A computational study for common network design in multi-commodity supply chains

In this paper, we study a supply chain network design problem which consists of one external supplier, a set of potential distribution centers, and a set of retailers, each of which is faced with uncertain demands for multiple commodities. The demand of each retailer is fulfilled by a single distribution center for all commodities. The goal is to minimize the system-wide cost including location, transportation, and inventory costs. We propose a general nonlinear integer programming model for the problem and present a cutting plane approach based on polymatroid inequalities to solve the model. Randomly generated instances for two special cases of our model, i.e., the single-sourcing UPL&TAP and the single-sourcing multi-commodity location-inventory model, are provided to test our algorithm. Computational results show that the proposed algorithm can solve moderate-sized problem instances efficiently.     

A multi-echelon production–inventory system with supply disruption

The article investigates an integrated multi-layer supply chain model consisting of supplier, manufacturer and retailer while supply disruption, machine breakdown, safety stock, maintenance breakdown occur simultaneously. At beginning of the production, manufacturer keeps some raw materials in stock received from second supplier at high price, as safety stock due to supply disruption of first supplier. Corrective maintenance is done immediately to restore its normal stage when machine breakdown occurs. Stock out situations at manufacturer and retailer are considered due to disruption of production for machine breakdown. The integrated expected costs of the chain in centralized (collaborating) and decentralized (Stakelberg approach) system are compared. A numerical example and its sensitivity analysis are provided to test feasibility of the model.     

A supplier selection and order allocation problem with stochastic demands

We consider a system comprising a retailer and a set of candidate suppliers that operates within a finite planning horizon of multiple periods. The retailer replenishes its inventory from the suppliers and satisfies stochastic customer demands. At the beginning of each period, the retailer makes decisions on the replenishment quantity, supplier selection and order allocation among the selected suppliers. An optimisation problem is formulated to minimise the total expected system cost, which includes an outer level stochastic dynamic program for the optimal replenishment quantity and an inner level integer program for supplier selection and order allocation with a given replenishment quantity. For the inner level subproblem, we develop a polynomial algorithm to obtain optimal decisions. For the outer level subproblem, we propose an efficient heuristic for the system with integer-valued inventory, based on the structural properties of the system with real-valued inventory. We investigate the efficiency of the proposed solution approach, as well as the impact of parameters on the optimal replenishment decision with numerical experiments.     

An integrated retail space allocation and lot sizing models under vendor managed inventory and consignment stock arrangements

In this paper, we develop integrated retail shelf space allocation and inventory models for a single item with a stock dependent demand. The integrated models are developed for a supply chain operating under vendor-managed inventory (VMI) and consignment stock (CS) agreement. More precisely, the supplier is responsible for initiating orders on behalf of the retailer and decides about the size of each order, the quantity to be displayed on the shelves, and the reorder point. In addition, the supplier owns the stock at the retailer’s premises until it is sold. We develop mathematical models to assess the benefits accrued by both parties as a result of the adoption of VMI–CS partnership. Results from the numerical experimental study show that such partnership is more attractive to all supply chain members when the retailer provides a flexible display capacity. Moreover, the supplier can use his/her selling price and the maximum allocated shelf space as negotiation means to benefit from the partnership.     

A hierarchical model of the impact of RFID practices on retail supply chain performance

The primary purpose of this study was to evaluate the impact of radio frequency identification (RFID) practices on supply chain performance. We examined eight variables of RFID applications grouped in two categories: location (supplier’s warehouse, retailer’s central warehouse, retailer’s local warehouse, retailer’s owned stores) and utilisation (standards, transportation, pallet level, specialised software). Given the inherent difficulty in assessing supply chain performance and the widespread use of different performance models, such as the SCOR and balanced scorecard, we developed a list of performance indicators. Factor analysis produced 7 supply chain performance factors: supplier, inventory, distribution, ordering, plan, sales, and forecasting.Empirical data were collected via an online survey administered to 300 retail companies. 130 usable questionnaires were returned, for a 43.3% response rate. To the best of our knowledge, this is the first study to provide an analytical model that places supply chain performance indicators as dependent variables in a hierarchical regression equation with RFID variables as independent variables. Results found that the implementation of RFID practices significantly affect the supply chain performance in the following areas: supplier, inventory, distribution, plan, sales, and forecasting. RFID can improve the performance of distribution systems, including products dispatched and inventory in transit by 33.8% and stock availability by 45.6%. This study contributes to both the RFID and the supply chain performance literatures. Limitations and suggestions for further research are also discussed.     

横向整合战略下异质车辆库存路径优化模型

以实现供货商联盟期望物流成本最小化为目标,针对需求随机波动下的多供货商多产品库存路径问题（IRP）进行了研究。基于横向整合战略,设计了供货商联盟成员间车辆配送成本的合理分摊方式。考虑零售商配送软硬时间窗和库存服务水平要求,构建了多供货商多产品的异质车辆库存路径混合整数随机规划模型,并利用需求累积分布逆函数将其转化为确定型规划模型。然后设计改进遗传算法求解该确定型规划模型。算例分析结果显示,使用异质车辆配送可以比使用同质重型和轻型车辆分别降低供货商联盟总成本8.3%和11.92%,分别提升配送车辆装载率24%和17%。敏感性分析结果表明,无论供货商供货数量占联盟总供货数量比例和零售商商品需求变异系数如何变化,采用异质车辆配送的供货商联盟总成本都能得到有效降低;且需求变异系数越大,采用异质车辆配送的优势越明显。     

Supply chain system design integrated with risk pooling

This paper considers the location, production–distribution and inventory system design model for supply chain for determining facility locations and their capacity. Risk pooling effect, for both safety stock and running inventory (RI), have been incorporated in the system to minimize the supply chain cost along with determining facility location and capacity. In order to study the benefit of risk pooling for safety stock and RI two cases have been considered, first when retailers act independently and second when DCs-retailers work jointly. The model is formulated as mixed integer nonlinear problem and divided into two stages. The first stage determines the optimal locations for plants and flow relation between plants-DCs and DCs-retailers. At this stage the problem has been linearized using piece-wise linear function. Second stage enumerates the required capacity of opened plants and DCs. The first stage problem is further divided in two sub-problems using Lagrangean relaxation. First sub-problem determines the flow relation between plants and DCs whereas; second sub-problem determines the DCs- retailers flow. Solution of the sub-problems provides the lower bound for the main problem. Computational results reveal that main problem is within the 8.25% of the lower bound and significant amount of cost reduction can be achieved for safety stock and RI costs when DC-Retailer acts jointly.     

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.     

整合供应商选择的多层级选址-库存模型

针对多级供应链网络设计中选址和库存一体化决策问题,基于梯级库存策略,建立了整合供应商选择的多层级选址-库存模型。模型以网络中供应商的选择成本、工厂和配送中心的打开成本、层级之间的运输成本、库存成本、采购成本和生产成本之和最小为目标,同时对供应商的选择、工厂和配送中心的选址、配送中心对顾客的分配、层级之间的运输量、工厂和配送中心的订货批量进行决策。为了求解所建立的模型,设计了基于部分编码的粒子群优化算法。20个不同规模的算例测试表明：所建立的模型是有效的,能用于多层级供应链网络的设计;所设计的算法无论是在求解精度,还是在运算速度上都明显优于数学优化软件Lingo 9.0,尤其是当供应链网络中总节点数较大时。     

Efficient Solution of a Multi-commodity, Two-stage Distribution Problem with Constraints on Assignment of Customers to Distribution Centres

A two-stage, distribution-planning problem is addressed. Customers are to be served with different commodities from a number of plants, through a number of intermediate distribution centres (DCs). The possible locations for the DCs are given. For each location, there is a fixed cost for opening the DC concerned, as well as an operating cost and a maximum capacity. The demand of each customer for each commodity is known, as well as shipping costs throughout. There are also two additional important requirements. First, each customer must be served with all the products it requires from a single distribution centre. Secondly, it must be possible to ascertain the plant origin of each product quantity delivered. The objective is to choose the locations for opening DCs such that the total cost is minimised. The problem is modelled as a mixed-integer-programming problem and solved by branch and bound. Lower bounds are calculated through a series of structural transformations. Much of the power of the solution scheme also stems from frequent generation of good upper bounds. Results of extensive computational experiments are given and discussed.     

Inventory policy of a deteriorating item with variable demand under trade credit period

In this paper, an inventory model of a deteriorating item with stock and selling price dependent demand under two-level credit period has been developed. Here, the retailer enjoys a price discount if he pays normal purchase cost on or before the first level of credit period, or an interest is charged for the delay of payments. In return, retailer also offers a fixed credit period to his customers to boost the demand. In this regard, the authors develop an EOQ model incorporating the effect of inflation and time value of money over all the costs. Keeping the business of seasonal products in mind, it is assumed that planning horizon of business is random and follows a normal distribution with a known mean and standard deviation. The model is formulated as retailer’s profit maximization problem for both crisp and fuzzy inventory costs and solved using a modified Genetic Algorithm (MGA). This algorithm is developed following fuzzy age based selection process for crossover and gradually reducing mutation parameter. For different values of MGA parameters, optimum results are obtained. Numerical experiments are performed to illustrate the model.     

Analysis of the maximum level policy in a production-distribution system

We consider a production-distribution system, where a facility produces one commodity which is distributed to a set of retailers by a fleet of vehicles. Each retailer defines a maximum level of the inventory. The production policy, the retailers replenishment policies and the transportation policy have to be determined so as to minimize the total system cost. The overall cost is composed by fixed and variable production costs at the facility, inventory costs at both facility and retailers and routing costs. We study two different types of replenishment policies. The well-known order-up to level (OU) policy, where the quantity shipped to each retailer is such that the level of its inventory reaches the maximum level, and the maximum level (ML) policy, where the quantity shipped to each retailer is such that the inventory is not greater than the maximum level. We first show that when the transportation is outsourced, the problem with OU policy is NP-hard, whereas there exists a class of instances where the problem with ML policy can be solved in polynomial time. We also show the worst-case performance of the OU policy with respect to the more flexible ML policy. Then, we focus on the ML policy and the design of a hybrid heuristic. We also present an exact algorithm for the solution of the problem with one vehicle. Results of computational experiments carried out on small size instances show that the heuristic can produce high quality solutions in a very short amount of time. Results obtained on a large set of randomly generated problem instances are also shown, aimed at comparing the two policies.     

随机需求随机补货间隔零售商补货控制策略研究

研究分销系统中零售商的补货控制策略．分销系统中各零售商可独立决定自己的补到水平．零售商需求率是随机变量．服从某一泊松分布;分销中心循环为各零售商送货．送货间隔是随机变量．认为所有未满足的需求销售机会都丢失,零售商既要支付库存持有费用．又要支付缺货损失费用．给出了收益数学期望值函数,求出了送货间隔是均匀分布随机变量时使收益数学期望值最大化的零售商补到水平控制策略．     

随机中断环境下的库存控制研究

考虑一需求为复合Poisson分布、提前期为指数分布和短缺损失的连续检查库存系统. 在假设供应商和零售商工作和中断的持续时间服从独立指数分布条件下, 利用水平穿越法, 确定零售商库存水平的平稳分布函数, 在此基础上, 构建长程平均费用率模型, 并利用交叉熵法得到最优库存控制策略. 最后, 通过仿真实验, a分析了中断强度和系统参数对最优库存策略和平均费用率的影响.     

Impacts of supply disruptions and customer differentiation on a partial-backordering inventory system

In this paper, we study a single-product inventory system which involves a supplier, a retailer, and differentiated customers. The supplier provides products to the retailer which in turn sells products to its customers. The supplier is unreliable and is subject to random disruptions. The retailer adopts a periodic-review inventory policy, under which the retailer reviews its inventory position every a fixed period of time and decides whether a replenishment is needed or not. Partial backordering is applied when a stockout occurs. That is, under the situations of stockouts, customers can choose either to backorder products or to abandon the purchase. Customers are segmented into two classes according to their backordering probabilities. The customer class with high backordering probability is provided with high priority to receive backorders. In this paper we allow more than one outstanding orders to exist, which is not the case in the previous literature. We develop a simulation model for such an inventory system and investigate the impacts of supply disruptions and customer differentiation on this inventory system.     

Transshipment and safety stock under stochastic supply interruption in a production system

We consider a two-echelon system with one source supplying two locations with the same product. The random occurrence of interruptions at the source where downtime is also stochastic can result in stockouts at the two receiving locations. Our model studies the benefit of allowing each location to carry a safety stock where holding costs can be different at each location. The objective is to reduce overall cost at both locations. In some cases it is optimal to allow for a transshipment of inventory from the safety stock of one location to the other. We jointly solve for the optimal safety stock at each location and the optimal amount to be transshipped from a location to the other. We show that by conditioning on the transshipment direction the total cost becomes convex as a function of the safety stock levels at the receiving locations and the amount to be transshipped from a location to the other. Numerical examples are presented for different system cost parameters and probability distributions.     

Determinant on RFID technology investment for dominant retailer subject to inventory misplacement

Radio‐frequency identification (RFID) technology has been publicized as an effective way to solve the problem of inventory misplacement in academic research as well as in the user industries. In this paper, we consider a supply chain that consists of one supplier and one retailer where the retailer is the Stackelberg leader and makes the decisions first. The consignment contract is provided such that the supplier determines the order quantity, instead of the retailer. A Non‐RFID case, a supplier investing in RFID, and a retailer investing in RFID cases are analyzed and compared. By assuming an iso‐elastic demand function and the corresponding random factor follows uniform distribution, it is intriguing to find that both supplier and retailer have the incentive to take charge of the RFID tag cost, which is not revealed in previous research. Therefore, a case of joint investment in RFID technology is formulated to find out that there are upper and lower threshold values of RFID tag cost sharing rate; that is, if the tag cost sharing rate exceeds the upper value, it is beneficial for the supplier to invest in RFID; if the tag cost sharing rate is smaller than the lower value, it is beneficial for the retailer to invest in RFID; if the tag cost sharing rate is somewhere between these two values, both supplier and retailer are better‐off. Additionally, the end customer will be better‐off if the retailer invests in RFID.     

随机需求下的选址一库存配送系统集成规划模型及算法

研究了随机需求条件下由单供应商、候选分拨中心和分销点构成的选址-库存问题,分销点、分拨中心分别基于周期检查(R,s,Q)和连续检查(s,S)库存控制策略．综合考虑库存成本、运输成本和设施成本之间的均衡关系,建立了二级库存与无能力约束选址集成规划模型．给出了适合求解实际规模问题的拉格朗日松弛算法,提出了求解子问题的有效启发式方法,改进了次梯度优化方法．通过仿真试验验证了模型的正确性和算法的有效性．最后讨论了相对于传统规划方法,需求方差、服务水平、持有成本、提前期等关键库存控制参数对系统运营成本节约的影响规律．     

随机需求下的选址-库存配送系统集成规划模型及算法

研究了随机需求条件下由单供应商、候选分拨中心和分销点构成的选址－库存问题, 分销点、分拨中心分别基于周期检查(R, s,Q)和连续检查(s, S)库存控制策略. 综合考虑库存成本、运输成本和设施成本之间的均衡关系, 建立了二级库存与无能力约束选址集成规划模型. 给出了适合求解实际规模问题的拉格朗日松弛算法, 提出了求解子问题的有效启发式方法, 改进了次梯度优化方法. 通过仿真试验验证了模型的正确性和算法的有效性. 最后讨论了相对于传统规划方法, 需求方差、服务水平、持有成本、提前期等关键库存控制参数对系统运营成本节约的影响规律.     

Analysis on the effects of stock sharing on supply chain

Considering a two-period, two-part supply chain consisting of one supplier and multi-retailers, this paper studies the effects of stock sharing among retailers on the supply chain. By establishing analysis model and using simulation method, the effects of stock sharing mode and also the traditional mode without stock sharing on retailer, supplier and the whole supply chain’s performance are analyzed. The research results show that when supplier is in a dominant position, although only under certain conditions the stock sharing can stimulate retailer to increase order volume and make supplier to gain a better profit, it always make the profitability of retailer and supplier better than in the traditional mode. When supplier is in a dominant position, stock sharing can always stimulate retailer to increase their order volume, and the profitability of the retailer, supplier and the whole supply chain is always better than the traditional mode situation without stock sharing.