A vendor managed inventory model under contractual storage agreement

Vendor managed inventory (VMI) is a supply chain partnership strategy that allows a supplier to place orders on behalf of its customers. This paper considers a supply chain composed of a single vendor and multiple retailers operating under a VMI contract that specifies limits on retailers' stock levels. We address the problem of synchronizing the vendor's cycle time with the buyers' unequal ordering cycles by developing a mixed integer non-linear program that minimizes the joint relevant inventory costs under storage restrictions. We also propose a cost efficient heuristic to solve the developed optimization problem. We conducted computational experiments to assess the reduction in the total supply chain costs resulting from relaxing the restriction of equal ordering cycles. It is found that the heuristic generates greater cost savings in cases of increased variability in retailers' demand and cost parameters.     

An integrated approach for logistic and vendor managed inventory in supply chain

In this paper, a quaternary policy system towards integrated logistics and inventory aspect of the supply chain has been proposed. A system of multi retailers and distributors, with each distributor following a unique policy, will be analysed. The first policy is continuous time replenishment policy where the retailers’ inventory is replenished in every time interval. In the next three policies, inventory of the retailers will be replenished by some definite policy factors. The vendor managed inventory (VMI) system is used for updating the inventory of the retailers. An order-up-to policy (q, Q) is used for updating the inventory of distributors. Total erstwhile demands to the retailer will be used to determine the amount of inventory acclivity. Furthermore, the distributors will be sending the delivery vehicles to few fellow retailers who are shortlisted according to the policy, followed by the retailers and associated distributors. On the basis of random demand that the retailers are facing from end customers and the total demand that has incurred in the supply chain, products are unloaded to the selected retailers from the delivery vehicle. The path of the delivery vehicle is retrieved by dynamic ant colony optimization. In addition, a framework has been developed to measure the end-customer satisfaction level and total supply chain cost incorporating the inventory holding cost, ordering cost and the transportation cost. The framework has been numerically moulded with different settings to compare the performance of the quadruplet policies.     

基于确定需求的上游层面VMI模式的利益分配机制

假设外界需求确定,充分考虑供应商管理库存（VMI）对于供应链的影响,通过建立经济效果模型证明了上游层面VMI可使供应链上游整体受益.在此基础上,依据Stackelberg博弈及纳什均衡等理论,构建实施上游层面VMI后3种情境下的利益分配机制.该机制可体现在供应商所供产品价格契约的制定上,此契约既能弥补供应商因管理制造商库存而增加的成本,又可使制造商的利润得到保障,实现供需方的互惠共赢,还可为博弈主方在价格层面制定激励政策提供理论依据.     

基于博弈论和VMI的收益共享机制协调模型

以供应商和零售商组成的二阶段供应商管理库存（ＶＭＩ）供应链系统为研究对象,考虑随机需求下的ＶＭＩ系统中可能存在的滞销成本或缺货惩罚,建立了传统、Ｓｔａｃｋｅｌｂｅｒｇ博弈、Ｎａｓｈ协商的３种收益共享机制的协调模型,并得出Ｎａｓｈ协商能完美协调分散式ＶＭＩ供应链的结论．最后,通过数值算例对相关结论进行了验证和分析．     

Dynamic simulation assessment of collaboration strategies to manage demand gap in high-tech product diffusion

There is no question that many high-tech supply chains operate in a context of high process and market uncertainties due to shorter product life cycles. When introducing a new product, these supply chains must manage the cost of supply, including the cost of capacity and inventories, with revenues from the product’s demand over its life cycle. However, in early phase of introduction after earlier buyers purchase, there might be a demand gap for a period followed by a sudden surge. To stay responsive and serve the market downstream after such gaps, two important decisions must be made: (a) the sizing of the capacity, and (b) the level of collaboration. It is the intention of this paper to show that the chosen level of collaboration effects significantly on managing the gap in the demand trajectory in new high-tech product diffusion. We study the impact of different collaboration strategies like vendor managed inventory (VMI), jointly managed inventory (JMI), and a collaborative planning, forecasting & replenishment (CPFR) model using system dynamics based simulation and compare the results with a non-collaborative chain. Our results yield insights into effectiveness of collaboration in managing the dynamics of demand gap.     

Coordinating decisions by supply chain partners in a vendor-managed inventory relationship

We look into the linked decision making in the vendor-managed inventory (VMI) relationship. It is a supply chain management model, where the retailer decides the retail price while the vendor determines its capacity commitment. In this model, the retailer and the vendor should coordinate their decisions in order to maximize their individual profit or the total profit combining the two participants together. The vendor has to take into account the demand pattern throughout the product life cycle (PLC) when it decides its capacity commitment, which will affect its inventory management cost during the PLC, while the retailer should change the retail price over the PLC so as to maximize the revenues and minimize the inventory cost at the same time. Employing a system dynamics simulation approach based on differential game theory, which also takes into account the product characteristics such as the demand’s innovation and imitation effects, we analyze and confirm the dynamic coordination of key decision variables by the supply chain partners in the VMI relationship.     

Construct the stable vendor managed inventory partnership through a profit-sharing approach

In real life, the vendor managed inventory (VMI) model is not always a stable supply chain partnership. This paper proposes a cooperative game based profit-sharing method to stabilize the VMI partnership. Specifically, in a B2C setting, we consider a VMI program including a manufacturer and multiple online retailers. The manufacturer provides the finished product at the equal wholesale price to multiple online retailers. The online retailers face the same customer demand information. We offer the model to compute the increased profits generated by information sharing for total possible VMI coalitions. Using the solution concept of Shapley value, the profit-sharing scheme is produced to fairly divide the total increased profits among the VMI members. We find that under a fair allocation scheme, the higher inventory cost of one VMI member increases the surplus of the other members. Furthermore, the manufacturer is glad to increase the size of VMI coalition, whereas, the retailers are delighted to limit the size of the alliance. Finally, the manufacturer can select the appropriate retailer to boost its surplus, which has no effect on the surplus of the other retailers. The numerical examples indicate that the grand coalition is stable under the proposed allocation scheme.     

Analyzing the evolutionary stability of the vendor-managed inventory supply chains

One of the widely used strategies for achieving system integration in the arena of supply chain management is the vendor-managed inventory (VMI) approach. Although there exists a large amount of literature that examines various aspects of VMI, little looks at how this model evolves as the implementation progresses and matures. Therefore, this paper shows how to analyze the intrinsic evolutionary mechanism of the VMI supply chains by applying the evolutionary game theories. It is found that during the early stage of the VMI implementation, the upstream supplier will have some profit loss; however, as the transaction quantity increases in the long run, which will eventually benefit the entire chain, it is necessary for the downstream buyer to share profit with the upstream supplier to cover the supplier’s initial loss in order to exploit and sustain the benefits of the VMI. Additionally, the impact factors for VMI to become an evolutionary stable strategy are examined. All the results identify the conditions under which the VMI model is favorable over the traditional chain structure and shed lights on when and why collaboration is critical for a successful, long-term implementation of VMI.     

A hybrid vendor managed inventory and redundancy allocation optimization problem in supply chain management: An NSGA-II with tuned parameters

In this research, a bi-objective vendor managed inventory model in a supply chain with one vendor (producer) and several retailers is developed, in which determination of the optimal numbers of different machines that work in series to produce a single item is considered. While the demand rates of the retailers are deterministic and known, the constraints are the total budget, required storage space, vendor's total replenishment frequencies, and average inventory. In addition to production and holding costs of the vendor along with the ordering and holding costs of the retailers, the transportation cost of delivering the item to the retailers is also considered in the total chain cost. The aim is to find the order size, the replenishment frequency of the retailers, the optimal traveling tour from the vendor to retailers, and the number of machines so as the total chain cost is minimized while the system reliability of producing the item is maximized. Since the developed model of the problem is NP-hard, the multi-objective meta-heuristic optimization algorithm of non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to solve the problem. Besides, since no benchmark is available in the literature to verify and validate the results obtained, a non-dominated ranking genetic algorithm (NRGA) is suggested to solve the problem as well. The parameters of both algorithms are first calibrated using the Taguchi approach. Then, the performances of the two algorithms are compared in terms of some multi-objective performance measures. Moreover, a local searcher, named simulated annealing (SA), is used to improve NSGA-II. For further validation, the Pareto fronts are compared to lower and upper bounds obtained using a genetic algorithm employed to solve two single-objective problems separately.     

Fuzzy inference systems and inventory allocation decisions: Exploring the impact of priority rules on total costs and service levels

Inventory allocation decisions in a distribution system concern issues such as how much and where stock should be assigned to orders in a supply chain. When the inventory level of an inventory point is lower than the total number of items ordered by lower echelons in the chain, the decision of how many items to allocate to each ``competing'' order must take into consideration the trade-off between cost and service level. This paper proposes a decision-support system that makes use of fuzzy logic to consider inventory carrying, shortage and ordering costs as well as transportation costs. The proposed system is compared through simulation with three other inventory allocation decision support models in terms of cost and service levels achieved. Conclusions are then drawn.     

An integrated local search method for inventory and routing decisions

The present article studies an inventory routing model which integrates two important components of the supply chain: transportation logistics and inventory control. The distribution system examined consists of customers that face product demand at a deterministic and constant rate. Customer demand is satisfied by a fixed vehicle fleet located at the central depot. The aim of the problem is to determine the timing and size of the replenishment services together with the vehicle routes, so that the total transportation and inventory holding cost of the system is minimized. In methodological terms, we propose a solution approach applying two innovative local search operators for jointly dealing with the inventory and routing aspects of the examined problem, and Tabu Search for further reducing the transportation costs. The proposed algorithmic framework was tested on a set of new benchmark instances of various scales. It produced satisfactory results both in terms of effectiveness and robustness.     

Supply chain coordination with an option contract under vendor‐managed inventory

In this paper, we propose an option contract for a two‐echelon supply chain operating under vendor‐managed inventory (VMI). We find that the supply chain coordination and Pareto improvement can be achieved synchronously. As a comparison, a subsidy contract is introduced to coordinate the supply chain. The paper further considers the influence of a replenishment tactic on the performance of the supply chain. After introducing a replenishment tactic, the supply chain can replenish the products to satisfy unmet demand during the selling season. We further use an option contract to coordinate the supply chain, and a Pareto improvement can be gained. All our findings are numerically illustrated.     

考虑供应商选择的选址一库存一路径的联合优化

针对装配型制造企业供应链集成优化问题,建立了随机需求情形下整合供应商选择和各层级之间运输方式选择的多层级选址—库存模型。该模型通过对供应商的选择,装配厂和分销中心的选址,相邻两层级之间的分配服务关系及运输方式的确定,实现整体供应链网络成本最小化。为求解此混合整数非线性规划模型,设计了一种矩阵编码的改进自适应遗传算法。仿真实验表明,该算法的解的寻优能力明显优于标准遗传算法,得出了供应链总成本与装配厂的最大提前期存在一定规律性的结论。     

A study on inventory replenishment policies in a two-echelon supply chain system

Inventory control plays an important role in supply chain management. Properly controlled inventory can satisfy customers’ demands, smooth the production plans, and reduce the operation costs; yet failing to budget the inventory expenses may lead to serious consequences. The bullwhip effect, observed in many supply chain management cases, causes excessive inventory due to information distortion, i.e. the order amount is exaggerated while a minor demand variation occurs, and the information amplified dramatically as the supply chain moves to the upstream. In this paper, one of the main causes of bullwhip effect, order batching, is considered. A simplified two-echelon supply chain system, with one supplier and one retailer that can choose different replenishment policies, is used as a demonstration. Two types of inventory replenishment methods are considered: the traditional methods (the event-triggered and the time-triggered ordering policies), and the statistical process control (SPC) based replenishment method. The results show that the latter outperforms the traditional method in the categories of inventory variation, and in the number of backlog when the fill-rate of the prior model is set to be 99%. This research provides a different approach to inventory cost-down other than the common methods like: information sharing, order batch cutting, and lead time reduction. By choosing a suitable replenishment policy, the number of backorder and the cost of inventory can be reduced.     

基于VMI供应商资金受限的供应链协调策略

研究随机需求下供应商资金受限的供应链协调问题,基于供应商管理库存（VMI）建立零售商-供应商Stackelberg博弈模型,分析库存补贴策略和零售商预付款策略对供应链绩效的影响,并比较两种策略的适用范围。结果表明,零售商可以通过库存补贴策略消除分散决策下双重边际效应导致的供应链绩效损失,同时提高供应商和零售商利润。相比于库存补贴,零售商预付款策略可以消除由供应商资金受限导致的供应链绩效损失,并减小部分由双重边际效应导致的供应链绩效损失,实现帕累托改进,提高供应链整体绩效。     

随机需求下双渠道供应链库存动态交互优化

针对双渠道供应链库存系统导致的缺货与库存积压等问题，在线上线下均为随机需求的条件下，考虑生产延迟和物流延迟，建立了双渠道库存的单独控制、集中控制和交叉补货控制这三种模式的动态优化模型。首先，以库存动态微分方程为基础，创新性地以控制理论为指导思想，以泰勒展开和拉普拉斯变换为手段，得到双渠道库存系统的反馈传递函数；其次，考虑了交叉补货的进销存过程中的周期间交互、上下游间交互以及渠道间交互，利用延迟控制、反馈控制和比例-积分-微分（PID）控制构造了双输入、双输出的复杂交互系统，以此寻求双渠道库存系统自身以及渠道间的动态供需双平衡，优化双渠道库存持有量，降低缺货次数和缺货量并使其保持动态稳定状态；最后，通过数值仿真实验，对比三种双渠道库存控制策略。仿真结果表明，在线上线下渠道为不同分布的随机需求时，交叉补货控制的剩余库存比独立库存控制降低了4.9%，交叉补货控制的缺货率与独立控制和集中控制相比分别下降了66.7%和60%。实验结果表明，在线上线下渠道为不同分布的随机需求的情况下使用双渠道交叉补货策略能很好地降低库存持有量，减少缺货次数和缺货量，从而节约库存成本。     

随机需求下双渠道供应链库存动态交互优化

针对双渠道供应链库存系统导致的缺货与库存积压等问题,在线上线下均为随机需求的条件下,考虑生产延迟和物流延迟,建立了双渠道库存的单独控制、集中控制和交叉补货控制这三种模式的动态优化模型。首先,以库存动态微分方程为基础,创新性地以控制理论为指导思想,以泰勒展开和拉普拉斯变换为手段,得到双渠道库存系统的反馈传递函数;其次,考虑了交叉补货的进销存过程中的周期间交互、上下游间交互以及渠道间交互,利用延迟控制、反馈控制和比例-积分-微分（PID）控制构造了双输入、双输出的复杂交互系统,以此寻求双渠道库存系统自身以及渠道间的动态供需双平衡,优化双渠道库存持有量,降低缺货次数和缺货量并使其保持动态稳定状态;最后,通过数值仿真实验,对比三种双渠道库存控制策略。仿真结果表明,在线上线下渠道为不同分布的随机需求时,交叉补货控制的剩余库存比独立库存控制降低了4.9%,交叉补货控制的缺货率与独立控制和集中控制相比分别下降了66.7%和60%。实验结果表明,在线上线下渠道为不同分布的随机需求的情况下使用双渠道交叉补货策略能很好地降低库存持有量,减少缺货次数和缺货量,从而节约库存成本。     

A decision rule for coordination of inventory and transportation in a two-stage supply chain with alternative supply sources

This paper deals with a two-stage supply chain that consists of two distribution centers and two retailers. Each member of the supply chain uses a (Q,R) inventory policy, and incurs standard inventory holding and backlog costs, as well as ordering and transportation costs. The distribution centers replenish their inventory from an outside supplier, and the retailers replenish inventory from one of the two distribution centers. When a retailer is ready to replenish its inventory that retailer must decide whether it should replenish from the first or second distribution center. We develop a decision rule that minimizes the total expected cost associated with all outstanding orders at the time of order placement; the retailers then repeatedly use this decision rule as a heuristic. A simulation study which compares the proposed policy to three traditional ordering policies illustrates how the proposed policy performs under different conditions. The numerical analysis shows that, over a large set of scenarios, the proposed policy outperforms the other three policies on average.     

A hybrid genetic and imperialist competitive algorithm for green vendor managed inventory of multi-item multi-constraint EOQ model under shortage

The purpose of this paper is to develop a multi-item economic order quantity (EOQ) model with shortage for a single-buyer single-supplier supply chain under green vendor managed inventory (VMI) policy. This model explicitly includes the VMI contractual agreement between the vendor and the buyer such as warehouse capacity and delivery constraints, bounds for each order, and limits on the number of pallets. To create a kind of green supply chain, tax cost of green house gas (GHG) emissions and limitation on total emissions of all items are considered in the model. A hybrid genetic and imperialist competitive algorithm (HGA) is employed to find a near-optimum solution of a nonlinear integer-programming (NIP) with the objective of minimizing the total cost of the supply chain. Since no benchmark is available in the literature, a genetic algorithm (GA) is developed as well to validate the result obtained. For further validation, the outcomes are also compared to lower bounds that are found using a relaxed model in which all variables are treated continuous. At the end, numerical examples are presented to demonstrate the application of the proposed methodology. Our results proved that the proposed hybrid procedure was able to find better and nearer optimal solutions.     

基于混合需求的供应链多级库存协同订货模型

针对供应链多级库存系统存在混合需求的情况,建立了基于混合需求的多级库存协同订货模型。该模型假设在供应链中只有最下游节点面临的需求是独立需求,而其他上游节点面临的需求都是与之相关的相关需求。由于相关需求是一种块状需求,其库存成本构成与独立需求明显不同。因此,通过对多级库存系统的库存成本构成进行重新分析,分别给出了需求确定时不允许缺货和允许缺货的协同订货模型。另外,还通过对安全库存的分析给出了需求不确定时的协同订货模型。最后,给出了模型求解的遗传算法,并进行了实例仿真分析,展示了这种协同订货模型在混合需求的供应链中的实用性。