPDP fulfills a time consistency property, contents greedy players, and strengthen the coalition cohesiveness throughout the game. Finally we refine the concept of Core for Cooperative MDPs.     

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.     

Integrated inventory models considering the two-level trade credit policy and a price-negotiation scheme

This paper develops the integrated inventory models with permissible delay in payment, in which customers’ demand is sensitive to the buyer’s price. The models consider the two-level trade credit policy in the vendor–buyer and buyer–customer relationships in supply chain management. A simple recursive solution procedure is proposed for the integrated models to determine the buyer’s optimal pricing and production/order strategy. Although the total profit from the buyer and vendor increases together, the buyer’s share lessens. To compensate the buyer’s loss due to the cooperative relationship, a negotiation system is presented in order to allocate the profit increase to the vendor and buyer to determine the pricing and production/order strategy. A numerical example and sensitivity analysis are provided to illustrate the proposed model. The results indicate that the total profit from the buyer and vendor together can increase, although a price discount is given to the buyer in the proposed models.     

Computing payoff allocations in the approximate core of linear programming games in a privacy-preserving manner

We investigate privacy-preserving ways of allocating payoffs among players participating in a joint venture, using tools from cooperative game theory and differential privacy. In particular, we examine linear programming games, an important class of cooperative games that model a myriad of payoff sharing problems, including those from logistics and network design. We show that we can compute a payoff allocation in the approximate core of these games in a way that satisfies joint differential privacy.     

The optimal quantity discount that a supplier should offer

Quantity discounts are a useful mechanism for coordination. Here we investigate such discounts from the supplier's perspective, both from a non-cooperative game-theoretical approach and a joint decision model. Taking into account the price elasticity of demand, this analysis aids a sole supplier in establishing an all-unit quantity discount policy in light of the buyer's best reaction. The Stackelberg equilibrium and Pareto optimal solution set are derived for the non-cooperative and joint-decision cases, respectively. Our research indicates that channel efficiency can be improved significantly if the quantity discount decision is made jointly rather than non-cooperatively. Moreover, we extend our model in three directions: (1) the product is transported by a private fleet; (2) the buyer may choose to offer her customers a different percentage discount than that she obtained from the supplier; and (3) the case of heterogeneous buyers. Numerical case studies are employed throughout the paper to illustrate the practical applications of the models presented and the sensitivity to model parameters.     

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.     

Dynamic Network-Based Discriminatory Pricing

We study the dynamic pricing decisions for competitive network service providers. We assume that each competing firm follows a three-part pricing scheme, which consists of an ongoing membership fee, a usage fee for communications within the networks, and another usage fee for communications across the networks. The difference between the two usage fees is the network-based price discount that allows price discrimination. We study the firms problems as a differential game and establish the optimal pricing policy as a Nash equilibrium feedback strategy depending on only the network sizes (i.e., the number of subscribers). We compare the dynamic network-based discount with the static discount. In the special case of a uniform calling pattern, we find that the firm network-based dynamic discount is always lower than the static discount; we find also that the firm that has a larger network can offer a bigger discount. These results are useful particularly for managers. To get further insights into the dynamic pricing policies, we explore the case of symmetric competition using numerical simulation.Communicated by G. Leitmann