多货栈及变质情形下两种可替代物品的经济订货批量模型

研究了多货栈及变质情形下两种可替代物品的经济订货批量问题.在计划期内,若某一种易变质物品发生缺货,则可以被另一种易变质物品以一定的替代率代替补充,不同物品有不同的变质率,且要决定租用货栈的数量.以库存系统的总费用最小为目标函数,分别对货栈容量无限与有限的情形建立模型,证明了最优策略存在的唯一性,并分别给出了求解最优订购策略的算法,最后通过一个算例验证了算法的最优性.     

A partition approach to the inventory/routing problem

In this study we focus on the integration of inventory control and vehicle routing schedules for a distribution system in which the warehouse is responsible for the replenishment of a single item to the retailers with demands occurring at a specific constant (but retailer-dependent) rate, combining deliveries into efficient routes. This research proposes a fixed partition policy for this type of problem, in which the replenishment interval of each of the retailers’ partition region as well as the warehouse is accorded the power of two (POT) principle. A lower bound of the long-run average cost of any feasible strategy for the considered distribution system is drawn. And a tabu search algorithm is designed to find the retailers’ optimal partition regions under the fixed partition policy proposed. Computational results reveal the effectiveness of the policy as well as of the algorithm.     

A two-warehouse inventory model for deteriorating items under conditionally permissible delay in payment

For the capacity of any warehouse is limited, it has to rent warehouse (RW) for storing the excess units over the fixed capacity W of the own warehouse (OW) in practice. The RW is assumed to offer better preserving facilities than the OW resulting in a lower rate of deterioration and is assumed to charge higher holding cost than the OW. In this paper, a two-warehouse inventory model for deteriorating items is considered with constant demand under conditionally permissible delay in payment. The purpose of this study is to find the optimal replenishment policies for minimizing the total relevant inventory costs. Useful theorems to characterize the optimal solutions have been derived. Furthermore, numerical examples are provided to illustrate the proposed model, sensitivity analysis of the optimal solutions with respect to major parameters is carried out and some managerial inferences are obtained.     

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.     

Complements and substitutes among locations in the two-stage transshipment problem

This paper considers complementarity and substitutability among locations for a two-stage transshipment problem with locations being factories, warehouses, and demand centers. A direct generalization of properties known for the transportation problem would be that any two locations of different types are complements and any two locations of the same type are substitutes. Examples show that these properties need not hold for pairs of locations that include at least one warehouse. An algorithm of Nagelhout and Thompson (European J. Operational Res. 6 (1981) 149–161) for locating warehouses is based on the incorrect supposition that any two warehouses are substitutes, and an example shows that their algorithm need not generate an optimal solution as claimed. For pairs of locations that do not include a warehouse, complementarity and substitutability properties hold just as in the transportation problem.     

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.     

Über die optimale lagerhaltung in einem system von lagern: eine näherugslösung

This paper investigates the N-Warehouse-Problem under the condition of linear cost-functions and constant profit made from transport (per unit stored) from warehouse i to warehouse j, i ≠ j. Applying this model we obtain and approximation for the optimal decision in a model where transportation profit does not remain constant. A new expression for the expected costs in introduced, which facilitates the comparison of the costs with those of N independent warehouse. In the appendix several problems are solved.     

Possibility and necessity representations of fuzzy inequality and its application to two warehouse production-inventory problem

In this paper, possibility and necessity representations of fuzzy inequality constraints are presented and then crisp versions of the constraints are derived. Here analogous to chance constraints, real-life necessity and possibility constraints in the context of two warehouse multi-item dynamic production-inventory control system are defined and defuzzified following fuzzy relations. Hence, a realistic two warehouse multi-item production-inventory model with fuzzy constraints has been formulated for a finite period of time and solved for optimal production with the objective of having maximum profit. The rate of production is unknown, assumed to be a function of time and considered as a control variable. Also the present system produces some defective units alongwith the perfect ones and the rate of produced defective units is stochastic in nature. Demand of the good units is stock dependent and known and the defective units are sold at a reduced price. The space required per unit item and available storage space are assumed to be imprecise. The inequality of budget constraints is also imprecise. The space and budget constraints are expressed as necessity and/or possibility types. The model is reduced to an equivalent deterministic model using fuzzy relations and solved for optimum production function using Pontryagin’s optimal control policy, the Kuhn–Tucker conditions and generalized reduced gradient (GRG) technique. The model is illustrated numerically and values of demand, optimal production function and stock level are presented in both tabular and pictorial forms.     

A deterministic order level inventory model for deteriorating items with two storage facilities

In this paper a deterministic inventory model is developed for a single deteriorating item which is stored in two different warehouses. A rented warehouse is used to store the excess units over the fixed capacity W of the own warehouse. The rented warehouse is assumed to charge higher unit holding cost than the own warehouse, but to offer a better preserving facility resulting in a lower rate of deterioration for the goods than the own warehouse. The optimal stock level for the beginning of the period is found and the model developed is shown to agree with the order level model for non deteriorating items with a single storage facility. An illustration to show the applicability of the model is also presented.     

A two-echelon inventory model for a deteriorating item with stock-dependent demand,partial backlogging and capacity constraints

This study investigates a two-echelon supply chain model for deteriorating inventory in which the retailer’s warehouse has a limited capacity. The system includes one wholesaler and one retailer and aims to minimise the total cost. The demand rate in retailer is stock-dependent and in case of any shortages, the demand is partially backlogged. The warehouse capacity in the retailer (OW) is limited; therefore the retailer can rent a warehouse (RW) if needed with a higher cost compared to OW. The optimisation is done from both the wholesaler’s and retailer’s perspectives simultaneously. In order to solve the problem a genetic algorithm is devised. After developing a heuristic a numerical example together with sensitivity analysis are presented. Finally, some recommendations for future research are presented.     

考虑车载容量的多区型仓库拣货路径优化研究

拣货作业是仓库核心作业之一,占据仓库运营大量的时间成本和资金成本.针对多区型仓库拣货路径优化问题,对多区型仓库布局、货位坐标、路径等问题进行了定义,构建了多区型仓库拣货路径优化建模,接着通过大量实验确定了人工鱼群算法在求解拣货路径问题时的最优算法参数组合,通过演示性实验验证了模型与算法的有效性,最后从波次订单对实验结果...     

B2C电子商务仓库拣货路径优化策略应用研究

当前国内B2C电子商务仓库多为人至物的拣货模式,拣货作业成为其核心作业之一,占据仓库大量时间成本和资金成本,拣货路径优化成为企业亟需解决的问题。本文基于TSP对拣货路径进行建模,利用蚁群算法、模拟退火算法和禁忌搜索对该NP-hard问题进行求解,并同当前企业普遍采用的S型启发式策略进行对比,拣货时间节约13.35%。进一步得出当拣货品数量较少时应采用模拟退火算法求解,而当拣货品数量较大时采用蚁群算法仅进行一次迭代,则可以实现短时间得到相对较优的解。所得结果已应用于某大型电子商务企业,效果明显。     

An Integrated Inventory-Routing System for Multi-item Joint Replenishment with Limited Vehicle Capacity

In this paper, we develop a mathematical programming approach for coordinating inventory and transportation decisions in an inbound commodity collection system. In particular, we consider a system that consists of a set of geographically dispersed suppliers that manufacture one or more non-identical items, and a central warehouse that stocks these items. The warehouse faces a constant and deterministic demand for the items from outside retailers. The items are collected by a fleet of vehicles that are dispatched from the central warehouse. The vehicles are capacitated, and must also satisfy a frequency constraint. Adopting a policy in which each vehicle always collects the same set of items, we formulate the inventory-routing problem of minimizing the long-run average inventory and transportation costs as a set partitioning problem. We employ a column generation approach to determine a lower bound on the total costs, and develop a branch-and-price algorithm that finds the optimal assignment of items to vehicles. We also propose greedy constructive heuristics, and develop a very large-scale neighborhood (VLSN) search algorithm to find near-optimal solutions for the problem. Computational tests are performed on a set of randomly generated problem instances.The work of this author was supported by a scholarship of the Faculty of Engineering of Ubonratchathani University, Ubonratchathani, Thailand., The work of this author was supported in part by the National Science Foundation under Grant No. DMI-0085682.     

需求依赖于展示区库存水平的易腐品订购和转运策略

本文主要研究易腐品零售商的订货和转运策略。零售商的库存分为两部分,即展示区/货架库存和仓库库存。零售商定期向供应商订货,零售商收到订购的商品首先将其中一部分商品存放在展示区中,余下的部分储存在仓库。展示区的空间是有限的,并且需求依赖于展示区商品的库存量。本文首先建立了以平均利润最大化为目标的库存优化模型并对模型最优解的存在性进行了分析,然后得到了求解最优订购量、转运量、转运时间间隔以及再订购点的算法,最后给出了不同参数条件下的算例。     

A solution approach to the inventory routing problem in a three-level distribution system

We consider the infinite horizon inventory routing problem in a three-level distribution system with a vendor, a warehouse and multiple geographically dispersed retailers. In this problem, each retailer faces a demand at a deterministic, retailer-specific rate for a single product. The demand of each retailer is replenished either from the vendor through the warehouse or directly from the vendor. Inventories are kept at both the retailers and the warehouse. The objective is to determine a combined transportation (routing) and inventory strategy minimizing a long-run average system-wide cost while meeting the demand of each retailer without shortage. We present a decomposition solution approach based on a fixed partition policy where the retailers are partitioned into disjoint and collectively exhaustive sets and each set of retailers is served on a separate route. Given a fixed partition, the original problem is decomposed into three sub-problems. Efficient algorithms are developed for the sub-problems by exploring important properties of their optimal solutions. A genetic algorithm is proposed to find a near-optimal fixed partition for the problem. Computational results show the performance of the solution approach.     

需求受库存影响下具有固定保质期物品的最优订货策略

带有固定保质期物品的订货是供应链终端销售系统的一个重要决策问题,假设需求依赖库存展示水平并考虑"后进先出"的销售策略而建立了相应的库存决策模型,其中物品在固定保质期内仍具有常数的变质速率.然后以系统平均利润最大化为目标讨论了模型最优解的存在性及唯一性,并提供了寻求模型整体最优解的简单方法.最后给出应用实例,并分析了模型参数变化对最优订货策略的影响.     

Approximate evaluation of multi-location inventory models with lateral transshipments and hold back levels

We consider a continuous-time, single-echelon, multi-location inventory model with Poisson demand processes. In case of a stock-out at a local warehouse, a demand can be fulfilled via a lateral transshipment (LT). Each warehouse is assigned a pre-determined sequence of other warehouses where it will request for an LT. However, a warehouse can hold its last part(s) back from such a request. This is called a hold back pooling policy, where each warehouse has hold back levels determining whether a request for an LT by another warehouse is satisfied. We are interested in the fractions of demand satisfied from stock (fill rate), via an LT, and via an emergency procedure from an external source. From these, the average costs of a policy can be determined. We present a new approximation algorithm for the evaluation of a given policy, approximating the above mentioned fractions. Whereas algorithms currently known in the literature approximate the stream of LT requests from a warehouse by a Poisson process, we use an interrupted Poisson process. This is a process that is turned alternatingly On and Off for exponentially distributed durations. This leads to the On/Off overflow algorithm. In a numerical study we show that this algorithm is significantly more accurate than the algorithm based on Poisson processes, although it requires a longer computation time. Furthermore, we show the benefits of hold back levels, and we illustrate how our algorithm can be used in a heuristic search for the setting of the hold back levels.     

需求率基于库存的变质物品的两货栈模型

针对需求受库存水平影响的变质品的两货栈系统,本文首先考虑了允许缺货但缺货要补情形下,分别给出了L₁系统(库存系统只用自己的货栈存放物品)和L₂系统(库存系统使用自己货栈和租用货栈存放物品)时,销售商的库存和运输策略模型。其次给出了允许缺货但缺货不补L₁系统和L₂系统时,销售商的库存和运输策略,并对模型最优解作了相关分析,最后给出算例,给销售商实际的库存管理提供了理论依据。     

The warehouse-inventory-transportation problem for supply chains

Warehouses play a vital role in mitigating variations in supply and demand, and in providing value-added services in a supply chain. However, our observation of supply chain practice reveals that warehousing decisions are not included when developing a distribution plan for the supply chain. This lack of integration has resulted in a substantial variation in workload (42–220%) at our industry partner’s warehouse costing them millions of dollars. To address this real-world challenge, we introduce the warehouse-inventory-transportation problem (WITP) of determining an optimal distribution plan from vendors to customers via one or more warehouses in order to minimize the total distribution cost. We present a nonlinear integer programming model for the WITP considering supply chains with multiple vendors, stores, products, and time-periods, and one warehouse. The model also considers worker congestion at the warehouse that could affect worker productivity. A heuristic based on iterative local search is developed to solve industry-sized problems with up to 500 stores and 1000 products. Our experiments indicate that the distribution plans obtained via the WITP, as compared to a sequential approach, result in a substantial reduction in workload variance at the warehouse, while considerably reducing the total distribution cost. These plans, however, are sensitive to aisle configuration and technology at the warehouse, and the level and productivity of temporary workers.     

Supply chain models for an assembly system with preprocessing of raw materials

In this paper, we investigate the material procurement and delivery policy in a production system where raw materials enter into the assembly line from two different flow channels. The system encompasses batch production process in which the finished product demand is approximately constant for an infinite planning horizon. Two distinct types of raw materials are passed through the assembly line before to convert them into the finished product. Of the two types of raw materials, one type requires preprocessing inside the facility before the assembly operation and other group is fed straightway in the assembly line. The conversion factors are assigned to raw materials to quantify the raw material batch size required. To analyze such a system, we formulate a nonlinear cost function to aggregate all the costs of the inventories, ordering, shipping and deliveries. An algorithm using the branch and bound concept is provided to find the best integer values of the optimal solutions. The result shows that the optimal procurement and delivery policy minimizes the expected total cost of the model. Using a test problem, the inventory requirements at each stage of production and their corresponding costs are calculated. From the analysis, it is shown that the rate and direction change of total cost is turned to positive when delivery rates per batch reaches close to the optimal value and the minimum cost is achieved at the optimal delivery rate. Also, it is shown that total incremental cost is monotonically increasing, if the finished product batch size is increased, and if, inventory cost rates are increased. We examine a set of numerical examples that reveal the insights into the procurement-delivery policy and the performance of such an assembly type inventory model.