CAMPBELL SOUP'S CONTINUOUS REPLENISHMENT PROGRAM: EVALUATION AND ENHANCED INVENTORY DECISION RULES

Campbell Soup's continuous replenishment (CR) program is a novel innovation designed to improve the efficiency of inventory management throughout the supply chain. With CR (1) retailers pay a constant wholesale price but continue to participate in consumer promotions, (2) retailers transmit to the supplier daily inventory information via electronic data interchange (EDI), and (3) the supplier assumes responsibility for managing retailer inventories, i.e., vendor managed inventories (VMI). We develop simple inventory management rules to operate CR, and we test these rules with a simulation using actual demand data provided by Campbell Soup. On this sample we find that retailer inventories were reduced on average by 66% while maintaining or increasing average fill rates. This improvementreduces a retailer's cost of goods sold by 1.2%, which is significant in the low profitmargin grocery industry. Furthermore, these savings could have been achieved without VMI.     

Potentially self-defeating: Group buying in a two-tier supply chain

Retailers have an incentive to cooperate in the form of group buying (GB) when a supplier provides quantity discounts, because wholesale price under GB depends on total purchasing quantity rather than individual purchasing (IP) quantity. Most previous studies on GB focus on the benefits that buyers get but ignore the supplier׳s response to GB. In this paper, we take the supplier׳s response into consideration, and present a game model with a single supplier and two symmetric competing retailers in two systems: the retailers purchase individually, and the retailers group buy. Under a general quantity discount schedule, each system has a unique sub-game perfect equilibrium. The comparison between IP and GB suggests that GB may sabotage the benefits of all members in the supply chain (i.e., the supplier, the retailers, and the consumer). Retailers may hold contradictory attitudes toward GB before and after the publishing of the discount schedule. These insights are shown to be robust for the case when more than two retailers are involved, as well as the case when the supplier enjoys economies of scale based on the order volume. We suggest that a mixed discount schedule may help prevent the potential damage of GB. In addition, with significant economies of scale, the supplier and retailers may be better off under GB. Then GB can be a favorable purchasing strategy.     

库存成本变化的VMI供应链协调

提出了库存成本变化的经济订货批量(EOQ)模型，基于该模型研究了库存成本变化时供应商管理库存(VMI)系统的最优协议问题。在该系统中，订货商和供应商达成缺货成本共担协议：当缺货发生时，供应商需要向订货商支付缺货补偿。订货商和供应商分散决策，订货商通过设计协议来减少其成本，而供应商通过制定补货决策来缩小自身成本。通过与传统系统和整合系统的比较，得出了库存成本变化时VMI系统的最优补货决策和缺货成本共担协议。采用数值算例验证了分析结果。结果表明，当且仅当供应商预期成本等于整合系统的最小总成本与固定缺货罚金之和时，VMI系统与整合系统具有相同的补货决策和系统绩效，即能够实现供应链协调。     

Optimal responses to stockouts: Lateral transshipment versus emergency order policies

In the retail industry, stockouts have a significant effect on a firm׳s profitability. When a stockout takes place, retailers often apply one of two strategies to resolve the issue – placing an emergency order with their supplier or arranging a lateral transshipment with a nearby partner store. Choosing the optimal response to a stockout is complicated by customers׳ spontaneous reactions. Customers who find that a product is out of stock may choose to give up on the purchase, to wait for delivery (through emergency order or lateral transshipment), or go to a partner store to search for the product on their own. In this study, under a single-period setting with two retail stores, we investigate the optimal inventory decisions under each strategy, and conduct a comparison between lateral transshipment and emergency order options. We also analyze the effects of the customer requesting rate and switching rate on the optimal inventory decision. Through numerical analysis, the two strategies are compared in terms of inventory levels and profitability. The results suggest that in addition to the cost associated with each of these strategies, the customers׳ behavior in response to a stockout has a significant effect on the optimal decision. The emergency order strategy is a better option when more customers request deliveries or when more customers switch to another store. Extending this analysis, we also examine the combined strategy when an emergency order is placed after a transshipment fails to fulfill unmet demands, and explore the circumstances under which this strategy provides the highest additional profit for the stores. Finally, we also find that a higher requesting rate does not necessarily increase profits, particularly when there is a high customer switching rate, because requesting emergency order or transshipment reduces switching demand.     

物流联合外包下库存管理模式对供应链运作的影响

针对由供应商、第三方物流服务商和零售商组成的供应链,考虑供需双方将物流服务联合外包给第三方物流服务商、共同承担运费的情形,探究供应商管理库存和寄售库存两类库存管理模式的引入对供应链运作及合同设计的影响。分别在传统的零售商管理库存、仅引入寄售库存的零售商管理寄售库存以及同时引入供应商管理库存和寄售库存的供应商管理寄售库存三种模式下,构建了第三方物流服务商主导、供应商和零售商跟随的序贯非合作博弈模型,证明了所有模式下均衡的订购量/寄售量均存在且唯一,并探讨了均衡结果随零售商运费分摊比例、转移支付价格两个关键参数的变化。横向对比三种模式下的均衡结果和集中决策下的最优结果,发现：零售商管理库存模式下的均衡订购量总是低于零售商管理寄售库存模式以及集中决策下的结果,而其他库存管理模式下的订购量并非一定低于集中决策下的结果;不同库存管理模式下,均衡状态下的订购量/寄售量及供应链总的期望收益大小关系取决于供应商和零售商的类边际(毛利)贡献率,从而表明,供应链环境下,上下游成员企业的收益结构、盈利水平等对于库存决策及库存模式的选取有重要影响。此外,在绝大多数情形下,不同库存管理模式下的均衡订购量与集中决...     

区分仓库与货架库存需求影响效应的零售商库存决策

既往有关库存水平影响需求条件下的库存问题研究中,通常对终端库存水平是否存在货架与零售商仓库库存水平的区别未作深入探讨。本文的研究认为,现实中许多零售商拥有仓库,其现有库存水平包括仓库库存和货架库存两部分,而影响需求的仅为与货架展示能力相关的库存,因此有必要对二者的需求影响效应进行区分。在明确这一区别的前提下,本文首先建立了供应商管理库存情况下库存水平影响需求问题的一般库存模型,给出零售商的最优订货策略;并考虑货架的容量限制,给出零售商启用仓库的判断条件。由于仓库库存仅在能够影响货架展示能力的条件下才能够影响消费需求,本文还进一步讨论了在零售商拥有仓库时,区分货架与仓库的库存水平影响需求条件下的最优库存与订货决策。这对于经营不同特征商品的零售商在进行是否需要拥有仓库,以及拥有仓库条件下的库存决策具有很好的参考价值。     

Beyond Information Sharing: An Empirical Analysis of Vendor‐Managed Inventory

Using a unique, item‐level data set, we examined benefits to downstream firms (distributors) from the decision‐transfer component of vendor‐managed inventory (VMI), the feature that distinguishes VMI from other information‐sharing, collaborative supply chain programs. Our major findings are that the decision‐transfer component of VMI adds significant benefits to the downstream firm in terms of inventory and stockout reductions above and beyond information sharing, and that these two benefits may be realized at different times following VMI implementation; that is, inventory reduction, initially, may be the major benefit to distributors from VMI, while the benefits of stockout reduction may more likely be realized after the first year of implementation. In addition, VMI provides benefits to the upstream firm (manufacturer) by reducing the downstream firm's inventory variability, a likely contributor to the bullwhip effect. Based on our empirical analysis, the decision‐transfer component of VMI, on average, reduces inventory levels by 7%, stockouts by 31%, and inventory variability by 9%.     

供应商管理库存应对突发事件

本文研究短生命周期供应链,它由一个生产商和一个销售商组成,供应商替销售商管理库存。首先指出供应商管理库存同样存在激励冲突,出现双边际效应,即分权决策下供应商的存货量小于供应链利润最大的库存量。接下来,提出一个使供应链达到合作的合约--未售货物补偿合约,即,销售商要对没有售完的货物进行补偿。该合约具有参数简单,管理费用低,且能将供应链利润在供应商和销售商之间任意分配。然后研究当突发事件导致供应商的生产费用(包括采购费用,运输费用等)发生变化对供应链的影响。最后,提出一个能应对突发事件并使供应链达到合作的合约。利用数值例子说明合约的价值。     

供需不确定下基于MOI和VMI模式的供应链协同比较研究

为分析供应链运作机制对降低随机供应商产出和随机需求的影响,对比研究了两供应商-单制造商系统在MOI和VMI两种模式下的供应链协同模型。MOI模式下,制造商管理并持有库存,提出了供应风险共享的协同机制;VMI模式下,供应商管理并持有库存,提出了收益共享与额外惩罚的协同机制。分析了集中决策、MOI和VMI模式下的最优批量决策,证明了VMI模式下存在唯一的纳什均衡。研究还发现,VMI模式更容易协调供应链,有效降低供需不确定的影响。MOI模式下的供应链可实现帕累托改进,但不能实现协调;而当参数满足一定关系时,VMI模式下供应链的期望利润可达到集中决策。     

The Impact of Forecast Errors on Early Order Commitment in a Supply Chain*

Supply chain partnership involves mutual commitments among participating firms. One example is early order commitment, wherein a retailer commits to purchase a fixed‐order quantity and delivery time from a supplier before the real need takes place. This paper explores the value of practicing early order commitment in the supply chain. We investigate the complex interactions between early order commitment and forecast errors by simulating a supply chain with one capacitated supplier and multiple retailers under demand uncertainty. We found that practicing early order commitment can generate significant savings in the supply chain, but the benefits are only valid within a range of order commitment periods. Different components of forecast errors have different cost implications to the supplier and the retailers. The presence of trend in the demand increases the total supply chain cost, but makes early order commitment more appealing. The more retailers sharing the same supplier, the more valuable for the supply chain to practice early order commitment. Except in cases where little capacity cushion is available, our findings are relatively consistent in the environments where cost structure, number of retailers, capacity utilization, and capacity policy are varied.     

Storage constrained vendor managed inventory models with unequal shipment frequencies

We consider a supply chain where a vendor manages its multiple retailers' stocks under a vendor managed inventory (VMI) contract that specifies upper stock limits at the retailers' premises and overstock costs for exceeding those limits. We formulate a mixed integer nonlinear program that minimizes total supply chain costs and allows unequal shipment frequencies to the retailers. We develop an algorithm to solve its relaxed version which provides a lower bound cost solution. We propose a cost efficient heuristic procedure to generate delivery schedules to the retailers. We conduct a sensitivity analysis to provide insights on the performance of the proposed heuristic. Results show that our heuristic finds optimal or near optimal solutions, and it proposes substantial savings compared to the total supply-chain cost in the cases where there is no VMI and where there is VMI but with equal shipment frequencies to retailers.     

基于库存分担策略的装配系统准时供货模型研究

本文考虑一个由多供应商和单制造商构成的装配系统。当市场的需求时间无法确定时,制造商通过对供应商设定合理的库存分担策略来降低自身成本,供应商则需要自行决定对制造商的补货时间并承担相应的库存持有成本和延迟惩罚成本。文章同时建立了供应商之间的纳什博弈模型和以制造商为主方的主从博弈模型,以找到供应商的最佳供货时间和制造商最优的库存承担时限。通过对比不同模式下供应链的整体绩效,找到实现供应链协调运作的必要条件,并通过数据分析进一步证明相关结论。     

Managing stochastic demand in an Inventory Routing Problem with transportation procurement

We study an Inventory Routing Problem in which the supplier has a limited production capacity and the stochastic demand of the retailers is satisfied with procurement of transportation services. The aim is to minimize the total expected cost over a planning horizon, given by the sum of the inventory cost at the supplier, the inventory cost at the retailers, the penalty cost for stock-out at the retailers and the transportation cost. First, we show that a policy based just on the average demand can have a total expected cost infinitely worse than the one obtained by taking into account the overall probability distribution of the demand in the decision process. Therefore, we introduce a stochastic dynamic programming formulation of the problem that allows us to find an optimal policy in small size instances. Finally, we design and implement a matheuristic approach, integrating a rollout algorithm and an optimal solution of mixed-integer linear programming models, which is able to solve realistic size problem instances. Computational results allow us to provide managerial insights concerning the management of stochastic demand.     

VMI供应链下考虑补货策略的的契约设计

结合(r,Q)和(s,S)两种库存补货策略,提出了货权属供应商的VMI供应链的契约设计问题。采用风险分担的思想,给出了两种可行的风险分担的契约形式。在离散需求下,通过参数试验的形式,分别研究了两种契约形式对供应链效率的影响。研究结果表明,两种契约能够使得供应链的效率达到满意,同时对于影响效率的参数有一定的鲁棒性,并且在一定情况下能协调供应链。相比收益分享契约,引入风险分享的契约形式能够使得供应链协作的效率更高。研究结论对VMI契约设计有参考意义。     

Inventory and transshipment decisions in the rationing game under capacity uncertainty

In this paper, we consider the inventory decisions of two retailers who are supplied by a single supplier with uncertain capacity. When capacity is allocated in proportion to the retailers׳ orders, the retailers compete for the capacity by inflating their orders (i.e., the rationing game). In addition, we allow the retailers to implement transshipment between them such that they cooperate by transshipping the surplus stock of one to another who is out of stock. Our analysis of Nash equilibrium orders shows that, while order inflation in the equilibrium orders persists in the rationing game with transshipment, it may not occur if the amount of capacity shortage is small and the transshipment prices are low. Thus, carefully chosen transshipment prices may alleviate order inflation behavior. We also characterize centralized orders that maximize the total profit of the retailers and compare them to equilibrium orders. In particular, we investigate coordinating transshipment prices that induce the retailers to choose centralized orders. Our numerical analysis shows that, even for two identical retailers, coordinating transshipment prices exist in a more limited range of parameter values in the rationing game than they do outside the rationing game due to capacity uncertainty and limitation.     

Supplier competition and its impact on firm׳s sourcing strategy

Most research on firms׳ sourcing strategies assumes that wholesale prices and reliability of suppliers are exogenous. It is of our interest to study suppliers׳ competition on both wholesale price and reliability and firms׳ corresponding optimal sourcing strategy under complete information. In particular, we study a problem in which a firm procures a single product from two suppliers, taking into account suppliers׳ price and reliability differences. This motivates the suppliers to compete on these two factors. We investigate the equilibria of this supplier game and the firm׳s corresponding sourcing decisions. Our study shows that suppliers׳ reliability often plays a more important role than wholesale price in supplier competition and that maintaining high reliability and a high wholesale price is the ideal strategy for suppliers if multiple options exist. The conventional wisdom implies that low supply reliability and high demand uncertainty motivate dual-sourcing. We notice that when the suppliers׳ shared market/transportation network is often disrupted and demand uncertainty is high, suppliers׳ competition on both price and reliability may render the sole-sourcing strategy to be optimal in some cases that depend on the format of suppliers׳ cost functions. Moreover, numerical study shows that when the cost or vulnerability (to market disruptions) of one supplier increases, its profit and that of the firm may not necessarily decrease under supplier competition.     

基于Stackelberg博弈的变质物品分销网络设计模型

研究了一类短销售期的变质物品的分销网络设计问题.假定零售商的缺货成本依赖于分配给为其提供服务的分销中心的库存成本,供应商在销售期末给零售商提供第二次订货机会,供应商根据零售商的订货决策确定分销中心的最优选址和确定每个分销中心为哪些零售商提供服务,从而最小化总的运作成本(选址成本,运输成本,库存成本和变质成本),其中分销中心的运输成本和库存成本依赖于零售商确定的订货数量;而零售商则根据供应商的决策确定自身的最优订货决策,利用Stackelberg博弈分析的方法,建立了一类变质物品的分销网络设计模型,并使用拉格朗日松弛算法求解,最后通过数值算例分析了模型最优解对于参数的敏感性.     

The Impact of Information Sharing and Advance Order Information on a Supply Chain with Balanced Ordering

This paper considers a supply chain with one supplier and multiple retailers that face exogenous heterogeneous end‐customer demands, where all parties utilize base‐stock policies. Each retailer is restricted to order once in every order cycle and their orders are replenished in a balanced manner within the cycle. Our study investigates the impact of information sharing and advance order information (AOI) on the supply chain. We find that the supplier benefits from the two mechanisms via two important factors, the information about observed end‐customer demands and the decision on re‐establishing the replenishment sequence. We derive the supplier's optimal sequence for stochastically comparable end‐customer demands with AOI and propose a sequencing rule for the setting with information sharing. Our numerical study examines the cost impacts of two proposed mechanisms on the entire supply chain.     

考虑公平关切行为下竞争零售商的最优联合购买策略研究

本文考虑一个由两个竞争的零售商和一个供应商组成的两级供应链,其中供应商可通过提供批量折扣契约向两家竞争的零售商销售产品,而零售商表现出纵向公平关切(即当获得利润小于供应商的利润时,其获得一个负效用)。并且,考虑的两个零售商为了获得较低的批发价格可能更喜欢团购,进而它们将选择最佳订单数量来最大化其自身的效用。利用经典的纳什议价解决方案作为公平参考点,本文主要研究竞争与公平关切行为将如何影响零售商的联合购买策略。研究发现,当零售商追求公平时,联合购买策略优于单独购买策略,且越大竞争强度使得使用联合购买策略的优势越明显。此外,当零售商表现出不同的公平关切程度时,若批量折扣比例比较低,对公平关切敏感的零售商的效用总是小于对公平关切不敏感的零售商的效用;否则,对公平关切敏感的零售商的效用总是大于对公平关切不敏感的零售商的效用。     

Coordinating a Supply Chain System with Retailers Under Both Price and Inventory Competition

We investigate a supply chain system with a common supplier selling to downstream retailers who are engaged in both price and inventory competition. We establish the existence and uniqueness of the pure‐strategy Nash equilibrium for the retailer game and study how a supplier can coordinate the system to achieve the best performance. Our main conclusions are as follows: First, a buyback contract can be used to coordinate retailers competing on both price and inventory in a sense that optimal retail prices and inventory levels arise as the Pareto‐dominant equilibrium. With symmetric retailers, the system optimum arises as the unique symmetric equilibrium. Second, the particular type of competition experienced by retailers (price versus inventory competition) affects the characteristics of the contract. Specifically, strong price competition leads to a coordination mechanism with a positive buyback rate, where the supplier subsidizes retailers for leftover inventories; however, strong inventory competition leads to a negative buyback rate, where retailers are punished for overstocking. Using a linear expected demand function, we further explore the impact of system parameters on the coordination contract and the competitive equilibrium. We also find that the performance of the supplier's optimal contract is asymptotic to the system optimal coordination contract as competition becomes fierce.