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.     

双周期可变供货协议的运转优化模型:以漫友为例

关注一个双周期且存在单一供应商和多个经销商组成的供应链生产和库存的分配优化问题：第1个期间,供应商根据经销商的订单进行生产。从第2期间开始,通过引入一个双周期调整协议,供应商为经销商提供了一个可以在第2期间重新调整库存的机会,即每个经销商可以从供应商那里购买额外库存或销售回多余库存（转运实际发货、收货等交割可在经销商之间进行）。研究运用建立数学模型论证了双周期情况下一个供应商和多个经销商组成的纵向集中而横向分散型系统（半分散型系统）的生产、库存及价格最优均衡模型,接着通过实例数据分析,对完全集中型、半分散型和完全分散型系统转运优化效果进行比较,结果显示,完全集中型优化效果最好(最高13%),但实现难度大;而半分散型是否强于完全分散型系统,取决于调节协议中约定的批发价与生产成本之间的差距因素,差距越小,则半分散型系统的优化效果越强（最高3.39%）。     

Coordination of joint pricing-production decisions in a supply chain

We consider the coordination of dynamic, joint pricing-production/ordering decisions in a decentralized supply chain where a manufacturer outsources her product distribution/retailing function to an independent distributor/retailer. The manufacturer produces and wholesales her product to the distributor who, after some further processing, sells the product to an external market. In a leader-follower setting with convex production/ordering cost functions, both parties make pricing and production/ordering decisions over a discrete, finite-time horizon (a selling season) to maximize their respective profits. For a given manufacturer's (the leader's) wholesale price schedule, we develop a simple forward algorithm to solve the distributor's problem optimally, and prove a planning horizon property of the solution. Our key result is to show the existence of a manufacturer's price schedule that induces distributor to adopt decisions in the decentralized setting to achieve the performance of a centralized supply chain. Based on this channel-optimal pricing policy we then develop an incentive scheme for the manufacturer to achieve channel coordination. A numerical example is provided to compare the performance of different policies and lo reinforce key managerial insights generated through analysis.     

Incorporating a delay mechanism in ordering policies into multi-echelon distribution systems

In this paper, we devise a framework for obtaining the optimal ordering policy in a single location, continuous-review inventory system with arbitrary inter-demand times. We show that it is optimal to order at demand arrival epochs only if the inter-demand time has a constant or decreasing failure rate. When the inter-demand time has an increasing failure rate, we show that the optimal policy is to delay the order. We then extend this policy to multi-echelon distribution systems consisting of one supplier and many retailers. Both decentralized and centralized systems are considered. We derive expressions and procedures for the evaluation of the total cost and the computation of optimal delay in all the considered settings. More importantly, we study the impact of our delay policy in all the settings. The numerical results indicate that for the single-location model, the optimal delay can significantly reduce the total cost. Results from the single-location model can be applied to the decentralized multi-echelon system, where the upstream supplier acts as a single-location system. The supplier order delay can also have a significant impact (either positive or negative) on the retailers' total cost as well as the system's total costs. Finally, the impact of supplier order delay is minimal in the centralized multi-echelon setting. We offer an intuitive explanation for this observation.     

基于Bertrand闭环供应链的企业价格博弈模型

设计了一个具有供应商和两个零售商组成的Bertrand双寡头价格博弈的主从闭环供应链系统,给出了分散和集中两种模式下批发价、零售价、回收价以及各方利润的具体表达式并进行了比较,研究了供应链整体利润与产品和废弃品替代率的关系。最后,在此基础上分析了分散模式下零售商和生产商的具体对策,提出了两阶段数量折扣协调策略实现帕累托改进,并求出了折扣率和补贴率的具体范围,为进一步研究更一般的闭环供应链系统打下理论基础。     

资金与碳排放双重约束下低碳供应链决策研究

在低碳供应链背景下,建立制造商存在资金和碳排放双重约束下的Stackelberg博弈定价模型。探究了无资金约束、提前支付和银行贷款3种情形下企业定价和制造商融资决策问题,并分析了相关因素对最优决策和利润的影响。研究表明,当银行利率小于提前支付折扣因子时,制造商始终选择提前支付融资模式;反之,制造商的融资模式选择会受到碳排放影响因子和碳价的影响。而消费者偏好绿色产品时,可以减少制造商的融资规模,但会造成制造商和零售商利润的减少。     

资金约束下基于零售商竞争的融资模式对比研究

以单供应商与多个零售商的供应链为研究背景,供应商是供应链上的核心企业,而零售商面临着资金约束,与供应商签订收益共享契约。供应商为中小企业提供两种融资方式：保兑仓融资和延迟支付融资。本文研究两种融资对供应链绩效以及供应链各方的影响,构建单供应商和多零售商的Stackelberg博弈模型,发现保兑仓融资模式能增加零售商的订货量,这两种融资模式在分散型供应链下,供应商都可以设置合适的收益分配系数和批发价格实现在集中型供应链下的协调,并能够保证供应商利润最大化。     

Analysis of order timing tradeoffs in multi-retailer supply systems

We analyse the implications of order timing decisions in multi-retailer supply systems in a single period, newsvendor setting. Specifically, we investigate a supply chain with multiple retailers and a single supplier where one of the retailers is considered a preferred or primary customer of the supplier. In the base model (delayed commitment), customers order after observing demand and the supplier rations its production quantity to retailers according to a generalised uniform allocation rule. In the early-commitment model, the primary retailer commits to an order quantity prior to the selling season and receives her order in full. We compare the expected supplier and retailer profits under each of these strategies and specify conditions under which a particular commitment scheme benefits the supplier, the primary retailer, and the entire system. Our findings indicate that the supplier prefers early commitment under mild conditions, whereas the primary retailer's preference depends on the tradeoff between the supply risk and demand risk. We also compare our findings with a single-retailer system, and observe that both the supplier and the primary retailer benefit from the existence of additional customers under delayed-commitment in many contexts.     

The impact of retailers’ alliance on manufacturer’s profit in a dual-channel structure

When a manufacturer adds a direct sales channel to its existing retail channel, retailers may cooperate with one another to respond to this new competition. Our study develops a Cournot competition model in a dual-channel supply chain consisting of a manufacturer and multiple retailers. In a Stackelberg decision model, the manufacturer first sets the direct sales quantity and wholesale price, and then the retailers decide the order quantities. The results indicate that forming an alliance is not always beneficial for retailers. When direct sales cost is high, there is less likelihood for retailers to collaborate. On the other hand, retailers will form an alliance when direct sales cost is sufficiently low. This will likely reduce the manufacturer’s profit. As such decreasing direct sales cost is not necessarily beneficial for the manufacturer because of the retailers’ possible collaborative efforts. In addition, the study finds that when demand fluctuation increases or the manufacturer’s information accuracy decreases, it is more likely that retailers will form an alliance. After relaxing the assumption of homogeneous retailers, our numerical study validates the possibility of partial alliance. If some retailers’ marginal costs are sufficiently high, we could see the formation of a partial alliance.     

Consumer search,transshipment, and bargaining power in a supply chain

We study a decentralised supply chain with one manufacturer and two symmetric retailers who could transship their excess inventory between each other. Without transshipment, the retailer’s unsatisfied customers search and buy the product at the other retailer with some probability. With transshipment, the retailer can transship the other retailer’s excess inventory to fulfil its own unmet demand. However, a transshipment price is often charged by one retailer for transshipping goods to another. We show the retailer’s profit is unimodal in the transshipment price, and the manufacturer’s profit increases in the customer search probability. Although the retailer’s preference over transshipment depends on the magnitude of search probability and transshipment price, the retailer may always prefer the transshipment no matter their magnitude. We then study the effect of bargaining power over the transshipment decision (whether to transship between retailers and at what transshipment price). Our analysis suggests that the manufacturer always prefers to control the transshipment price rather than to control whether to transship, while the retailer can prefer both. We also find that increasing bargaining power always benefits the manufacturer but could hurt the retailer. We finally check the robustness of our results by investigating the case with asymmetric retailers     

竞争环境下两级供应链提前订购模式研究

针对两个零售商和单一供应商组成的某易逝品供应链,在考虑零售商之间的价格竞争前提下,分析了供应商对零售商实施提前订购折扣销售模式的决策过程.应用报童模型和Stackelberg模型,研究了零售商的最佳订购时期以及供应商的最优折扣因子的制定策略,构建了相应的决策模型,并对模型最优性进行了分析.     

Bullwhip effect and complexity analysis in a multi-channel supply chain considering price game with discount sensitivity

This paper constructs a multi-channel supply chain that includes a manufacturer, a dual-channel retailer and an online retailer. The dual-channel retailer has a traditional channel and an online channel, while the manufacturer cooperates with the retailers and opens a direct channel simultaneously. The horizontal and historical price discount sensitivities are taken into account to establish the price-sensitive demand functions. A price game model with the heterogeneous expectations is proposed and analysed with the methods of the stability domain, the bifurcation diagram and the maximum Lyapunov exponent. The complexity and bullwhip effect of each channel are investigated with respect to the price adjustment speed and historical price discount sensitivity. The results show that a moderate or low price discount sensitivity keeps the system stable and a high price discount sensitivity brings the system into the twofold cycle state or chaotic state. It is interesting that if both online channels increase the adjustment speeds with similar strategy the system will enter chaos through the Neimark–Sacker bifurcation. The bullwhip effect is affected by the price adjustment speed and the price discount sensitivity, especially in the double-period or chaotic state, where the bullwhip of the overall supply chain is increased significantly. The results show that controlling price discount sensitivity is useful for supply chain node companies.     

考虑搭便车和风险规避的零售商定价、渠道选择策略

针对一个风险规避型零售商和一个风险中性制造商组成的供应链,考虑消费者服务“搭便车”行为,构建单渠道和零售商双渠道下零售商主导的均值-方差模型。通过逆向求解,得到并对比供应链成员的最优决策。最后通过算例分析验证表明,零售商双渠道价格与零售商的风险态度和市场需求波动呈反比,制造商批发价格变化则相反;零售商风险规避程度在一定范围内时,集中决策下的期望效用比分散决策下的高;零售商在“搭便车”下开通网络渠道不一定总是有利的,且存在搭便车比例、促销努力系数和风险规避度的取值区间使得零售商开通网络渠道有利可图;相反,在最优区间之外时,则会对利润造成负增长,因此企业应合理地控制自身风险规避程度和成本系数才能更好地在双渠道模式下获得超额利润。     

多供应商、多销售商的两级供应链库存模型研究

研究多个供应商、多个销售商组成的两级供应链的库存系统,在具有价格弹性的市场需求、允许供应商和销售商产生缺货的条件下,针对有无价格折扣的两种情况,分别建立了供应商、销售商各自的库存模型;结合满足供应商和销售商Pareto有效性,建立了含价格折扣的供应链系统整体盈利最大的库存模型.     

The implication of vendor inventory liability period in a decentralised assembly system

This paper investigates a decentralised assembly system that consists of one manufacturer and multiple suppliers who produce the complementary components. In a single selling season, the manufacturer initially sets a vendor inventory liability period (VILP) to control the suppliers’ delivery times, and the suppliers simultaneously determine when to deliver their components. Given the firms’ equilibrium strategies, we find that it is not wise for the manufacturer to set an overly long VILP, since having no inventory is not always beneficial to the manufacturer. A supplier may choose to postpone his delivery when the length of the VILP increases or the other suppliers’ deliveries are delayed, and either of these conditions is detrimental to the supplier’s profitability. We also examine the impact of VILP under different situations and find that having VILPs customised for different suppliers can reduce the manufacturer’s cost as well as improve the supply chain’s overall efficiency.     

多个损失厌恶零售商共存的一对多供应链 回购契约及其协调机理

为实现供应链的整体运作绩效最大,本文以一个风险中性的供应商和多个损失厌恶的零售商组成的两阶段供应链为研究对象,基于前景理论对损失厌恶的界定,采用考虑零售商损失厌恶系数的供应链回购契约模型。论证得出,多个存在竞争关系的损失厌恶零售商存在唯一的纳什均衡总订购量使其期望效用最大;在零售商的损失厌恶程度较大或者数量较少的情况下,通过供应链回购契约的协调,存在唯一的回购价格使得供应链的整体运作绩效最大,实现供应链协调。     

Optimal stocking strategies for inventory mechanism with a stochastic short-term price discount and partial backordering

Price discount is an important research topic in the field of inventory management. The existing research on this topic mainly considers fixed price discount, but ignores the situation in which stochastic short-term price discount may be involved. In this paper, we study an inventory problem considering stochastic short-term price discount and partial backordering. To address this problem, we propose an optimal replenishment and stocking model to maximise the retailers' profit. After that, a cost–benefit analysis-based heuristic method for solving the developed model is presented by considering two scenarios depending on whether a replenishment point belongs to a discount period or not. Furthermore, an algorithm is provided to elicit an optimal ordering policy from multiple solutions derived from the given heuristic solution method. Finally, a real case is offered to demonstrate the application of the proposed model, followed by a sensitivity analysis. The results indicate that a retailer can identify the optimal replenishment policy with the aim of achieving maximal profit in situations where stochastic short-term price discount and partial backordering are considered for certain inventory problems at hand. In addition, sensitivity analysis illustrates a fact that different values of the introduced parameters may influence the optimal replenishment policy.     

An application of designing products and processes for supply chain management

In this paper we describe an application of designing products and processes for supply chain management at a large electronics products manufacturer. The objective of our research project was to reduce the costs of complexity resulting from a proliferation of parts and processes in the manufacturer's supply chain. In order to perform this analysis, we developed the Supply Chain Modeling and Analysis Tool (SCMAT). SCMAT models decentralized supply chains and is less data-in tensive and yet more general than previous work in this area.     

基于讨价还价博弈的ATO供应链零部件生产及补货策略

通过建立ATO供应链中最终产品制造商与其两个供应商间的讨价还价合作模型,研究了ATO供应链的零部件生产补货策略和相应的利润分配策略,并探讨了供应链中各合作主体议价能力对最优解的影响。研究发现,ATO供应链应随着最终产品销售价格的提高而增加零部件产量,随最终产品组装成本或零部件生产成本的提高而减少零部件产量;随着最终产品制造商对其中一个供应商议价能力的增强,该供应商零部件的转移价格及其利润会降低,而另外一个供应商的零部件转移价格和利润会提高;若最终产品制造商比另外一个供应商的议价能力强,其期望利润会得到提高,反之,则会降低。     

Demand information sharing and channel choice in a dual-channel supply chain with multiple retailers

In this paper, under a dual-channel supply chain consisting of a manufacturer and multiple retailers, we investigate vertical and horizontal information sharing in different channel structures and the manufacturer’s choice on whether or not to keep a direct channel. To this end, we first study the dual-channel structure where uncertain demand is a linear function of price with a generalised-distribution base demand and show that the retailers have incentives to share information horizontally but not vertically, while the manufacturer is better off with vertical information sharing but its expected profit is not affected by horizontal information sharing. We next examine the retail-channel structure and find the basic results remain unchanged. Finally, we provide closed-form internal and external conditions under which the manufacturer can benefit from owning a dual-channel structure. Our study extends the existing literature by combining information sharing and dual-channel choice, introducing channel difference, discussing the impact of channel structure on horizontal and vertical sharing as well as providing interesting managerial insights for channel choice.