Pricing and ordering decisions of two competing supply chains with different composite policies: a Stackelberg game-theoretic approach

In today’s global highly competitive markets, competition happens among supply chains instead of companies, as the members of supply chains. So, the partners of the chains seek to apply efficient coordinating strategies like discount, return, refund, buyback, or the other coordinating policies to abate the operation costs of the chains and subsequently increase market shares. Hence, because of the importance and application of these strategies in the current non-exclusive markets, in this study, we introduce different composite coordinating strategies to enhance the coordination of the supply chains. Here, we consider two competing supply chains where both chains launch the same product under different brands to the market by applying different composite coordinating strategies. Each supply chain comprises one manufacturer and a group of non-competing retailers where the manufacturer receives raw materials from an outside supplier and transforms them into a finished product; then, the products are sold to the retailers to satisfy the demands of market. In the first chain, a composite (QFF) policy, which is the combination of quantity and freight discount, as well as free shipping quantity policies, are considered between upstream and downstream members while in the second one, different composite polices are considered between upstream and downstream members such that the supplier offers a composite policy, as the first chain, to the manufacturer and the manufacturer proposes a composite (QPR) policy, which is the combination of quantity discount and partial-refund customer return policies, to the retailers. The main objective of the paper is to determine the optimal selling prices and the order quantities of the manufacturer and the retailers in each chain in presence of different composite coordinating strategies. A Stackelberg game-theoretic approach is employed between the members of each chain where the manufacturer is a follower and the retailers are leaders. The concavity of profit functions is proved. Finally, the applicability of the models is justified by presented numerical examples. Moreover, the effects of these strategies on the decisions of the chains’ partners are examined.     

Inventory performance of some supply chain inventory policies under impulse demands

This paper attempts to study the impact of impulsive demand disturbances on the inventory-based performance of some inventory control policies. The supply chain is modelled as a network of autonomous supply chain nodes. The customer places a constant demand except for a brief period of sudden and steep change in demand (called demand impulse). Under this setting, the behaviour of each inventory policy is analysed for inventory performance of each node. It is found that the independent decision-making by each node leads to a bullwhip effect in the supply chain whereby demand information is amplified and distorted. However, under a scenario where the retailer places a constant order irrespective of the end customer demand, the inventory variance was actually found to decrease along the supply chain. The variance of the inventory remained constant along the chain when only the actual demands are transmitted by each node. The results also showed that the inventory policy which is best for one supply chain node is generally less efficient from a supply chain perspective. Moreover, the policy which performs poorly for one node can be most efficient for the supply chain. In a way, our results also provide a case for coordinated inventory management in the supply chain where all members prepare a joint inventory management policy that is beneficial for all the supply chain nodes. The results have significant industrial implications.     

Optimal ordering policy for a price-setting newsvendor with option contracts under demand uncertainty

In this article, we investigate the newsvendor problem in a joint ordering and pricing setting in the presence of option contracts under demand uncertainty. At the beginning of a single selling season, the newsvendor who faces additive stochastic demand can obtain goods through two ways: ordering from a firm or purchasing and exercising call options. Single ordering (ordering from a firm only or purchasing and exercising call options only) and mixed ordering (ordering from a firm and purchasing and exercising call options simultaneously) cases are investigated. We find that the newsvendor’s optimal pricing and ordering strategies exist and are unique for both cases, respectively. In addition, when both cases are available, mixed ordering is the newsvendor’s optimal ordering policy. If only single ordering is available, the newsvendor prefers ordering from a firm when demand risk is low, while enjoys purchasing and exercising call options when demand risk is high. We also find that with option contracts, the newsvendor’s optimal order quantity and maximum expected profit are all decreasing in the option price and exercise price of product, while the optimal retail price in terms of option price and exercise price of product are intricate. Moreover, we show that, mixed ordering is more capable to deal with supply price volatility risk.     

考虑零售商过度自信的供应链决策与协调

将过度自信引入到供应链中,通过构建由一个供应商和一个过度自信的零售商组成的二级供应链模型,分析了过度自信的零售商与供应商的决策。结果表明,零售商过度自信能够实现供应链协调,但供应商的回购契约会破坏这种协调;当零售商接收到市场不利信息时供应商的回购契约失效,当零售商接收到市场有利信息时供应商利润随过度自信程度增加而减少。进一步在模型中引入收益共享契约,使得订购量和供应商的利润均增加,并实现了供应链协调。最后,通过数值算例验证并阐明了相关结论。     

具有风险规避者加盟的供应链协作回购契约机制研究

探讨了一类具有风险规避特性的零售商加盟的供应链协作契约机制设计问题.研究了零售商为风险中性时选择的订货行为和零售商为风险规避者时的订货行为,研究结果表明具有风险规避性的零售商最优订货量要比风险中性的零售商选择的最优订货量小,同时还发现供应商为激励具有风险规避特性的零售商所支付的单位商品回购价格,要比激励风险中性的零售商所支付的单位回购价格高.此外还证明了单位商品回购价格随零售商的风险规避系数增加而增加,并通过案例分析验证了该结论.     

Inventory misplacement and demand forecast error in the supply chain: profitable RFID strategies under wholesale and buy-back contracts

We investigate RFID adoption strategies under wholesale price and buy-back contracts in a supply chain with one manufacturer and one retailer who faces inventory misplacement and demand forecast error. RFID can alleviate the misplacement problem, and can reduce demand forecast error by shortening order lead time. By a newsvendor model, we characterise the optimal contract terms in the supply chain without and with RFID adoption, respectively. We further analyse how the contract terms depend on RFID-related parameters (e.g. salable rate and demand forecast error). We find that both without and with RFID, the wholesale price contract will lead to the double marginalisation problem, while the buy-back contract can coordinate the supply chain. We show that the supply chain adopts RFID if and only if the tagging cost is below a threshold; the threshold is in negative correlation to the demand forecast error. The supply chain is more willing to adopt RFID under the buy-back contract than under the wholesale price contract. RFID adoption can sometimes lessen the double marginalisation problem under the wholesale price contract, improving the supply chain efficiency. A smaller RFID tagging cost or a reduced forecast error do not necessarily lead to higher supply chain efficiency.     

Optimal policies of a two-echelon serial inventory system with general limited capacities

We study optimal policies of capacitated two-echelon serial inventory systems under periodic review. For a system with smaller downstream capacity, we fully characterise the optimal policy as a further modified echelon base stock policy using an intuitive backward induction. The key lies in the magnitude relation between the initial upstream stock level and the downstream capacity. For a system with smaller upstream capacity, we demonstrate that the optimal policy is of a more complex structure where there can be at most four/five target levels up to which the upstream/downstream echelon tries to produce/order. The numbers of levels and their values depend on the length of remaining horizons and the amount of initial upstream inventories. We also specify these potential target levels and then suggest a way to simplify the search of optimal solutions.     

供应链中供需节点企业相互激励模型研究

供应链中供需节点企业之间的协作问题是供应链管理的核心问题.在考虑制造商因建立过剩的供货能力而承担一定风险的情况下,考察由一个制造商和一个销售商组成的简单供应链中的协作状况.在供货能力作为内生变量的情况下,提出了一种制造商和销售商之间相互激励模型,结果表明该模型可以有效增加制造商和销售商的收益.采用数值算例验证了该激励模型的有效性.     

突发事件且非对称信息下的供应链回购契约模型

考虑由一个制造商和一个零售商组成的供应链,在随机市场需求下,分析了回购契约对供应链的协调作用;探讨了突发事件导致市场需求和零售商边际成本同时变化且变化后的零售商边际成本是不对称信息时回购契约对供应链的协调作用,研究表明：基准的回购契约对突发事件下的供应链不再发挥协调作用,为此,给出了供应链应对突发事件的最优应对策略,并调整了原来的回购契约使其具有抗突发事件性。用一个算例对比加以说明。      

Rebate, returns and price protection policies in channel coordination

We study channel coordination policies for products subject to midlife price declines during their short product life cycles. Using a two-period supply chain model consisting of one supplier and one retailer, we identify policies and/or conditions under which the supply chain can be coordinated and a win-win situation can be guaranteed. We also provide algorithms to determine the win-win policy parameters. We show that if there are two purchase opportunities, then under linear or decreasing (the more you buy, the lower price you pay) pricing strategies, there may not exist a win-win policy. Our analysis shows that several findings in the single-period models prevalent in the supply chain research literature to date do not extend to the two-period model with two purchase opportunities. For example, returns policies and revenue sharing contracts are no longer equivalent. Also, quantity discounts may never lead to a win-win situation. In fact, the supplier may need to charge more for large orders in order to achieve a win-win outcome. Finally, the analytical framework of this paper can be applied to situations in which the price is constant but production costs change over time.     

Optimal echelon stock policies for multi-stage supply chains in fuzzy environments

This paper investigates decision-making in multi-echelon serial supply chain management in the presence of imprecision or uncertainty arising from human reasoning, emphasising the computational resolution. The proposed analysis method is based on a combination of the extension principle and the alpha-representation in fuzzy theory and optimisation theory. The problem is first formulated as a fuzzy optimisation model with several fuzzy parameters. To conserve the fuzziness of the input information of the supply chain, such as forecast market demands and inventory costs, a pair of two-level mathematical programs is proposed to identify the lower and upper bounds of the fuzzy performance at different possibility levels, so that the complete membership function can be described. Four example scenarios are solved to demonstrate the validity of the proposed analysis method. The proposed methodology is widely applicable with different types of membership functions for fuzzy parameters, positive lead times or other more complicated cases. The managerial implications are also discussed for reference by decision-makers.     

公平偏好下基于Stackelberg博弈的回购契约研究

引入公平偏好,构建了供应商与零售商进行Stackelberg博弈的回购契约模型,采用逆向归纳法分析了批发价的制定、回购契约的协调性以及供应链成员的公平偏好行为对批发价的影响。研究表明：无论是否考虑公平偏好,回购契约都不能实现供应链协调且公平偏好行为不会影响零售商的最优订购量。此外,供应商提供的批发价随着零售商公平偏好系数的增加而降低,但随供应商公平偏好的增加而升高。     

On deficiencies of common ordering policies for multi-level inventory control

We consider two common types of ordering policies for multi-level inventory control: installation stock (R,Q)-policies and echelon stock (R,Q)-policies. The batch quantities are assumed to be given, but each policy is optimized with respect to its reorder point R. We demonstrate that there is no bound for the worst case performance ratio of these policies when applied to distribution inventory systems with a central warehouse and a number of retailers.     

Pricing and ordering decisions in a supply chain with imperfect quality items and inspection under buyback of defective items

In this article, the economic production and inventory model in a three-layer supply chain including one distributor, one manufacturer and one retailer for a single-product and general demand functions under three scenarios is developed. We assume that during the production process, both healthy and defective items are generated. As the first scenario, we develop the first model, in which the defective items are not reworked and all considered as scrape, while in the second model, we assume that the defective items are reworked and are sold as perfect item. In the second scenario, we assume that defective item can be sold with lower price than the selling price. Moreover, raw materials with imperfect quality are sent back from a distributor to outside supplier under a lower price. Determining the order quantity of the distributor and the selling prices of the distributor and the manufacturer as well as the retailer was the goal of this article such that the total profit of each member is maximised. In order to solve the models, the Stackelberg approach is employed between the members, and the concavity of the profit functions is proved using several theorems. Then, closed form solutions are derived for the decision variables and a solution algorithm is proposed to determine the optimal solutions. Finally, a numerical example is presented to illustrate the applicability of the model.     

Optimal policies in hybrid manufacturing/remanufacturing systems with random price-sensitive product returns

We study a production planning problem in which a manufacturer aims to meet a random market demand by manufacturing new product and remanufacturing returned product. The product returns are random and price-sensitive. To maximise his profit, the manufacturer needs to optimally decide on the acquisition price for the returned product as well as the quantities of the new product to be manufactured and the returned product to be remanufactured. We investigate two cases based on the relative lengths of the manufacturing and remanufacturing lead times. (1) In the case with a shorter manufacturing lead time, the manufacturer first decides his acquisition price for the returned product before the production starts, and then decides the quantities of manufacturing/remanufacturing after the product returns are realised. (2) In the case with a shorter remanufacturing lead time, the manufacturer first decides the manufacturing quantity and the acquisition price simultaneously, and then the remanufacturing quantity based on the quantity of manufactured and returned products. Each case is formulated as a two-stage stochastic optimisation problem, and the corresponding optimal polices of both are characterised and derived.     

The boomerang returns? Accounting for the impact of uncertainties on the dynamics of remanufacturing systems

Recent years have witnessed companies abandon traditional open-loop supply chain structures in favour of closed-loop variants, in a bid to mitigate environmental impacts and exploit economic opportunities. Central to the closed-loop paradigm is remanufacturing: the restoration of used products to useful life. While this operational model has huge potential to extend product life-cycles, the collection and recovery processes diminish the effectiveness of existing control mechanisms for open-loop systems. We systematically review the literature in the field of closed-loop supply chain dynamics, which explores the time-varying interactions of material and information flows in the different elements of remanufacturing supply chains. We supplement this with further reviews of what we call the three ‘pillars’ of such systems, i.e. forecasting, collection, and inventory and production control. This provides us with an interdisciplinary lens to investigate how a ‘boomerang’ effect (i.e. sale, consumption, and return processes) impacts on the behaviour of the closed-loop system and to understand how it can be controlled. To facilitate this, we contrast closed-loop supply chain dynamics research to the well-developed research in each pillar; explore how different disciplines have accommodated the supply, process, demand, and control uncertainties; and provide insights for future research on the dynamics of remanufacturing systems.     

Multi-echelon service models for inventory systems under different rationing policies

In this paper we model the service performance of two-echelon divergent production networks consisting of one central stock-point feeding a number of end stock-points where the external demand is realized. The systems we consider allow all stock-points to hold inventory and use periodic review ordering policies at all levels. Whenever the lower echelon has insufficient inventory to cover all upper echelon requisitions some policy to ration the available material is needed. Concentrating on one push and one pull rationing policy, we explore the system dynamics and develop models for three popular measures of the system service performance. All models make use of non-dimensional ratios which drastically reduce the number of parameters involved. Although these models are only approximate, numerical and simulation results demonstrate the adequacy of the approximations involved.     

Coordination of pricing,inventory, and production reliability decisions in deteriorating product supply chains

In this article, we study a two-level supply chain model for deteriorating items, in which the supplier’s production system is unreliable and the retailer’s demand is price-sensitive. The supplier’s production line may randomly shift from the in-control state to the out-of-control state. When the production line is in the out-of-control state, a proportion of the produced products will have bad quality. To mitigate the out-of-control risks, the supplier can improve the production line reliability by investing in high-quality machines, highly skilled workers, or advanced maintenance technologies. We start with the study of pricing and inventory problems concerning endogenous reliability in the integrated and decentralised scenario. To better illustrate the proposed models, two applicable algorithms are designed to determine the optimal production reliability, ordering quantity, and prices. Then, a cooperative reliability investment and revenue-sharing contract is proposed to coordinate the supply chain. Numerical examples and sensitivity analysis of the equilibrium strategies and coordinating results on key system parameters (e.g. deterioration rate, production rate, etc.) are given to verify the effectiveness of the contract, and meanwhile get some managerial insights.     

Optimal batch ordering policies for assembly systems with guaranteed service

For a supply chain modelled as a multi-echelon inventory system, effective management of its inventory at each stock is critical to reduce inventory costs while assuring a given service level to customers. In our previous work, we used the guaranteed-service approach (GSA) to design optimal echelon batch ordering policies for continuous-review serial systems with Poisson customer demand and fixed order costs. The approach assumes that the final customer demand is bounded and each stock has a guaranteed service time in the sense that the demand of its downstream stock can always be satisfied in the service time. This paper extends this work by considering more general assembly systems. We first derive an analytical expression for the total cost of the system in the long run. The problem of finding optimal echelon batch ordering policies for the system can then be decomposed into two independent sub-problems: order size decision sub-problem and reorder point decision sub-problem. We develop efficient dynamic programming algorithms for the two sub-problems. Numerical experiments on randomly generated instances show the effectiveness of the proposed approach.     

供应链库存协调问题研究综述

供应链库存协调的研究具有很大的理论和现实意义,现已成为企业界和学术界关注的焦点,许多研究者进行了并且还在继续进行相关的研究工作。在查看大量文献的基础上,阐述了供应链库存协调的意义和概念,在此基础之上,从协调机制角度分5个方面对供应链库存协调的研究进行综述,提出未来研究的方向。为读者了解此领域的研究现状提供了依据。