An integrated model for warehouse and inventory planning

The purpose of this article is to evaluate the value of integrating tactical warehouse and inventory decisions. Therefore, a global warehouse and inventory model is presented and solved. In order to solve this mathematical model, two solution methodologies are developed which offer different level of integration of warehouse and inventory decisions. Computational tests are performed on a real world database using multiple scenarios differing by the warehouse capacity limits and the warehouse and inventory costs. Our observation is that the total cost of the inventory and warehouse systems can be reduced drastically by taking into account the warehouse capacity restrictions in the inventory planning decisions, in an aggregate way. Moreover additional inventory and warehouse savings can be achieved by using more sophisticated integration methods for inventory and warehouse decisions.     

A two warehouse inventory model for a deteriorating item with partially/fully backlogged shortage and fuzzy lead time

An optimization inventory policy for a deteriorating item with imprecise lead-time, partially/fully backlogged shortages and price dependent demand is developed under two-warehouse system. For display and storage, the retailer hires one warehouse of finite capacity at market place, treated as own warehouse (OW) and another warehouse of large capacity as it may be required at a distance place from the market, treated as rented warehouse (RW). Holding cost at RW decreases with the increase of distance from the market place. Units are transferred from RW to OW in bulk release pattern and sold from OW. Using the nearest interval approximation method the estimated fuzzy average profit function is defuzzified and transformed to multiple crisp objective functions which are solved by Global Criteria Method. The models are illustrated numerically. Sensitivity of the inventory costs on the location of RW has been depicted graphically. Also loss in profit due to deteriorations for both models have been presented.     

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。     

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.     

Simple Models and Insights for Warehouse Sizing

This study is concerned with minimizing the total discounted cost of operating an inventory system and providing the warehouse space necessary to accommodate the replenishment lots, under the assumption of constant product demand. The use of an approximation objective function for the single-item case allows the optimal warehouse size as well as the ratio of relevant investment costs to relevant inventory costs to be written in closed-form. Based upon the value of this ratio, circumstances are identified under which an integrated approach is justified, and others under which the inventory policy and storage capacity can be determined sequentially. The multi-item version of the problem under study is solved by the Lagrangian multiplier method, given that no coordination takes place between the items. Finding the optimal Lagrange multiplier can be accomplished efficiently by the Newton–Raphson method.     

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.     

Investigation of two-warehouse inventory problems in interval environment under inflation via particle swarm optimization

ABSTRACT

In this paper, a two-warehouse inventory problem has been investigated under inflation with different deterioration effects in two separate warehouses (rented warehouse, RW, and owned warehouse, OW). The objective of this investigation is to determine the lot-size of the cycle of the two-warehouse inventory system by minimizing the average cost of the system. Considering different inventory policies, the corresponding models have been formulated for linear trend in demand and interval valued cost parameters. In OW, shortages, if any, are allowed and partially backlogged with a variable rate dependent on the duration of the waiting time up to the arrival of the next lot. The corresponding optimization problems have been formulated as non-linear constrained optimization problems with interval parameters. These problems have been solved by an efficient soft computing method, viz. practical swarm optimization. To illustrate the model, a numerical example has been solved with different partially backlogging rates. Then to study the effect of changes of different system parameters on the optimal policy, sensitivity analyses have been carried out graphically by changing one parameter at a time and keeping the others at their original values. Finally, a fruitful conclusion has been reached regarding the selection of an appropriate inventory policy of the two-warehouse system.     

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。     

Two storage inventory problem with dynamic demand and interval valued lead-time over finite time horizon under inflation and time-value of money

A finite time horizon inventory problem for a deteriorating item having two separate warehouses, one is a own warehouse (OW) of finite dimension and other a rented warehouse (RW), is developed with interval-valued lead-time under inflation and time value of money. Due to different preserving facilities and storage environment, inventory holding cost is considered to be different in different warehouses. The demand rate of item is increasing with time at a decreasing rate. Shortages are allowed in each cycle and backlogged them partially. Shortages may or may not be allowed in the last cycle and under this circumstance, there may be three different types of model. Here it is assumed that the replenishment cycle lengths are of equal length and the stocks of RW are transported to OW in continuous release pattern. For each model, different scenarios are depicted depending upon the re-order point for the next lot. Representing the lead-time by an interval number and using the interval arithmetic, the single objective function for profit is changed to corresponding multi-objective functions. These functions are maximized and solved by Fast and Elitist Multi-objective Genetic Algorithm (FEMGA). The models are illustrated numerically and the results are presented in tabular form.     

A model based evaluation of a commonly used rule of thumb for warehouse layout

A model is formulated to describe the cost effects of alternative warehouse layouts in a dedicated storage warehouse that utilizes dual address order picking cycles. The model is utilized to evaluate a common warehouse layout rule of thumb where stock levels are determined using economic order quantities, and stock locations are obtained using the cube per order index. A simple heuristic procedure is devised to utilize the cost model to obtain warehouse layouts with lower total inventory and order picking cost than those obtained using the rule of thumb. Four test problems are generated to assess the difficulty of obtaining improved warehouse layouts. It is shown that the heuristic procedure can achieve significantly improved warehouse layouts with minimal computational effort.     

销售率线性依赖瞬时库存水平的两货栈决策模型

在成熟期的存货影响销售环境下,考虑销售率线性依赖瞬时库存水平,不允许缺货,研究了一类非变质性物品的两货栈库存决策问题.建立了以系统平均总利润最大为目标的决策模型,分析了系统最优库存策略的存在性和唯一性,并给出了求解模型的有效方法.分析结果表明,库存管理者利用租用货栈进行订货决策时,除了要充分考虑企业自身的库存容量外,还取决于自有货栈产品相关参数对库存系统绩效的边际贡献率.     

应对突发状况的装备备件供应网络虚拟库存策略研究

研究突发状况引起装备维修备件需求大增时,供应网络中维修站点备件库存策略问题.基于多维修站点的虚拟库构建应对突发状况的备件库存期望成本模型,考虑突发状况的发生概率和突发状况对维修站点的影响概率,比较分析了突发状况发生引起维修需求大增的情况下,维修站点独立应对和构建虚拟库横向联合应对的库存期望成本,通过算例对这两种库存期望成本模型进行了数值分析,验证了构建虚拟库应对突发状况的有效性.     

Model and algorithm for inventory/routing decision in a three-echelon logistics system

This paper addresses an integrated inventory and routing problem in a three-echelon logistics system, which consists of a supplier, a central warehouse and a group of retailers. The inventory decision of each member and the routing decision among members of the system are made simultaneously, with the objective of minimizing the overall average cost of the system. A strategy named fixed partition and power-of-two (FP–POT) is proposed for the considered problem and a variable large neighborhood search (VLNS) algorithm, which is a special case of variable neighborhood search (VNS) algorithm, is developed. The efficiency of the strategy as well as the algorithm is illustrated by comparing computational results with a lower bound. The advantage of the proposed VLNS algorithm is further shown by getting better results for the problems in a two-echelon logistics system, which have been solved by a Tabu Search algorithm recently.     

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.     

Inventory model with deteriorating items,ramp-type demand and partially backlogged shortages for a two warehouse system

In this paper, we consider a two warehouse inventory model, an owned one (OW) and a rented one (RW). Inventory deteriorates in the two warehouses at different constant rates, demand rate is a general ramp-type function of time and shortages are partially backlogged at a constant rate. Existence and uniqueness of the optimal solution is discussed. An algorithm is developed to obtain the overall optimal replenishment policy, which would enable the manager to decide upon the feasibility of renting a warehouse. The dynamics of the model and application of the algorithm are demonstrated through numerical examples. Sensitivity analysis is conducted with respect to model parameters and some important observations are drawn.     

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.     

Coordinated control of distribution supply chains in the presence of fuzzy customer demand

This paper considers a single product inventory control in a Distribution Supply Chain (DSC). The DSC operates in the presence of uncertainty in customer demands. The demands are described by imprecise linguistic expressions that are modelled by discrete fuzzy sets. Inventories at each facility within the DSC are replenished by applying periodic review policies with optimal order up-to-quantities. Fuzzy customer demands imply fuzziness in inventory positions at the end of review intervals and in incurred relevant costs per unit time interval. The determination of the minimum of defuzzified total cost of the DSC is a complex problem which is solved by applying decomposition; the original problem is decomposed into a number of simpler independent optimisation subproblems, where each retailer and the warehouse determine their optimum periodic reviews and order up-to-quantities. An iterative coordination mechanism is proposed for changing the review periods and order up-to-quantities for each retailer and the warehouse in such a way that all parties within the DSC are satisfied with respect to total incurred costs per unit time interval. Coordination is performed by introducing fuzzy constraints on review periods and fuzzy tolerances on retailers and warehouse costs in local optimisation subproblems.     

一个带有增加量价格折扣的两货栈库存模型

已有的确定性两货栈(其中一个是自己货栈(OW);另一个是租用货栈(RW))库存模型通常不考虑增加量价格折扣,然而在实际生活中,增加量价格折扣却是促使库存管理者加大订货量的一个重要原因.本文通过考虑增加量价格折扣而将两货栈系统作了进一步扩展,在采用间隔式运输模式运送RW的物品到OW的情形下,建立了一个带有增加量价格折扣并允许短缺的两货栈库存模型,提供了一种寻求最优库存策略的简单方法.     

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.