A two-level distribution inventory system with stochastic lead time at the lower echelon

We consider a two-level distribution inventory system with a number of identical retailers at the lower echelon and a single supplier at the upper echelon. The replenishment policy is continuous review policy (R, Q) at all installations. We assume independent Poisson demands with stochastic lead time for the retailers and a constant transportation time for replenishing supplier orders from an external warehouse. Unsatisfied demands are assumed to be lost in the retailers and unsatisfied retailer orders are backordered in the supplier. We develop an approximate cost function to find optimal reorder points for given batch sizes in all installations, and the related accuracy is assessed through simulation. We present numerical examples for the gamma distributed lead time for the retailers orders at the supplier.     

Modeling and solving a one-supplier multi-vehicle production-inventory-distribution problem with clustered retailers

This paper considers a supply chain management problem which integrates production, inventory, and distribution decisions. The supply chain is composed of one supplier production facility and several retailers located in a given geographic region. The supplier is responsible for the production and the replenishment of the inventory of retailers, in a vendor managed inventory (VMI) context. The distance between retailers is negligible compared to the distance between the supplier and the retailers’ region. Thus, for each vehicle, there is a major fixed cost for traveling to the cluster of retailers and a minor fixed cost for visiting each individual retailer. The problem consists of determining quantities to be produced, quantities to be delivered to retailers, vehicles to be used, and retailers to be serviced by each vehicle. This problem is an extension of the one warehouse multi-retailer problem with the consideration of production planning and storage and vehicle capacity limitations in addition to fixed vehicle utilization costs and retailer servicing costs. The objective is to minimize a total cost composed of production, transportation, and inventory holding costs at the supplier and at the retailers. Two mixed integer linear programming formulations are proposed and six families of valid inequalities are added to strengthen these formulations. Two of these families are new and the others are adapted from the literature. The numerical results show that the valid inequalities considerably improve the quality of the formulations. Moreover, the parameters that influence the most computational times are analyzed.     

General bounds for the optimal value of retailers’ reorder point in a two-level inventory control system with and without information sharing

In this study, an inventory system consisting of a single product, one supplier, and multiple identical retailers is considered. Each retailer replenishes inventory from the supplier according to the well known (R,Q) policy. Transit times are constant and retailers face independent Poisson demand. The supplier utilizing the retailers' information in decision making for replenishment policy with a given order size starts with m initial batches (of size Q) and places an order in a batch of size Q to an outside source when a new order is placed. In this inventory system, excess demand is backordered, delayed orders are satisfied on a first-come first-serve basis, and no partial shipment is allowed. By partitioning the cost function of this system, general upper and lower bounds for the optimal value of R are determined. Based on several numerical examples, it is shown that these bounds (especially the lower bound) allow the optimal reorder point to be found more effectively with a shorter solving time.     

基于确定需求的作业层库存路径问题研究

研究了传统零售商管理库存模式下,基于确定需求的由一个供应商多个零售商组成的两级配送系统中作业层库存路径问题.首先采用传统C-W节约算法,讨论了供应商和零售商独立决策时的订货与配送策略.然后基于时间距离的思想,在滚动周期策略的框架下,设计了两级系统的联合配送策略.最后,用具体算例比较了独立决策和联合决策下的系统年度费用,验证了联合配送策略的有效性,并给出了相应的作业层日常运营补货时间和车辆路径.     

Evaluation of supply chain structures using a delayed product differentiation process

In this paper, we consider a two-level supply chain consisting of a retailer and n “non-identical” customers. The retailer orders different perishable products in response to the demands of the customers. The unsatisfied demand at a retailer is partially backlogged with a time-proportional backlogging rate. We formulate models for a postponement system and an independent system to minimize the total average cost function per unit time for ordering and keeping n “non-instantaneous deteriorating items.” An algorithm is given to derive the optimal solutions of the proposed models. The impact of the deterioration rate on the inventory replenishment policies is studied with the help of both theoretical and numerical results.     

Optimal pricing and replenishment policies of an EOQ model for non-instantaneous deteriorating items with shortages

This paper discusses the optimal pricing and replenishment policies of an economic order quantity model for non-instantaneous deteriorating items with partial backlogging over an infinite time horizon. The model is studied under the replenishment policy starting with no shortages. The backlogging rate is any non-increasing function of the waiting time up to the next replenishment. The objective of this model is to maximize the total profit which includes the sales revenue, purchasing cost, set up cost, holding cost, shortage cost, and opportunity cost due to lost sales. Here, the selling price, replenishment quantity, replenishment cycle length, and the time duration of the positive inventory level are taken as decision variables to maximize the profit of the inventory system. The existence and the uniqueness of the solution of the proposed inventory system are examined. We suggest a solution procedure to find the optimal solution of the described model. Numerical examples are presented to determine the developed model and the solution procedure. Sensitivity analysis of the optimal solution with respect to major parameters is carried out and some useful managerial results are obtained.     

基于熵的直运型供应链库存协调研究

为解决不对称信息下直运型供应链库存协调问题,提出了一种基于信息熵的库存协调方法。首先,研究了由一个供应商和一个分销商组成的直运型供应链系统,给出了库存保管成本信息不对称下的库存协调补偿机制,并从供应商角度提出了优化模型。模型中含有一个与供应商所掌握信息量相关的参数。为选择恰当的模型参数,提出了运用极大熵准则,确定库存保管成本分布概率的基本方法。最后,给出了一个应用示例。计算结果表明,协调后供应商和分销商的利润都有一定程度的增加。     

Solving a multi-product distribution planning problem in cross docking networks: An imperialist competitive algorithm

Cross docking is a distribution strategy to efficiently control the physical flow of inventory. In this approach, the concept of warehouse shifts from a place for holding the inventory to a site for receiving, classifying, and shipping to the product destination in a very short time. Shipments are typically kept for less than 24 h in the cross dock. The major advantage of this strategy is to reduce the cycle time and inventory level while fulfilling customer’s demands. In general, relevant studies are based on one-product type delivery and pickup assumption whereas in reality, customers are likely to order different types of products in various amounts. This paper focuses on considering the scheduling problem of cross docking multi-product type deliveries and pickups, so that the objective, minimizing the summation of transportation cost and holding cost, can be satisfied. The efficiency and capability of the mathematical model is evaluated by presenting a case study and sensitivity analysis of the parameters influencing the problem. In order to solve the model, as the problem is NP-hard, an efficient heuristic procedure to provide effective initial solution within reasonable computational times is applied and then improved by an imperialist competitive algorithm. Computational results which consist of comparing the proposed heuristic and meta-heuristic with optimal solution obtained by Generalized Algebraic Modeling System show that the suitability of the proposed solving approach is quite sensible for solving such complicated problems.     

Adaptive inventory control models for supply chain management

Uncertainties inherent in customer demands make it difficult for supply chains to achieve just-in-time inventory replenishment, resulting in loosing sales opportunities or keeping excessive chain-wide inventories. In this paper, we propose two adaptive inventory-control models for a supply chain consisting of one supplier and multiple retailers. The one is a centralized model and the other is a decentralized model. The objective of the two models is to satisfy a target service level predefined for each retailer. The inventory-control parameters of the supplier and retailers are safety lead time and safety stocks, respectively. Unlike most extant inventory-control approaches, modelling the uncertainty of customer demand as a statistical distribution is not a prerequisite in the two models. Instead, using a reinforcement learning technique called action-value method, the control parameters are designed to adaptively change as customer-demand patterns changes. A simulation-based experiment was performed to compare the performance of the two inventory-control models.     

Optimal replenishment policies for deteriorating control wafers inventory

This paper considers a control wafers replenishment problem with inventory deterioration. In the process, control wafers begin to deteriorate after the pre-disposition. The objective of this research is to minimize the total cost of control wafers, where the cost includes ordering cost, holding cost and purchase cost. We first formulate the control wafers inventory problem as a dynamic programming model. We then transform the control wafers’ inventory problem into the mixed 0–1 linear programming model. An illustrative example with four cases is used to illustrate the practicality of these models, and sensitivity analysis is applied to understand the impact of parameters to these models. The results demonstrate that the proposed mixed 0–1 linear programming model is an effective tool for determining the replenishment of control wafers for multi-periods.     

Supplier selection and order splitting in multiple-sourcing inventory systems

Supplier selection and inventory control are critical decision processes in single-item multiple-supplier systems. An integer linear programming model is proposed to help managers determine the reorder level, choose the best suppliers, and place the optimum order quantities so that the total average inventory cost is minimum, and constraints of supplier ability, quality, and demand are considered. An algorithm combining the branch-bound algorithm and enumeration algorithm is developed to solve the problems. Application of the proposed model in an automobile industry shows that it is effective.     

Supplier selection and order splitting in multiple-sourcing inventory systems

Supplier selection and inventory control are critical decision processes in single-item multiple-supplier systems. An integer linear programming model is proposed to help managers determine the reorder level, choose the best suppliers, and place the optimum order quantities so that the total average inventory cost is minimum, and constraints of supplier ability, quality, and demand are considered. An algorithm combining the branch-bound algorithm and enumeration algorithm is developed to solve the problems. Application of the proposed model in an automobile industry shows that it is effective.     

Model and algorithm for fuzzy joint replenishment and delivery scheduling without explicit membership function

We study a joint replenishment and delivery scheduling (JRD) problem in which a central warehouse serves n-retailers in the presence of vague operational conditions such as ordering cost and inventory holding cost. In the proposed fuzzy set-based approach, an exact membership function is not assumed and instead can be approximated using piecewise linear functions based on alpha level sets because of their easy handling and efficiency. Subsequently, the fuzzy total cost is defuzzified by the widely used signed distance method to ranking fuzzy numbers. However, due to the JRD's difficult mathematical properties, efficient and effective solution procedures for the problem have eluded researchers. To find an optimal solution, an effective and efficient differential evolution (DE) algorithm is designed. After determining the appropriate parameters of the DE by parameter tuning test, the effectiveness of the DE is verified by numerical examples. We compare the DE with the available best approach and results show that DE can solve this non-deterministic polynomial hard problem in a robust way with a high convergence rate and low average error.     

基于改进蚁群算法的多供应商选择问题求解

为克服传统供应商选择过程中只针对单一物资供应过程和面向单一供应商选择过程的局限性,以质量、成本、交货期和交货提前期为评估指标,以最小化评估指标综合值为目标,建立了针对多品种供应条件下多供应商选择的0-1整数规划模型.基于蚁群算法,构造了适合该模型特征的改进蚁群求解算法,并阐述了其求解过程.通过模拟算例及对比分析表明,该方法是有效、可行的,它可为企业进行多品种供应的多供应商选择问题提供了可参考的模型和求解算法.     

一种多周期随机需求生产/库存模型

为使存贮、生产和缺货等费用的总和最小，建立了一种多周期随机需求生产／库存模型，该模型采用（S，Q）策略对生产和库存进行控制，即当成品库存降至8时准备生产，生产量为Q。通过对该模型费用函数特性的分析，设计了一种迭代学习算法，根据该算法可以得出系统的最优生产准备点及最优生产量。将所提出的迭代学习算法与遗传算法进行了比较，结果显示，两者所得到的控制量是吻合的，且迭代学习算法的求解速度更快，从而证实所建立的模型和提出的迭代学习算法是正确有效的。     

Scheduling and replenishment plan for an integrated deteriorating inventory model with stock-dependent selling rate

An integrated approach is used to clarify the critical issues of scheduling and replenishment planning in an advanced inventory system under stock-dependent selling rate environment. This is because integration removes the barriers between enterprises and improves overall performance. A close collaboration such as just-in-time (JIT) operations also improves product quality of the supply chain. Different from the single-stage inventory model, this study develops an integrated two-stage production-inventory deteriorating model for the buyer and the supplier with stock-dependent selling rate, as well as considering imperfect items and JIT multiple deliveries. Our paper proposes a significant method using a time-weighted-inventory approach to analyze the supplier’s saw-tooth holding cost. We derive the optimal number of inspection, optimal deliveries and the optimal delivery-time interval. A numerical example is also presented to illustrate the theory. The results show that the fixed demand rate, the holding cost and the unit inspection cost are critical in the management of the deteriorating inventory model.     

基于时间的供应商管理库存整合补货模式下的牛鞭效应研究

为比较基于时间的供应商管理库存整合补货模式和传统补货模式对零售业供应链中牛鞭效应的影响,概述了供应商管理库存在零售业供应链中的应用情况,构建了两种补货模式的系统动力学模型。通过仿真,定量地比较了两种补货模式中供应商和零售商对泊松流随机需求输入的订单响应率的波动。另外,为了比较基于时间的供应商管理库存整合补货模式下补货周期对牛鞭效应的影响,通过改变参数设置模拟了不同补货周期下供应商和零售商的订单响应率波动。结果显示,与传统模式相比,基于时间的供应商管理库存整合补货对牛鞭效应有明显的改善;供应商管理库存整合补货的补货周期对牛鞭效应存在明显的影响,较长周期下的牛鞭效应相对于较短周期要严重。     

Simultaneous coordination of capacity building and price decisions in a decentralized supply chain

In this paper, we investigate the simultaneous coordination of price and capacity building decisions in a dyadic supply chain. This problem is a combination of capacity reservation problem and pricing problem. While the coordination of supply chain with stochastic demand and fixed prices has received much attention in the literature, price-dependent and stochastic demand has been less considered. We study the latter case where a price-setting retailer faces a linear decreasing demand with respect to price. To capture the uncertainty of the demand, we add a stochastic variable to the demand function. In addition, we incorporate production rate and inventory cost on the supplier side. We propose Revenue Sharing Reservation Contract with Penalty (RSRP) as a coordination mechanism to align the price and capacity decisions. We then extend the model to include multiple retailers which are geographically dispersed. We next conduct a comprehensive numerical example with an extensive sensitivity analysis to understand the behavior and robustness of the supply chain under a RSRP, and finally, we draw some managerial implications.     

Possibilistic inventory and supplier selection model for an assembly system

In this paper, the problem of inventory lot-sizing and supplier selection for an assembly system is considered, where the supplier available capacities are assumed as ambiguous dynamic parameters. In this scenario, which is a frequent case in large assembly-based factories such as automobile manufacturers, the final product is assembled from multiple components with different conversion factors, which can be sourced from multi-capacitated suppliers through the multi-period horizon of imprecise demand. Due to high shut-down costs of assembly lines, it is assumed that production never stops even though some components may not be available. Therefore, the unfinished products are transferred to a buffer zone and preserved there until the lacking components become available. In this study, a possibilistic mixed integer mathematical model, with fuzzy objective function and soft constraints, is developed to determine which component in what quantities, from which suppliers, and in which periods should be ordered. The model, inspired by the real case of the Iran Khodro Car Company, aims to maximize the profit while keeping a high customer service level by avoiding shortages. This model also considers the ambiguity of dynamic parameters such as demand, suppliers’ available capacities, prices, and holding and shortage costs. To solve the problem, the possibilistic model is first converted into an auxiliary crisp multi-objective model. Through an interactive fuzzy approach, the suggested multi-objective problem is then transformed into an equivalent single-objective model. Finally, a particle swarm optimization is proposed to achieve the overall satisfactory compromise solution. A numerical sample is used to validate the proposed model.     

供需链中的结盟企业库存管理

供需链中核心企业与结盟企业在风险分担和库存信息上存在不对称，在提货时存在“局部利益最大化”问题，核心企业仅能通过提货量控制结盟企业库存。结加存管理包括根据外部事件及反馈信息进行结盟企业库存维护和利用提货量来控制结盟企业库存，本文建立了结盟企业库存维护的形式化模型和库存控制的随机模型，并提出了一种层次型混合算法。