Price discount based on early order commitment in a single manufacturer–multiple retailer supply chain

Early order commitment (EOC) is a strategy for supply chain coordination, wherein the retailer commits to purchasing from a manufacturer a fixed order quantity a few periods in advance of the regular delivery lead time. In this paper, we formulate and analyze the EOC strategy for a decentralized, two-level supply chain consisting of a single manufacturer and multiple retailers, who face external demands that follow an autocorrelated AR(1) process over time. We characterize the special structure of the optimal solutions for the retailers’ EOC periods to minimize the total supply chain cost and discuss the impact of demand parameters and cost parameters. We then develop and compare three solution approaches to solving the optimal solution. Using this optimal cost as the benchmark, we investigate the effectiveness of using the wholesale price-discount scheme for the manufacturer to coordinate this decentralized system. We give numerical examples to show the benefits of EOC to the whole supply chain, examine the efficiency of the discount scheme in general situation, and provide the special conditions when the full coordination is achieved.     

The value of early order commitment in a two-level supply chain

One approach to supply chain coordination is early order commitment, whereby a retailer commits to purchase a fixed-order quantity at a fixed delivery time before demand uncertainty is resolved. In this paper, we develop an analytical model to quantify the cost savings of an early order commitment in a two-level supply chain where demand is serially correlated. A decision rule is derived to determine whether early order commitment will benefit the supply chain, and accordingly to determine the optimal timing for early commitment. Our results indicate that the supply chain would experience greater savings from early order commitment when – (a) the inventory item receives less value-added activities at the retailer site; (b) the manufacturing lead time is short; (c) demand correlation over time is positive but weak; or (d) the delivery lead time is long (if a condition exists). We also propose a rebate scheme for the supply chain partners to share the gains of practicing early order commitment.     

A study on lead-time discount coordination for deteriorating products

Goods flowing through supply chains usually deteriorate. Such goods may corrupt, volatilize, and degenerate over time and thus cause the decline of their values or quantity. This study focuses on lead-time coordination for supply chains with deteriorating products which facilitates member cooperation and long-time relationships, thus increasing profit for the entire supply chain. A two-level supply chain with a single supplier and a single retailer is considered, in which the product deteriorates in the same manner for both the supplier and retailer, which is allowed to have shortages. A lead-time discount coordination strategy is used to maximize the profit of the entire supply chain by appropriately determining the optimal order quantity and lead-time. A numerical example is given, and sensitivity analyses are performed to analyze the influence of various parameters on the overall profit. The results can help managers establish long-term cooperative relationships in supply chains.     

需求预测更新条件下两阶段电子商务供应链契约协调

研究了一类在贝叶斯需求预测更新情形下,生命周期中采用B2C与C2B两阶段进行产品销售的供应链模型,研究发现无法使用单一契约来协调供应链。在此基础上,设计了具有供应商价格折扣契约与零售商承诺订购契约的两阶段供应链契约协调机制,证明了两阶段协调机制能够实现供应链的帕累托改进。算例分析表明了两阶段契约协调机制的有效性,并发现能够实现供应链完美协调的契约参数不一定在帕累托集合内,供应链不一定能够达到完美协调;且由于零售商与供应商的最优契约参数不同,需要通过零售商与供应商之间的谈判达到纳什均衡。     

Multi-period modeling of two-way price commitment under price-dependent demand

This paper examines the use of price-commitment policies in dynamic contracting in multiple-period, finite-time horizons. Two specific forms of price commitment are considered: one on the part of the retailer through a retail-fixed-markup contract and one on the part of the manufacturer through a price-protection contract. Optimal policies for each form of price commitment are analytically derived, as are optimal policies for the traditional price-only and centralized supply chain scenarios that we use as comparisons. We prove that optimal retail price and order size solutions exist in each period under the assumption of non-increasing price-dependent demand. We show that the existence of retailer inventory between periods causes the optimal policies to differ from a static single-period model. Further, we show that a supplier offers a price-protection policy as a signal to the retailer to resolve the gaming that naturally occurs under price-only; this effectively decouples the multi-period dynamic contracting setting into repeated single-period scenarios. However, the resulting behavior can actually inhibit supply chain performance. On the retail commitment side, we find that retail-fixed-markup policies are quite effective in improving supply chain efficiency. We show that such policies can lead to Pareto-improvement over price-only contracts and can even coordinate the supply chain in some situations.     

Coordinating order quantity decisions in the supply chain contract under random demand

In this paper, we are concerned with the coordinating quantity decision problem in a supply chain contract. The supply chain contract is composed of one manufacturer and one retailer to meet the random demand of a single product with a short lifecycle. Our analysis show that the retailer expects to obtain higher profit under proper ordering policies, which can also maximize the expected profit of the supply chain. The manufacturer may induce the retailer to order the coordinated quantity by adjusting the unit return price. As a result, the supply chain is expected to achieve the optimal expected profit.     

Single-supplier/multiple-buyer supply chain coordination: Incorporating buyers’ expectations under vertical information sharing

We address the coordination problem in a single-supplier/multiple-buyer supply chain. The supplier wishes to coordinate the supply chain by offering quantity discounts. To obtain their complete cost information, the supplier exchanges his own cost parameters with buyers leading to vertical information sharing. The supplier thinks that the buyers, as they have access to supplier’s setup and holding cost information, may demand a portion of the anticipated coordination savings based on the partial information they hold about the cost structure of the entire supply chain. We model each buyer’s expectations based on her limited view of the entire supply chain which consists of herself and the supplier only. These expectations are then incorporated into the modeling of the supply chain, which results in a generalization of the traditional Stackelberg type models. We discuss alternative efficiency sharing mechanisms, and propose methods to design the associated discount schemes that take buyers’ expectations into account. In designing the discount schemes, we consider both price discriminatory and non-price discriminatory approaches. The study adds to the existing body of work by incorporating buyers’ expectations into a constrained Stackelberg structure, and by achieving coordination without forcing buyers to explicitly comply with the supplier’s replenishment period in choosing their order quantities. The numerical analysis of the coordination efficiency and allocation of the net savings of the proposed discount schemes shows that the supplier is still able to coordinate the supply chain with high efficiency levels, and retain a significant portion of the net savings.     

时滞变质品供应链的数量折扣协调模型

在由单个批发商与单个零售商组成的两级时滞变质品供应链中,分别建立分散决策和集中决策下供应链系统的单位时间利润函数,通过比较得到集中决策优于分散决策的条件。引入数量折扣契约对时滞变质品供应链进行协调,促使整个供应链系统实现集中决策下的最优状态。设计收益共享合同来合理分配协调后的利润增量,保证批发商和零售商的单位时间利润都比协调前有所增加,从而实现供应链系统的帕累托改善。最后,通过数值算例演示了两种决策模式的单位时间利润情况,并分析了关键参数对供应链系统及各成员企业单位时间利润水平的影响。     

Coordination of cooperative cost-reduction efforts in a supply chain partnership

We study cooperative cost reduction in a decentralized supply chain with a single manufacturer and multiple suppliers. The manufacturer assembles components that are procured from the suppliers to produce a final product. Both the manufacturer and the suppliers invest in reducing the unit production costs of the components. We see that neither of the two well-known conventional contracts, the wholesale price contract and the cost-plus pricing contract, generally coordinates the supply chain, i.e., under both of these types of contract, the individual optimal cost-reduction efforts of players deviate from the centralized system-optimal solution. However, this result is not surprising because these contracts encourage either only the manufacturer or only the suppliers alone to invest in cost reduction.     

Managing a dual-channel supply chain under price and delivery-time dependent stochastic demand

Several leading manufacturers recently combined the traditional retail channel with a direct online channel to reach a wider range of customers. We examine such a dual-channel supply chain under price and delivery-time dependent stochastic customer demand. We consider five decision variables, the price and order quantity for both the retail and the online channels and the delivery time for the online channel. Uncertainty frequently arises in both retail and online channels and so additional inventory management is required to control shortage or overstock and that has an effect on the optimal order quantity, price, and lead time. We developed mathematical models with the profit maximization motive. We analyze both centralized and decentralized systems for unknown distribution function of the random variables through a distribution-free approach and also for known distribution function. We examine the effect of delivery lead time and customers’ channel preference on the optimal operation. For supply chain coordination a hybrid all-unit quantity discount along a franchise fee contract is used. Moreover, we use the generalized asymmetric Nash bargaining for surplus profit distribution. A numerical example illustrates the findings of the model and the managerial insights are summarized for centralized, decentralized, and coordinated scenarios.