A Two-Warehouse Probabilistic Order-Level Inventory Model for Deteriorating Items

In this paper an order-level probabilistic inventory model for deteriorating items with two warehouses is developed. It is assumed that the production rate is infinite and shortages are allowed. The rates of deterioration of items in the two warehouses are different. Also, a single-warehouse version for deteriorating items is discussed. This paper also considers a two-warehouse model for non-deteriorating items. An illustrative example offers a comparative study of the optimum cost for varying shortage cost.     

Application of fuzzy optimization to a supply chain network design: A case study of an edible vegetable oils manufacturer

This study applies fuzzy sets to integrate the supply chain network of an edible vegetable oils manufacturer. The proposed fuzzy multi-objective linear programming model attempts to simultaneously minimize the total transportation costs. The first part of the total transportation costs is between suppliers and silos; and rest one is between manufacturer and warehouses. The approach incorporates all operating realities and actual flow patterns at production/distribution network with reference to demands of warehouses, capacities of tin and pet packaging lines. The model has been formulated as a multi objective linear programming model where data are modeled by triangular fuzzy numbers. Finally, the developed fuzzy model is applied for the case study, compiled the results and discussed.     

An inventory sharing and allocation method for a multi-location service parts logistics network with time-based service levels

We consider a model to allocate stock levels at warehouses in a service parts logistics network. The network is a two-echelon distribution system with one central warehouse with infinite capacity and a number of local warehouses, each facing Poisson demands from geographically dispersed customers. Each local warehouse uses a potentially different base stock policy. The warehouses are collectively required to satisfy time-based service targets: Certain percentages of overall demand need to be satisfied from facilities within specified time windows. These service levels not only depend on the distance between customers and the warehouses, but also depend on the part availabilities at the warehouses. Moreover, the warehouses share their inventory as a way to increase achieved service levels, i.e., when a local warehouse is out of stock, demand is satisfied with an emergency shipment from another close-by warehouse. Observing that the problem of finding minimum-cost stock levels is an integer non-linear program, we develop an implicit enumeration-based method which adapts an existing inventory sharing model from the literature, prioritizes the warehouses for emergency shipments, and makes use of a lower bound. The results show that the proposed inventory sharing strategy results in considerable cost reduction when compared to the no-sharing case and the method is quite efficient for the considered test problems.     

停产后服务备件存储点的选择与库存问题研究

分析了停产后服务备件的三种存储模式,以主要基层仓库和常规基层仓库模式为基本模式,建立了选址库存模型,将两级库存体系不变模式和单级库存体系模式作为特例加以讨论,并设计了基于遗传算法的迭代算法求解选址库存问题,通过仿真算例验证了模型和方法的可行性和有效性.通过分析,主要基层仓库和常规基层仓库模式能够将成本优势与客户服务水平良好结合,是一种较好的模式.     

Planning and coordination of production and distribution facilities for multiple commodities

We study an integrated logistics model for locating production and distribution facilities in a multi-echelon environment. Designing such logistics systems requires two essential decisions, one strategic (e.g., where to locate plants and warehouses) and the other operational (distribution strategy from plants to customer outlets through warehouses). The distribution strategy is influenced by the product mix at each plant, the shipments of raw material from vendors to manufacturing plants and the distribution of finished products from the plants to the different customer zones through a set of warehouses. First we provide a mixed integer programming formulation to the integrated model. Then, we present an efficient heuristic solution procedure that utilizes the solution generated from a Lagrangian relaxation of the problem. We use this heuristic procedure to evaluate the performance of the model with respect to solution quality and algorithm performance. Results of extensive tests on the solution procedure indicate that the solution method is both efficient and effective. Finally a `real-world' example is solved to explore the implications of the model.     

Multi-source facility location–allocation and inventory problem

We consider a joint facility location–allocation and inventory problem that incorporates multiple sources of warehouses. The problem is motivated by a real situation faced by a multinational applied chemistry company. In this problem, multiple products are produced in several plants. Warehouse can be replenished by several plants together because of capabilities and capacities of plants. Each customer in this problem has stochastic demand and certain amount of safety stock must be maintained in warehouses so as to achieve certain customer service level. The problem is to determine number and locations of warehouses, allocation of customers demand and inventory levels of warehouses. The objective is to minimize the expected total cost with the satisfaction of desired demand weighted average customer lead time and desired cycle service level. The problem is formulated as a mixed integer nonlinear programming model. Utilizing approximation and transformation techniques, we develop an iterative heuristic method for the problem. An experiment study shows that the proposed procedure performs well in comparison with a lower bound.     

A Plant and Warehouse Location Problem

A model is proposed for the simultaneous location of plants and warehouses among a given set of possible locations in order to satisfy a given demand at minimum cost. The demand of each customer may be satisfied directly from a plant or through a warehouse. The model also applies to the design of a distribution network with two levels of warehouses. A branch-and-bound algorithm, which generalizes previous work by Efroymson and Ray and others, is presented, computational experience is reported on.     

Development of an Air Force Warehouse Logistics Index to continuously improve logistics capabilities

For the effective operation of air power in the modern war, the logistics systems of Air Force warehouses need to be well-maintained. The best logistics system can be established through continuous improvements in logistics capabilities. Although there have been some studies on key performance indicators for logistics capability, they have neither considered the structural relationship among various influential factors, nor the feedback mechanisms in warehouse logistics capabilities. In this study, we propose a structural equations model (SEM) to develop an Air Force Warehouse Logistics Index (WLI). The concept of a Customer Satisfaction Index is used to assess the WLI for strategic improvement plans for various warehouse groups. It is expected that our model can be used to evaluate the logistics support capability of ROKAF (Republic of Korea Air Force) warehouses and contribute to warehouse modernization plans.     

A new partial pooling structure for spare parts networks

Motivated by real-life spare parts networks, we introduce a new spare parts inventory model with lateral transshipment. We consider a multi-item, multi-location, single-echelon system with base stock control and aggregate mean waiting time constraints. The local warehouses are divided into two types: main and regular local warehouses. Lateral transshipment is allowed from main local warehouses only. A practical advantage of this structure is that only a limited number of local warehouses has to be equipped to provide lateral transshipment. This structure represents a new form of partial pooling, with no pooling (zero main locals) and full pooling (zero regular locals) as special cases. We develop an accurate and fast approximate evaluation method, and exploit this method in a heuristic procedure for the base stock level determination. We show that only a small number of main locals is sufficient to obtain most of the full pooling benefits. We also apply our methods to case data of ASML, an original equipment manufacturer in the semiconductor supplier industry. As a result of our work ASML was able to improve spare parts planning.     

A two warehouse inventory model for deteriorating items with a linear trend in demand and shortages

In this paper, we develop a deterministic inventory model with two warehouses (one is the existing storage known as own warehouse (OW) and the other is hired on rental basis known as rented warehouse (RW). The model allows different levels of item deterioration in both warehouses. The demand rate is supposed to be a linear (increasing) function of time and the replenishment rate is infinite. The stock is transferred from RW to OW in continuous release pattern and the associated transportation cost is taken into account. Shortages in OW are allowed and excess demand is backlogged. For the general model, we give the equations for the optimal policy and cost function and we discuss some special cases. A numerical example is given to illustrate the solution procedure of the model. Finally, based on this example, we conduct a sensitivity analysis of the model.     

Deterministic inventory model for deteriorating items with capacity constraint and time-proportional backlogging rate

In this paper, a deterministic inventory model for deteriorating items with two warehouses is developed. A rented warehouse is used when the ordering quantity exceeds the limited capacity of the owned warehouse, and it is assumed that deterioration rates of items in the two warehouses may be different. In addition, we allow for shortages in the owned warehouse and assume that the backlogging demand rate is dependent on the duration of the stockout. We obtain the condition when to rent the warehouse and provide simple solution procedures for finding the maximum total profit per unit time. Further, we use a numerical example to illustrate the model and conclude the paper with suggestions for possible future research.     

Redesigning a warehouse network

To take advantage of economies of scale, a growing number of firms have begun to explore the possibility of integrating supply chain activities. The advent of such a possibility would necessitate the redesign of a warehouse network. Typically, a warehouse redesign problem involves the consolidation of regional warehouses into a fewer number of master stocking points and the subsequent phase-out of redundant or underutilized warehouses without deteriorating customer services. This paper develops a mixed-integer programming model to solve the warehouse redesign problem. The usefulness of the model was validated by its successful application to a real-world problem and by its sensitivity analyses when used with changing scenarios within a warehouse network configuration.     

A cost operator approach to multistage location-allocation

The multistage factory-warehouse location-allocation problem is to decide on locations of warehouses and shipping amounts from the factories through the warehouses to meet customer demands in such a way that the total fixed plus variable costs are minimized. Capacity constraints at factories and warehouses are also imposed.We present a cost operator algorithm for solving this problem. The algorithm takes into account the network structure and the submodularity of the objective function. Computational results with problems taken from the literature as well as new problems are provided.     

带有两货栈及时变需求的变质性物品的最优EOQ模型(英)

本文针对一般的时变需求与两个货栈（自己货栈和租用货栈），建立了变质性物品的最优确定性EOQ模型，提供了用来寻求最优补充策略的方法，并就线性需求出示了两个数值例子．     

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.     

Design and planning of supply chains with integration of reverse logistics activities under demand uncertainty

In this paper, a mixed integer linear programming (MILP) formulation is developed for the design and planning of supply chains with reverse flows while considering simultaneously production, distribution and reverse logistics activities. It is also considered products’ demand uncertainty using a scenario tree approach. As main goal the model defines the maximization of the expected net present value and the results provide details on sizing and location of plants, warehouses and retailers, definition of processes to install, establishment of forward and reverse flows and inventory levels to attain. The model is applied to a representative European supply chain case study and its applicability is demonstrated.     

A large-scale application of the partial coverage uncapacitated facility location problem

The traditional, uncapacitated facility location problem (UFLP) seeks to determine a set of warehouses to open such that all retail stores are serviced by a warehouse and the sum of the fixed costs of opening and operating the warehouses and the variable costs of supplying the retail stores from the opened warehouses is minimized. In this paper, we discuss the partial coverage uncapacitated facility location problem (PCUFLP) as a generalization of the uncapacitated facility location problem in which not all the retail stores must be satisfied by a warehouse. Erlenkotter's dual-ascent algorithm, DUALOC, will be used to solve optimally large (1600 stores and 13?000 candidate warehouses) real-world implemented PCUFLP applications in less than two minutes on a 500?MHz PC. Furthermore, a simple analysis of the problem input data will indicate why and when efficient solutions to large PCUFLPs can be expected.     

Determining optimal lot size for a two-warehouse system with deterioration and shortages using net present value

In this paper, we develop a deterministic inventory model for deteriorating items with two warehouses by minimizing the net present value of the total cost. Deterioration rates of items in the two warehouses may be different. In addition, we allow for shortages and complete backlogging. We then prove that the optimal replenishment policy not only exists but also is unique under some condition. Further, the result reveals that the reorder interval based on the average total cost, if it exists, must be longer than that derived using net present value. Finally, we use Yang’s [H.L. Yang, European Journal of Operational Research 157 (2004) 344–356] numerical example to illustrate the model and conclude the paper with suggestions for possible future research.     

Computationally Efficient Solution of a Multiproduct,Two-Stage Distribution—Location Problem

A two-stage distribution planning problem, in which customers are to be served with different commodities from a number of plants, through a number of intermediate warehouses is addressed. The possible locations for the warehouses are given. For each location, there is an associated fixed cost for opening the warehouse concerned, as well as an operating cost and a maximum capacity. The demand of each customer for each commodity is known, as are the shipping costs from a plant to a possible warehouse and thereafter to a customer. It is required to choose the locations for opening warehouses and to find the shipping schedule such that the total cost is minimized. The problem is modelled as a mixed-integer programming problem and solved by branch and bound. The lower bounds are calculated through solving a minimum-cost, multicommodity network flow problem with capacity constraints. Results of extensive computational experiments are given.     

Service differentiation through selective lateral transshipments

We consider a multi-item spare parts problem with multiple warehouses and two customer classes, where lateral transshipments are used as a differentiation tool. Specifically, premium requests that cannot be met from stock at their preferred warehouse may be satisfied from stock at other warehouses (so-called lateral transshipments). We first derive approximations for the mean waiting time per class in a single-item model with selective lateral transshipments. Next, we embed our method in a multi-item model minimizing the holding costs and costs of lateral and emergency shipments from upstream locations in the network. Compared to the option of using only selective emergency shipments for differentiation, the addition of selective lateral transshipments can lead to significant further cost savings (14% on average).