A two-echelon inventory model for a deteriorating item with stock-dependent demand,partial backlogging and capacity constraints

This study investigates a two-echelon supply chain model for deteriorating inventory in which the retailer’s warehouse has a limited capacity. The system includes one wholesaler and one retailer and aims to minimise the total cost. The demand rate in retailer is stock-dependent and in case of any shortages, the demand is partially backlogged. The warehouse capacity in the retailer (OW) is limited; therefore the retailer can rent a warehouse (RW) if needed with a higher cost compared to OW. The optimisation is done from both the wholesaler’s and retailer’s perspectives simultaneously. In order to solve the problem a genetic algorithm is devised. After developing a heuristic a numerical example together with sensitivity analysis are presented. Finally, some recommendations for future research are presented.     

Integrated location and two-echelon inventory network design under uncertainty

In this paper, we propose a two-stage stochastic model to address the design of an integrated location and two-echelon inventory network under uncertainty. The central issue in this problem is to design and operate an effective and efficient multi-echelon supply chain distribution network and to minimize the expected system-wide cost of warehouse location, the allocation of warehouses to retailers, transportation, and two-echelon inventory over an infinite planning horizon. We structure this problem as a two-stage nonlinear discrete optimization problem. The first stage decides the warehouses to open and the second decides the warehouse-retailer assignments and two-echelon inventory replenishment strategies. Our modeling strategy incorporates various probable scenarios in the integrated multi-echelon supply chain distribution network design to identify solutions that minimize the first stage costs plus the expected second stage costs. The two-echelon inventory cost considerations result in a nonlinear objective which we linearize with an exponential number of variables. We solve the problem using column generation. Our computational study indicates that our approach can solve practical problems of moderate-size with up to twenty warehouse candidate locations, eighty retailers, and ten scenarios efficiently.     

A periodic-review inventory control policy for a two-level supply chain with multiple retailers and stochastic demand

We consider a time-based inventory control policy for a two-level supply chain with one warehouse and multiple retailers in this paper. Let the warehouse order in a fixed base replenishment interval. The retailers are required to order in intervals that are integer-ratio multiples of the base replenishment interval at the warehouse. The warehouse and the retailers each adopt an order-up-to policy, i.e. order the needed stock at a review point to raise the inventory position to a fixed order-up-to level. It is assumed that the retailers face independent Poisson demand processes and no transshipments between them are allowed. The contribution of the study is threefold. First, we assume that when facing a shortage the warehouse allocates the remaining stock to the retailers optimally to minimize system cost in the last minute before delivery and provide an approach to evaluate the exact system cost. Second, we characterize the structural properties and develop an exact optimal solution for the inventory control system. Finally, we demonstrate that the last minute optimal warehouse stock allocation rule we adopt dominates the virtual allocation rule in which warehouse stock is allocated to meet retailer demand on a first-come first-served basis with significant cost benefits. Moreover, the proposed time-based inventory control policy can perform equally well or better than the commonly used stock-based batch-ordering policy for distribution systems with multiple retailers.     

An algorithm for solving the multi-period online fulfillment assignment problem

This paper develops an optimal solution procedure for the multi-period online fulfillment assignment problem to determine how many and which of a retailer/e-tailer’s capacitated regional warehouse locations should be set up to handle online sales over a finite planning horizon. To reduce the number of candidate solutions in each period, dominance rules from the facility location literature are extended to handle the nonlinear holding and backorder cost implications of our problem. Computational results indicate that multi-period considerations can play a major role in determining the optimal set of online fulfillment locations. In 92% of our test problems, the multi-period solution incorporated fewer openings and closings than myopic single period solutions. To illustrate the use of the model under changing demands, the multi-period solution yielded different supply chain configurations than the myopic single period solution in over 37% of the periods.     

随机弹性需求下供应链销售价格与提前期联合决策及协调机制

研究了市场需求随机且对销售价格及提前期敏感的条件下,供应链如何制定最优的销售价格、提前期以及库存因子使得利润最大化。首先,分析了集中决策与分散决策供应链的最优决策,发现集中决策与分散决策模式下的提前期与库存因子是相同的,但分散决策下的销售价格更高、期望利润更低,且分散决策与集中决策供应链的利润之比随着需求对价格的敏感程度的增大而增大。然后建立了收入共享与成本分担的协调机制,并分析了其最优决策。研究发现,协调决策机制可以有效地压缩提前期,并能同时使供应链达到帕累托改进,但不能达到完美协调,而且还发现协调决策下制定的最优销售价格比分散决策要低。最后通过数值计算对三种供应链决策模式下的绩效进行了比较分析,结果表明供应链利润随着需求方差增大而减小,提前期压缩程度随着材料成本承担比例增大而增大。上述结论可以为企业制定销售价格与提前期决策以及企业间的协调提供有益的指导。     

基于无缺陷退货的供应链成本补贴策略

在一个供应商与一个零售商组成的供应链中,讨论了逆向物流中的无缺陷退货问题。无缺陷退货的成本很高,并且都是由供应商承担。为了减少无缺陷退货的数量,需要零售商付出努力,因此供应商应当对零售商的努力成本进行补贴。当零售商的成本可以验证时,证明了成本分担合同可以协调供应链,并且讨论了供应链的利润分配问题;如果零售商的成本不易验证,供应商也可以采用零售努力水平的线性补贴合同达到相同的目的;最后结合数值算例说明了所得结果并分析了渠道内存在Pareto改进的可能性。     

First- and second-price sealed-bid auctions applied to push and pull supply contracts

We investigate a newsvendor-type retailer sourcing problem under demand uncertainty who has the option to source from multiple suppliers. The suppliers’ manufacturing costs are private information. A widely used mechanism to find the least costly supplier under asymmetric information is to use a sealed-bid reverse auction. We compare the combinations of different simple auction formats (first- and second-price) and risk sharing supply contracts (push and pull) under full contract compliance, both for risk-neutral and risk-averse retailer and suppliers. We show the superiority of a first-price push auction for a risk-neutral retailer. However, only the pull contracts lead to supply chain coordination. If the retailer is sufficiently risk-averse, the pull is preferred over the push contract. If suppliers are risk-averse, the first-price push auction remains the choice for the retailer. Numerical examples illustrate the allocation of benefits between the retailer and the (winning) supplier for different number of bidders, demand uncertainty, cost uncertainty, and degree of risk-aversion.     

零售商主导的模糊供应链博弈——考虑销售努力的情形

以包含一个制造商与一个零售商的两级供应链为研究对象,考虑零售商居于主导地位并付出销售努力时供应链各成员的决策。结合经济环境的不确定性,将市场需求函数和制造商的制造成本、零售商的经营成本视为模糊变量;运用斯塔克尔伯格模型刻画零售商和制造商之间的博弈过程,并引入期望值模型、机会约束模型来解决最优决策问题;通过一个数值算例证明了供应链博弈模型的有效性。研究表明,在均衡结果中,考虑到零售商所承担的销售努力成本,其总体期望值利润相比于制造商而言偏低,但单位产品边际利润较高。原因在于,零售商的主导地位使其不仅通过销售努力提高产品销量,提高了供应链的整体利润,同时也能够采用压低批发价格的方式,使自身在供应链中获取更多收益。     

供应商存在供应风险时供应链融资模式选择研究

在单供应商和单零售商组成的二级供应链中,零售商面临资金约束,有保兑仓融资和延迟支付融资两种途径完成订货货款的交付,在考虑供应风险时,本文研究零售商对融资模式的选择问题。得知在这两种融资途径下,若供应比率期望值在临界值以下,供应商为了协调好供应链状态,多倾向于设置比较恰当的批发价格;因自有营运资金比率(即零售商与供应商的比率)表现为波动性特征,通常在供应风险波动的情况下,供应商为保证自身利润的最大化,可向零售商提供适宜的融资模式。     

碳限额及交易下零售商低碳宣传的双渠道供应链决策与协调

在碳限额及交易下,考虑制造商碳减排技术投入和零售商低碳宣传,分别构建了无低碳宣传成本分摊、低碳宣传成本分摊的分散决策和集中式决策博弈模型通过对模型的分析,指出通过碳减排成本和低碳宣传成本分摊能够实现双渠道供应链协调.研究结果表明:在碳限额及交易机制下,碳减排率与碳排放交易价格成正向变化关系,低碳宣传水平、双渠道供应链利润与碳排放交易价格成U变化关系;碳减排率、低碳宣传水平、双渠道供应链利润与消费者低碳偏好系数、低碳宣传对消费者的影响系数都成正向变化关系;碳减排率、低碳宣传水平、双渠道供应链利润都与低碳宣传成本、碳减排成本系数成反向变化关系.     

公平偏好下基于批发价契约的供应链 协调研究

文中基于Nash讨价还价博弈思想建立公平偏好框架,构建公平偏好效用体系,以此为基础对采用批发价契约的报童模型展开行为研究,采用数理模型和数值分析方法分析了零售商和供应商的公平偏好行为对零售商和供应链系统最优订货量的影响,即零售商和供应商同时关注公平时,零售商和供应链系统的最优订货量趋于保守;并发现零售商和供应链系统的最优订货量随零售商的公平偏好程度增加而递减,但随着供应商公平偏好程度增加而递增,且供应链系统最优订货量变化趋势比零售商明显．然后,在此基础上分析比较得到,无论供应商和零售商是否偏好公平,批发价契约都不能实现供应链协调．最后,对批发价、零售价、供应商生产成本、零售商缺货成本和供应商缺货成本进行敏感度分析．     

销售努力及双市场化期权下的三级供应链协调

本文针对需求随机且受到零售商销售努力影响的情况,研究了由制造商、分销商和零售商组成的三级供应链的协调问题。文章首先用双期权契约对三级供应链进行协调,即在制造商和分销商以及分销商和零售商之间都采用期权契约,发现在零售商独自承担努力成本的情况下仅通过双期权契约无法协调供应链。因此在双期权契约的基础上加入了努力成本共担契约,发现当期权价格满足某种线性关系以及零售商努力成本按特定比例分摊时,联合双期权契约和努力成本共担契约能顺利协调供应链。在此基础上,文章还引入了期权的市场化定价规则,研究了期权采用市场化定价规则对供应链协调产生的影响,研究表明,引入期权市场化定价规则增加了供应链协调需要满足的条件,降低了协调的可能性,且协调状态下的期权价格受到市场因素如利率、价格波动率等的影响。最后,文章给出了期权市场化定价规则下供应链协调的条件以及参数变化对协调的影响。     

Monotonicity properties of wholesale price contracts

This paper contributes to the supply chain contracts literature in economics and operations by performing qualitative sensitivity analysis of a wholesale price contract in a two-echelon supply chain setting. Order-theory tools are used to derive sufficient conditions for monotonicity of contract parameters.The upstream supplier is modeled as a Stackelberg leader. The supplier is assumed to have complete information about the costs and revenue function of the downstream retailer. It is shown that an equilibrium wholesale price weakly increases with an increase in the supplier production cost rate, but it may increase or decrease with an increase in the retailer cost rate. As either the supplier production cost or the retailer cost increases, the supplier profit decreases weakly. Additional sensitivity analysis is performed assuming certain properties of the retailer revenue function.Several well-known results in the supply chain contracting literature can be considered as special cases of the more general theorems developed here. In particular, this paper reexamines the analysis of a newsvendor supply chain problem by Lariviere and Porteus [Lariviere, M.A., Porteus, E.L., 2001. Selling to the newsvendor: An analysis of price-only contracts. Manufacturing & Service Operations Management 3, 293–305]. This paper generalizes and extends their work, by establishing properties of the newsvendor demand distribution that guarantee monotonicity of the contract parameters, without requiring a unique contract solution.     

Logistics cost sharing in supply chains involving a third-party logistics provider

In many cases, end customers are sensitive to a product’s logistics service level which is provided by a third-party logistics (3PL) provider, therefore, the continuous improvement of the logistics service is imperative and valuable. However, the problem is that improving the logistics service benefits all of them, but is costly to only the 3PL provider. The 3PL provider is not willing to do this. Sharing the logistics cost is one solution to this problem. This study investigates cost sharing in two kinds of supply chains, i.e., one manufacturer-one 3PL provider-one retailer supply chain and two manufacturers-one 3PL provider-one retailer supply chain. Two types of cost sharing mechanisms, i.e., decentralized cost sharing mechanisms and centralized cost sharing mechanisms, are explored. Decentralized cost sharing mechanisms are proposed as contracts that chain members separately decide their cost sharing portions to optimize their own profits, ignoring the collective impacts of their decisions on the channel as a whole. Centralized cost sharing mechanisms are in the situation that chain members negotiate their cost sharing portions so that their profits are the shares of the entire supply chain’s profit, implying that the supply chain is coordinated perfectly. This study aims to analyse how cost sharing mechanisms affect supply chain performance and under what conditions chain members are willing to engage in cost sharing mechanisms. Conditions necessary for cost sharing mechanisms to achieve win-win outcomes are identified.     

Analysis of a fuzzy economic order quantity model for deteriorating items under retailer partial trade credit financing in a supply chain

This paper investigates the economic order quantity (EOQ) — based inventory model for a retailer under two levels of trade credit to reflect the supply chain management situation in the fuzzy sense. It is assumed that the retailer maintains a powerful position and can obtain the full trade credit offered by the supplier yet the retailer just offers a partial trade credit to customers. The demand rate, holding cost, ordering cost, purchasing cost and selling price are taken as fuzzy numbers. Under these conditions, the retailer can obtain the most benefits. Study also investigates the retailer’s inventory policy for deteriorating items in a supply chain management situation as a cost minimization problem in the fuzzy sense. The annual total variable cost for the retailer in fuzzy sense is defuzzified using Graded Mean Integration Representation method. Then the present study shows that the defuzzified annual total variable cost for the retailer is convex, that is, a unique solution exists. Mathematical theorems and algorithms are developed to efficiently determine the optimal inventory policy for the retailer. Numerical examples are given to illustrate the theorems and the algorithms. Finally, the results in this paper generalize some already published results in the crisp sense.     

基于多种运输渠道的经济批量问题的多项式时间算法

为了集中管理, 降低成本, 增强竞争优势, 供应商通常只负责生产,而把产品的配送业务外包给某个配送中心, 由配送中心按照零售商的需求决定发货运输的方式和时间.这样供应商, 配送中心和零售商就构成了二级供应链系统.本文研究的是运输方式为不同参数的全单位数量折扣结构时, 二级供应链系统的经济批量问题.分析了最优解的性质,并对此问题的一种特殊情形给出一个多项式时间算法.     

基于广告、技术、奖励的二级供应链效益最大化研究

研究了做广告、引进先进技术、奖励员工对供应链效益影响问题.针对单个制造商与单个零售商组成的二级供应链,基于弹性需求,在促销-价格敏感需求、质量-敏感需求与奖励-敏感成本条件下构建模型.以整个供应链的利润之和最大,且制造商与零售商利润之差的平方和最小为目标.首先,通过Lagrange数乘法求解,判断对应的Hesse矩阵.其次,确定了广告、技术与奖励员工的最佳投入量,实现供应链效益最大化,提高供应链的经济效益.同时,也通过收益共享,实现供应链的协调性,优化供应链产业结构.最后运用数值实验来具体说明各因素对供应链最大效益的影响.     

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.     

考虑消费者低碳偏好的供应链企业减排成本分摊比较研究

在低碳环境下,研究了单一制造商和单一零售商组成的两级低碳供应链成本分摊决策问题。考虑消费者具有环保意识,因此在购买产品时会考虑产品的碳排放。分别讨论了零售商参与减排成本分摊契约和双方Nash讨价还价成本分摊契约两种形式对碳减排、产品定价和整个供应链及其成员收益的影响。研究发现,在两种契约形式中,零售商都可以实现与制造商共同降低碳排放的目标,从而促进制造商提高碳减排率,提高供应链利润。但是基于Nash讨价还价方式的减排成本分摊契约的供应链绩效高于零售商成本分摊契约下的供应链绩效。同时消费者低碳偏好增加可以激励零售商更多地分摊减排成本,在此基础上,利用Nash讨价还价模型确定了零售商为制造商提供减排成本分摊的比例范围及其最优解。最后,通过数值分析验证了减排因子对不同决策结构的定价、零售商减排分摊比例、供应链利润等决策的影响。     

Channel coordination in green supply chain management

Environmental consciousness has become increasingly important in everyday life and business practice. The effort to reduce the impact of business activities on the environment has been labelled as green supply chain management. Any major greening project would require efforts on the part of the entire supply chain. However, very few studies have addressed the issue of coordinating the green supply chain. We consider the problem of coordination of a manufacturer and a retailer in a vertical supply chain, who put in efforts for ‘greening’ their operations. We address some pertinent questions in this regard such as extent of effort in greening of operations by manufacturer or retailer, level of cooperation between the two parties, and how to coordinate their operations in a supply chain. The greening efforts by the manufacturer and retailer result in demand expansion at the retail end. The decision variables of the manufacturer are wholesale price and greening effort, while those of the retailer are retail price and its greening effort. We find that the ratio of the optimal greening efforts put in by the manufacturer and retailer is equal to the ratio of their green sensitivity ratios and greening cost ratios. Further, profits and efforts are higher in the integrated channel as compared to the case of the decentralized channel. Finally, a two-part tariff contract is found to produce channel coordination in this problem. A numerical example illustrates the results.