A two-stage queueing network on form postponement supply chain with correlated demands

To ease the conflict between quick response and product variety, more and more business models are developed in supply chains. Among these, the form postponement (FP) strategy is an efficient tool and has been widely adopted. To the supply chain with FP strategy, the design mostly involves two problems: determination of customer order decoupling point (CODP) position and semi-finished product inventory control. In this paper, we develop a two-stage tandem queueing network with MAP arrival to address this issue. Particularly, we introduce a Markov arrival process (MAP) to characterize the correlation of the demand. By using of matrix geometric method, we derive several performance measure of the supply chain, such as inventory level and unfill rate. Our numerical examples show that both the variance and the correlation coefficient of the demand lead to more delayed CODP position and more total cost.     

A queuing approach for inventory planning with batch ordering in multi-echelon supply chains

This paper presents stylized models for conducting performance analysis of the manufacturing supply chain network (SCN) in a stochastic setting for batch ordering. We use queueing models to capture the behavior of SCN. The analysis is clubbed with an inventory optimization model, which can be used for designing inventory policies . In the first case, we model one manufacturer with one warehouse, which supplies to various retailers. We determine the optimal inventory level at the warehouse that minimizes total expected cost of carrying inventory, back order cost associated with serving orders in the backlog queue, and ordering cost. In the second model we impose service level constraint in terms of fill rate (probability an order is filled from stock at warehouse), assuming that customers do not balk from the system. We present several numerical examples to illustrate the model and to illustrate its various features. In the third case, we extend the model to a three-echelon inventory model which explicitly considers the logistics process.     

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.     

Incorporating inventory and routing costs in strategic location models

We consider a supply chain design problem where the decision maker needs to decide the number and locations of the distribution centers (DCs). Customers face random demand, and each DC maintains a certain amount of safety stock in order to achieve a certain service level for the customers it serves. The objective is to minimize the total cost that includes location costs and inventory costs at the DCs, and distribution costs in the supply chain. We show that this problem can be formulated as a nonlinear integer programming model, for which we propose a Lagrangian relaxation based solution algorithm. By exploring the structure of the problem, we find a low-order polynomial algorithm for the nonlinear integer programming problem that must be solved in solving the Lagrangian relaxation sub-problems. We present computational results for several instances of the problem with sizes ranging from 40 to 320 customers. Our results show the benefits of having an integrated supply chain design framework that includes location, inventory, and routing decisions in the same optimization model.     

Designing multi-echelon service parts networks with finite repair capacity

We propose an approach to model and solve the joint problem of facility location, inventory allocation and capacity investment in a two echelon, single-item, service parts supply chain with stochastic demand. The objective of the decision problem is to minimize the total expected costs associated with (1) opening repair facilities, (2) assigning each field service location to an opened facility, (3) determining capacity levels of the opened repair facilities, and (4) optimizing inventory allocation among the locations. Due to the size of the problem, computational efficiency is essential. The accuracy of the approximations and effectiveness of the approach are analyzed with two numerical studies. The approach provides optimal results in 90% of scenarios tested and was within 2% of optimal when it did not.We explore the impact of capacity utilization, inventory availability, and lead times on the performance of the approach. We show that including tactical considerations jointly with strategic network design resulted in additional cost savings from 3% to 12%. Our contribution is the development of a practical model and approach to support the decision making process of joint facility location and multi-echelon inventory optimization.     

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.     

Improving service rate for a tree-type three-echelon supply chain system with backorders at retailer's level

This research deals with a distributive or tree-type three-echelon production-distribution supply chain system with allowable backorder. Allowing backorder could reduce the total of a production-distribution system by reducing holding cost due to the lower average inventory, even though backorders carry some cost and lower a company's goodwill. The main purpose of this research is to develop replenishment policies for a tree-type three-echelon supply chain system with allowable backorder. The supply chain network is composed of a producer, multiple distributors, and multiple retailers. This research attempts to improve service rate by reducing the backorder at the retailer level. The distributors are allowed to ship product to retailer quicker in order to reduce backorder. The total cost function of the proposed model is developed. Since the total cost function contains some integer variables, differentiating the function with respect to the variables could not be used as a basis to solve for the optimal solutions. A branching search process was utilized to find the integer solutions. A numerical example is used to demonstrate improvement in service rate and total cost using the model.     

Multi-location transshipment problem with capacitated transportation

We consider coordination among stocking locations through replenishment strategies that take explicitly into consideration transshipments, transfer of a product among locations at the same echelon level. We incorporate transportation capacity such that transshipment quantities between stocking locations are bounded due to transportation media or the location’s transshipment policy. We model different cases of transshipment capacity as a capacitated network flow problem embedded in a stochastic optimization problem. Under the assumption of instantaneous transshipments, we develop a solution procedure based on infinitesimal perturbation analysis to solve the stochastic optimization problem, where the objective is to find the policy that minimizes the expected total cost of inventory, shortage, and transshipments. Such a numerical approach provides the flexibility to solve complex problems. Investigating two problem settings, we show the impact of transshipment capacity between stocking locations on system behavior. We observe that transportation capacity constraints not only increase total cost, they also modify the inventory distribution throughout the network.     

Designing two-echelon supply networks

A modern distribution network design model needs to deal with the trade-offs between a variety of factors, including (1) location and associated (fixed) operating cost of distribution centers (DCs), (2) total transportation costs, and (3) storage holding and replenishment costs at DCs and retail outlets. In addition, network design models should account for factors such as (4) stockouts, by setting appropriate levels of safety stocks, or (5) capacity concerns, which may affect operating costs in the form of congestion costs. The difficulty of making such trade-offs is compounded by the fact that even finding the optimal two-echelon inventory policy in a fixed and uncapacitated distribution network is already a hard problem. In this paper, we propose a generic modeling framework to address these issues that continues and extends a recent stream of research aimed at integrating insights from modern inventory theory into the supply chain network design domain. Our approach is flexible and general enough to incorporate a variety of important side constraints into the problem.     

风险厌恶条件下竞争报童问题的二层规划模型

有效应用数学规划方法研究报童类产品的库存管理,能够降低企业的成本和风险,从而提高企业的经济效益.此类问题的研究,目前主要集中在应用Nash博弈研究竞争报童问题以及零售商所持风险态度对供应链库存水平的影响.试图研究序贯决策下的竞争报童问题模型以及零售商所持风险态度对供应链库存水平的影响.由此建立了二层规划模型.算例表明序贯决策的竞争报童问题中,总订购量随风险厌恶程度的提高而降低.     

Evaluation of cycle-count policies for supply chains with inventory inaccuracy and implications on RFID investments

Inventory record inaccuracy leads to ineffective replenishment decisions and deteriorates supply chain performance. Conducting cycle counts (i.e., periodic inventory auditing) is a common approach to correcting inventory records. It is not clear, however, how inaccuracy at different locations affects supply chain performance and how an effective cycle-count program for a multi-stage supply chain should be designed. This paper aims to answer these questions by considering a serial supply chain that has inventory record inaccuracy and operates under local base-stock policies. A random error, representing a stock loss, such as shrinkage or spoilage, reduces the physical inventory at each location in each period. The errors are cumulative and are not observed until a location performs a cycle count. We provide a simple recursion to evaluate the system cost and propose a heuristic to obtain effective base-stock levels. For a two-stage system with identical error distributions and counting costs, we prove that it is more effective to conduct more frequent cycle counts at the downstream stage. In a numerical study for more general systems, we find that location (proximity to the customer), error rates, and counting costs are primary factors that determine which stages should get a higher priority when allocating cycle counts. However, it is in general not effective to allocate all cycle counts to the priority stages only. One should balance cycle counts between priority stages and non-priority stages by considering secondary factors such as lead times, holding costs, and the supply chain length. In particular, more cycle counts should be allocated to a stage when the ratio of its lead time to the total system lead time is small and the ratio of its holding cost to the total system holding cost is large. In addition, more cycle counts should be allocated to downstream stages when the number of stages in the supply chain is large. The analysis and insights generated from our study can be used to design guidelines or scorecard systems that help managers design better cycle-count policies. Finally, we discuss implications of our study on RFID investments in a supply chain.     

A dynamic inventory model with supplier selection in a serial supply chain structure

Considering the inherent connection between supplier selection and inventory management in supply chain networks, this article presents a multi-period inventory lot-sizing model for a single product in a serial supply chain, where raw materials are purchased from multiple suppliers at the first stage and external demand occurs at the last stage. The demand is known and may change from period to period. The stages of this production–distribution serial structure correspond to inventory locations. The first two stages stand for storage areas for raw materials and finished products in a manufacturing facility, and the remaining stages symbolize distribution centers or warehouses that take the product closer to customers. The problem is modeled as a time-expanded transshipment network, which is defined by the nodes and arcs that can be reached by feasible material flows. A mixed integer nonlinear programming model is developed to determine an optimal inventory policy that coordinates the transfer of materials between consecutive stages of the supply chain from period to period while properly placing purchasing orders to selected suppliers and satisfying customer demand on time. The proposed model minimizes the total variable cost, including purchasing, production, inventory, and transportation costs. The model can be linearized for certain types of cost structures. In addition, two continuous and concave approximations of the transportation cost function are provided to simplify the model and reduce its computational time.     

The impact of information sharing in a two-level supply chain with multiple retailers

Information sharing is an important component of cooperation in supply chain management. This paper presents a study to evaluate the impact of information sharing on inventory and expected cost in a two-level supply chain with multiple retailers. Three levels of information sharing are given and the optimal inventory policy under each level is derived. We show that both the inventory level and expected cost of the manufacturer decrease with an increase in the level of information sharing.     

An integrated producer–buyer supply chain with delivery cost under stochastic transportation time

An integrated producer–buyer supply chain is used to simultaneously determine the optimum levels of the safety stock, delivery quantity, and number of shipments in this paper. The scenario is created by scheduling a single-setup at the producer with multiple deliveries to the buyer, and all shipments to the buyer are equal-sized batches. This study attempts to study the effects of delivery cost and transportation time, assumes that there is a stochastic transportation time between both producer and buyer, and that shortages are allowed. The transportation time is assumed to be Weibull distributed. The objective functions of the integrated model include the setup cost, inventory carrying cost, and delivery cost. We analyze the scenario where the delivery cost is explicitly considered in the model rather than considered as part of the fixed ordering cost or insignificant. A numerical example is also presented to demonstrate the proposed model using actual shipping rate data. In particular, the results show that when the producer's and buyer's carrying costs are low, and/or the mean time of transportation and delivery costs are high, then this can benefit both parties with regard to sharing total profit.     

The plant location problem with demand-dependent setup costs and centralized allocation

Suppose that customers are situated at the nodes of a transportation network, and a service company plans to locate a number of facilities that will serve the customers. The objective is to minimize the sum of the total setup cost and the total transportation cost. The setup cost of a facility is demand-dependent, that is, it depends on the number of customers that are served by the facility. Centralized allocation of customers to facilities is assumed, that is, the service company makes a decision about allocation of customers to facilities. In the case of a general network, the model can be formulated as a mixed integer programming problem. For the case of a tree network, we develop a polynomial-time dynamic programming algorithm.     

A linear time algorithm for inverse obnoxious center location problems on networks

For an inverse obnoxious center location problem, the edge lengths of the underlying network have to be changed within given bounds at minimum total cost such that a predetermined point of the network becomes an obnoxious center location under the new edge lengths. The cost is proportional to the increase or decrease, resp., of the edge length. The total cost is defined as sum of all cost incurred by length changes. For solving this problem on a network with m edges an algorithm with running time ${\mathcal{O}(m)}$ is developed.     

A bi-criteria hybrid metaheuristic for analysing an integrated automotive supply chain

The automotive industry is one of the most important manufacturing sectors in the world due to its economic impact and technological complexities. While supply chain performance can have a dramatic impact on the automotive industry, there are multiple, often conflicting objectives that typically are used to optimize performance. We model the trade-off between cost and service level, and present a bi-criteria heuristic optimization methodology for a two-stage, integrated automotive supply chain. Our problem contains sequence-dependent setups on parallel machines and auxiliary resource assignments. We minimize the total cost of setups, inventory holding, and transportation costs, and the maximum percentage of outsourced parts per customer, simultaneously. We use our proposed method to solve a set of problem instances that are based on industrial data. Our proposed method generates approximate Pareto (efficient) solutions in a timely manner for use in practice.     

带批次和临时库存的越库配送车辆路径问题研究

从零售业供应链整合入手,构建供应商、配送中心和零售点构成的协同配送网络,研究带批次和临时库存的越库配送车辆路径问题.将越库过程分为取货、分拣和配货三个阶段,考虑配送中心分拣能力,分批次设置车辆协同到达配送中心的服务时刻,据此建立以最小化车辆运输成本、临时库存成本和固定成本为目标的数学模型.考虑问题特征,设计一种混合变邻...     

An analytical method for cost analysis in multi-stage supply chains: A stochastic network model approach

This paper studies the cost distribution characteristics in multi-stage supply chain networks. Based on the graphical evaluation and review technique, we propose a novel stochastic network mathematical model for cost distribution analysis in multi-stage supply chain networks. Further, to investigate the effects of cost components, including the procurement costs, inventory costs, shortage costs, production costs and transportation costs of supply chain members, on the total supply chain operation cost, we propose the concept of cost sensitivity and provide corresponding algorithms based on the proposed stochastic network model. Then the model is extended to analyze the cost performance of supply chain robustness under different order compensation ability scenarios and the corresponding algorithms are developed. Simulation experiment shows the effectiveness and flexibility of the proposed model, and also promotes a better understanding of the model approach and its managerial implications in cost management of supply chains.     

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.