How a dominant retailer might design a purchase contract for a newsvendor-type product with price-sensitive demand

A dominant retailer will purchase a newsvendor-type product from a manufacturer, who incurs a unit manufacturing cost k. The expected retail demand is a function of the unit retail price p. How should the retailer design her purchase contract? For this increasingly prevalent but inadequately studied scenario, we propose plausible adaptations of several contract formats that have been widely studied in the dominant-manufacturer context. For both symmetric-k and asymmetric-k-knowledge situations, we present performance results of these contracts. Our results then reveal that the performance of these contract formats under our scenario differs considerably from what one would surmise from the well-known results published for closely related scenarios. For example, the widely studied buyback and revenue-sharing formats turn out to be largely ineffective when implemented by a dominant retailer. In contrast, the two-part tariff format performs well relative to the theoretically optimal “menu of contracts.” Our results highlight the need to study purchase contract formats designed specifically for dominant-retailer newsvendor-product channels.     

Pricing decisions for substitutable products with a common retailer in fuzzy environments

The pricing problem of substitutable products in a fuzzy supply chain is analyzed by using game theory in this paper. There are two substitutable products produced by two competitive manufacturers respectively and then sold by one common retailer to the consumers. Both the manufacturing cost and the customer demand for each product are characterized as fuzzy variables. How the two manufacturers and the common retailer make their own pricing decisions about wholesale prices and retail prices are explored under four different scenarios, and the corresponding expected value models are developed in this paper. Finally, a numerical example is given to illustrate the effectiveness of the proposed supply chain models.     

Pricing and two-tier advertising with one manufacturer and one retailer

This paper considers the pricing decisions and two-tier advertising levels between one manufacturer and one retailer where customer demand depends on the retail price and advertisement by a manufacturer and a retailer. We solve a Stackelberg game with the manufacturer as the leader and the retailer as the follower. With price sensitive customer demand and a linear wholesale contract, we obtain the optimal decisions by the manufacturer and the optimal responses by the retailer. Our results show that cost sharing of local advertising does not work well, it is better for the manufacturer to advertise nationally and offer the retailer a lower wholesale price.     

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 in multiple-item procurement auctions with a common to all items fixed cost

In a sealed bid multiple-item procurement auction, bidders may incur a fixed cost, which is common to all items. The paper develops pricing methods which ensure that a preset percentage profit level is always realized and the fixed cost is completely recovered, even if the eventual order is for some of the items at reduced quantities. One approach sets constraints and determines acceptable orders. Another alternative is to provide appropriate discounts. Finally, a third method considers fixed prices and imposes constraints that address the exposure problem of recovering the fixed cost. These methods may also be used for pricing combinatorial auctions.     

Supply-chain coordination model with insufficient production capacity and option for outsourcing

In this paper, a mathematical model is developed to analyze the situation of lost sales from the supply-chain coordination perspective. In a two-stage supply chain, the supplier’s production capacity is less than the annual demand of the retailer. The supplier may recover the deficit by procuring the same from an external source at a certain price and then supplying it back to the retailer. Here, the conditions have been derived when the practice of external procurement may be a viable solution to enhance the profits of both the supplier and retailer in a coordinated approach. A numerical example is carried out to illustrate the efficacy of the developed model and the procedure developed for solving the problem.     

Pricing stock and bond derivatives with a multi-factor Gaussian model

The martingale approach to pricing contingent claims can be applied in a multiple state variable model. The idea is used to derive the prices of derivative securities (futures on stock and bond futures, options on stocks, bonds and futures) given a continuous time Gaussian multi-factor model of the returns of stocks and bonds. The bond market is similar to Langetieg's multi-factor model, which has closed-form solutions. This model is a generalization of Vasicek's model, where the term structure depends on state variables following correlated mean reverting processes. The stock market is affected by systematic and unsystematic risk.     

存在价格差异的闭环供应链定价策略及契约协调

以零售商回收模式为对象,采用博弈论方法,研究再制造产品与新产品存在销售价格差异以及废旧产品存在回收价格差异时闭环供应链的定价策略及契约协调问题。对闭环供应链系统在分散决策和集中决策下的定价模型进行了分析,得到了系统各成员的最优定价策略和利润,发现分散决策会造成系统效率的损失。为此提出一种改进的特许经营费用契约对闭环供应链进行协调,使得闭环供应链系统不仅消除了"双重边际化"的问题,而且实现了完美协调。算例分析验证了定价策略及契约协调机制的有效性。     

Demand disruption and coordination of the supply chain with a dominant retailer

This paper develops two coordination models of a supply chain consisting of one manufacturer, one dominant retailer and multiple fringe retailers to investigate how to coordinate the supply chain after demand disruption. We consider two coordination schedules, linear quantity discount schedule and Groves wholesale price schedule. We find that, under the linear quantity discount schedule, the manufacturer only needs to adjust the maximum variable wholesale price after demand disruption. For each case of the disrupted amount of demand, the higher the market share of the dominant retailer, the lower its average wholesale price and the subsidy will be under the linear quantity discount schedule, while the higher its fraction of the supply chain’s profit will be under Groves wholesale price schedule. When the increased amount of demand is very large and production cost is sufficiently low, linear quantity discount schedule is better for the manufacturer. However, when the production cost is sufficiently large, Groves wholesale price schedule is always better. We also find that the disrupted amount of demand largely affects the allocation of the supply chain’s profit.     

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.     

面向制造成本甄别和销售努力激励的供应链协调契约研究

针对二级供应链中制造商隐藏成本信息和销售商隐藏努力行动引发的低效率问题, 结合委托代理理论, 引入一个虚拟第三方为利他的 委托人, 建立逆向选择和道德风险下供应链协调模型, 来甄别制造商的真实成本且对销售商的努力实施有效激励, 并通过模型求解得到供应链实现协调时各契约参数需满足的关系. 结果表明, 所设计的协调契约能够激励制造商自愿真实上报成本信息, 刺激销售商寻求低成本的制造商进行合作并付出最优努力. 最后, 通过算例分析验证了契约模型对供应链协调的有效性.     

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.     

Pricing and logit-based mode choice models of a transit and highway system with elastic demand

The objective of this paper is to enhance the insights into transport pricing mechanism and the corresponding mode choice behavior in a simple bi-modal transportation system with elastic demand. This system comprises a mass transit parallel to a bottleneck-constrained highway between a residential area and a workplace. We derive and compare three pricing schemes: the arbitrarily fixed pricing, the first-best pricing for a social optimum of the system, and the second-best pricing in the case of incapability of road toll. It is shown that the first-best pricing requires to implement a road toll and a transit fare simultaneously, and the optimal transit fare for the second-best solution should be set to be a weighted sum of the marginal external costs between auto and transit commuters. A numerical example is presented to illustrate how the pricing policies affect the demand implementation, the mode choice behavior and the efficiency of the whole transportation system.     

A Stackelberg game and its improvement in a VMI system with a manufacturing vendor

Vendor managed inventory (VMI) is an inventory management strategy to let a vendor manage his retailers’ inventories, which makes the vendor have the opportunity to obtain some inventory and market-related information of his retailers. This paper discusses how the vendor can take advantage of this information for increasing his own profit by using a Stackelberg game in a VMI system. The vendor here is a manufacturer who procures raw materials to produce a finished product and supplies it at the same wholesale price to multiple retailers. The retailers then sell the product in independent markets at retail prices. Solution procedures are developed to find the Stackelberg game equilibrium that each enterprise is not willing to deviate from for maximizing his own profit. The equilibrium makes the manufacturer benefited, and the retailers’ profits maximized. The equilibrium can then be improved for further benefiting the manufacturer and his retailers if the retailers are willing to cooperate with the manufacturer by using a cooperative contract. Finally, a numerical example and the corresponding sensitivity analysis are given to illustrate that: (1) the manufacturer can benefit from his leadership, and monopolize the added profit of the VMI system in some cases; (2) The manufacturer can further improve his own profit, and then the retailers’ profits by the cooperative contract, as compared to the Stackelberg equilibrium; (3) market and raw material related parameters have significant influence on every enterprise’s net profit.     

Optimal pricing for information goods with piracy and saturation effect

We analyze the pricing decision of a firm selling a product for which there is a significant and continuous saturation effect over time and that can be pirated. Assuming that the firm uses a skimming strategy, we solve three profit maximization models, given demand that is linearly decreasing in price. Few prices can be used over the life of the product. The effects of both piracy and saturation are combined in the first model. In the second model, the firm can invest in technology or copyright enforcement to reduce piracy. The third model describes the case in which piracy leads to increased awareness of the product and increased demand. Numerical sensitivity analysis and examples are used to illustrate the results. The results indicate that under strong piracy and saturation effects, a skimming strategy is suboptimal.     

The transformation method for the simulation and analysis of systems with uncertain parameters

In this paper, the transformation method is introduced as a powerful approach for both the simulation and the analysis of systems with uncertain model parameters. Based on the concept of α-cuts, the method represents a special implementation of fuzzy arithmetic that avoids the well-known effect of overestimation which usually arises when fuzzy arithmetic is reduced to interval computation. Systems with uncertain model parameters can thus be simulated without any artificial widening of the simulation results. As a by-product of the implementation scheme, the transformation method also provides a measure of influence to quantitatively analyze the uncertain system with respect to the effect of each uncertain model parameter on the overall uncertainty of the model output. By this, a special kind of sensitivity analysis can be defined on the basis of fuzzy arithmetic. Finally, to show the efficiency of the transformation method, the method is applied to the simulation and analysis of a model for the friction interface between the sliding surfaces of a bolted joint connection.     

Pricing and horizontal information sharing in a supply chain with capacity constraint

This paper aims to explore manufacturers horizontal information sharing strategy under competition. The model framework is based on a two-echelon supply chain composed of one upstream supplier and two downstream manufacturers with asymmetric capacity constraint. Analysis of the model establishes manufacturers’ information sharing strategies under different conditions and shows how supplier’s pricing decision can shape manufacturers’ information sharing incentives.     

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.     

Parametric error bounds for convex approximations of two-stage mixed-integer recourse models with a random second-stage cost vector

We consider two-stage recourse models with integer restrictions in the second stage. These models are typically non-convex and hence, hard to solve. There exist convex approximations of these models with accompanying error bounds. However, it is unclear how these error bounds depend on the distributions of the second-stage cost vector q. In this paper, we derive parametric error bounds whose dependence on the distribution of q is explicit: they scale linearly in the expected value of the ${?}_1$-norm of q.