Allocation of warehouse inventory with electronic data interchange and fixed order intervals

This paper considers the problem of allocating warehouse inventory to retailers where retailer orders and the replenishment of warehouse inventory occur periodically on a fixed schedule. We assume that the warehouse and the retailers have the opportunity to exchange demand information through Electronic Data Interchange (EDI). At the warehouse level, for instance, the available information on the retailer's demand may be utilized in determining the shipment quantities needed to meet the desired service level to the retailers. Unlike similar models focusing primarily on optimizing systems wide performance measures, in this paper we focus on the service level furnished to the retailers by the warehouse. To this end, three different allocation policies are considered: static, myopic, and dynamic rules characterizing the impact of available demand information on the resulting service levels. Numerical illustrations exemplify the allocation rules considered. An interesting though counter intuitive observation is that the existence of additional demand information cannot, a prior, be assumed superior.     

Analysis of a newsvendor which has errors in inventory data records

Although supply chain scholars very often assume the availability of error free data pertaining to the flow of goods that come in and go out of an inventory system as well as the on hand inventory level, some recent investigations show that this may not be true even in facilities where advanced item identification and data capture technologies such as the barcode system are used. This paper proposes a single period model where the inventory data capture process using the barcode system is prone to errors that lead to inaccuracies. In the first part of our work, we derive analytically the optimal policy in presence of errors when both demand and errors are uniformly distributed. In the second part, we examine quantitatively the impact of record inaccuracies on the performance of an inventory system, in terms of additional overage and shortage costs incurred.     

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.     

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.     

Stock Rationing in a Continuous Review Two-Echelon Inventory Model

In this paper we consider a 1-warehouse, N-retailer inventory system where demand occurs at all locations. We introduce an inventory model which allows us to set different service levels for retailers and direct customer demand at the warehouse. For each retailer a critical level is defined, such that a retailer replenishment order is delivered from warehouse stock if and only if the stock level exceeds this critical level. It is assumed that retailer replenishment orders, which are not satisfied from warehouse stock, are delivered directly from the outside supplier, instead of being backlogged. We present an analytical upper bound on the total cost of the system, and develop a heuristic method to optimize the policy parameters. Numerical experiments indicate that our technique provides a very close approximation of the exact cost. Also, we show that differentiating among the retailers and direct customer demand can yield significant cost reductions.     

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.     

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.     

Lot‐sizing policies for deterioration items under two‐level trade credit with partial trade credit to credit‐risk retailer and limited storage capacity

The main purpose of this article is to investigate the optimal wholesaler's replenishment decisions for deterioration items under two levels of the trade credit policy and two storage facilities in order to reflect the supply chain management situation within the economic order quantity framework. In this study, each of the following assumptions have been made: (1) The own warehouse with limited capacity always is not sufficient to store the order quantity, so that a rented warehouse is needed to store the excess units over the capacity of the own warehouse; (2) The wholesaler always obtains the partial trade credit, which is independent of the order quantity offered by the supplier, but the wholesaler offers the full trade credit to the retailer; (3) The wholesaler must take a loan to pay his or her supplier the partial payment immediately when the order is received and then pay off the loan with the entire revenue. Under these three conditions, the wholesaler can obtain the least costs. Furthermore, this study models the wholesaler's optimal replenishment decisions under the aforementioned conditions in the supply chain management. Two theorems are developed to efficiently determine the optimal replenishment decisions for the wholesaler. Finally, numerical examples are given to illustrate the theorems that are proven in this study, and the sensitivity analysis with respect to the major parameters in this study is performed. Copyright © 2016 John Wiley & Sons, Ltd.     

Prioritizing replenishments of the piece picking area

Having sufficient inventories in the forward or piece picking area of a warehouse is an essential condition for warehouse operations. As pickers consume the inventory in the piece racks, there is a risk of stockout. This can be reduced by the timely replenishment of products from the bulk reserve area to the forward area. We develop and compare three policies for prioritizing replenishments for the case where order picking and replenishments occur concurrently because of time restrictions. The first policy, based on the ratio of available inventory to wave demand, reduces the number of stockouts considerably. The other two more sophisticated policies reduce the number of stockouts even more but require much more computation time, and are more costly in terms of implementation, maintenance and software updates. We present the results of implementing one of these policies in the warehouse of a large cosmetics firm.     

Modeling and analysis of the causes of bullwhip effect in centralized and decentralized supply chain using response surface method

The “bullwhip” effect is a major cause of supply chain deficiencies. This phenomenon refers to grow the amplification of demand or inventory variability as it moves up the supply chain. Supply chain managers experience this variance amplification in both inventory levels and orders. Other side, dampening variance in orders may have a negative impact on customer service due to the increase in the inventory variance. This paper with simulating a three stage supply chains consisting of a single retailer, single wholesaler and single manufacturer under both centralized and decentralized chains. In this paper, it is intended to analysis the causes of bullwhip effect from two dimensions of order and inventory variance using the response surface methodology. The results show that in both supply chains, rationing factor is considered as the least important cause of bullwhip effect. While the wholesaler’s order batching and the chain’s order batching are considered as the main causes for the bullwhip effect in the decentralized and centralized chains, respectively.     

Evaluation of stock allocation policies in a divergent inventory system with shipment consolidation

In this paper we consider a one-warehouse N-retailer inventory system characterized by access to real-time point-of-sale data, and a time based dispatching and shipment consolidation policy at the warehouse. More precisely, inventory is reviewed continuously, while a consolidated shipment (for example, a truck) to all retailers is dispatched from the warehouse at regular time intervals. The focus is on investigating the cost benefits of using state-dependent myopic allocation policies instead of a simple FCFS (First-Come-First-Serve) rule to allocate shipped goods to the retailers. The analysis aims to shed some light on when, if ever, FCFS is a reasonable policy to use in this type of system? The FCFS allocations of items to retailers are determined by the sequence in which retailer orders (or equivalently customer demands) arrive to the warehouse. Applying the myopic policy enables the warehouse to postpone the allocation decision to the moment of shipment (from the warehouse) or the moments of delivery (to the different retailers), and to base it on the inventory information available at those times. The myopic allocation method we study is often used in the literature on periodic review systems.     

Comparing improvement strategies for inventory inaccuracy in a two-echelon supply chain

Classical inventory theory often assumes no discrepancies between recorded inventory and actual inventory. However, inventory records are usually inaccurate due to many reasons in practice. For example, inventory shrinkage refers to the difference between booked inventory that a company should have as a result of its sales, purchasing, and manufacturing processes and actual inventory that it has on hand. This paper concerns the impact of inventory shrinkage to a supply chain and investigates different strategies to deal with inventory shrinkage. We consider a single-period two-echelon supply chain consisting of a Stackelberg manufacturer and a retailer whose inventory is subject to shrinkage errors. Our analysis is based on a single-period newsvendor model and considers the following cases of order decisions: (a) the retailer ignores the inventory errors; (b) the retailer estimates the errors; (c) the retailer shares the inventory error information with the manufacturer; and (d) RFID technology is used to reduce or eliminate the errors. The first case is the base strategy and a common practice for many supply chains, the other two represent certain non-technological strategies of the retailer when dealing with inventory inaccuracy, and the last one represents a technology improvement strategy by the manufacturer to reduce or eliminate inventory shrinkage errors. We compare these improvement strategies and derive critical tag price for RFID implementation as a technological remedy for the inventory inaccuracy problem. Conditions for the profitability of RFID adoption are discussed.     

Optimality of Base-Stock and (s, S) Policies for Inventory Problems with Information Delays

Information delays exist when the most recent inventory information available to the inventory manager (IM) is dated; namely, the IM observes only the inventory level of an earlier period. We introduce information delays into the standard multiperiod stochastic inventory problem with backorders. We consider two types of information delays: (i) a constant delay and (ii) a random delay. We define an appropriate reference inventory position, which is a sufficient statistics for finding the optimal order quantity. We show that the optimal ordering policy is of base-stock type with respect to the reference inventory position and is of (s, S) type if there is also a fixed cost of ordering.All authors were supported in part by NSF Grant DMS-0509278.     

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 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.     

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.     

Inventory policy for an item with inflation induced purchasing price,selling price and demand with immediate part payment

In this paper, an inventory policy for an item is presented with inflation and selling price dependent demand under deterministic and random planning horizons allowing and not allowing shortages. In addition, there is a provision for (i) an immediate part payment (variable) to the wholesaler, (ii) borrowing some money from money lending source for the immediate part payment, (iii) earning a discount on purchasing price and relaxation on credit period from the wholesaler against the advance payment and (iv) delay in payment for the rest allowed by wholesaler. The payment to the source is made at the end of the business period with some interest charged. Against the above conjectures, inventory models under the finite (crisp) and random planning horizons have been formulated with respect to the retailer’s point of view for maximum profit. The nonlinear optimization method – Generalized Reduced Gradient (GRG) method is used to find the optimal solutions and the corresponding maximum profits for the different sets of given numerical data. Some sensitivity analyses are made and presented graphically. As particular cases, the results of the crisp models and the case without shortages are obtained from those of the stochastic model and the case with shortages respectively.     

Optimal ordering and transfer policy for an inventory with stock dependent demand

This paper deals with an ordering-transfer inventory model to determine the retailer’s optimal order quantity and the number of transfers per order from the warehouse to the display area. It is assumed that the amount of display space is limited and the demand rate depends on the display stock level. The objective is to maximize the average profit per unit time yielded by the retailer. The proposed models and algorithms are developed to find the optimal strategy by retailer. Numerical examples are presented to illustrate the models developed and the sensitivity analysis is also reported.     

传统分销系统的经销商的库存管理

目前我国快速消费品行业中的中小企业的分销系统大都是传统的分销系统,在它之中经销商是处于核心地位.本文通过对经销商的库存进行重点分析,以了解产生经销商跨区冲货的原因及如何有效控制经销商合理库存的方法.作者认为分销系统是一个典型的系统工程.     

On the value of customer information for an independent supplier in a continuous review inventory system

We consider the inventory control problem of an independent supplier in a continuous review system. The supplier faces demand from a single customer who in turn faces Poisson demand and follows a continuous review (R, Q) policy. If no information about the inventory levels at the customer is available, reviews and ordering are usually carried out by the supplier only at points in time when a customer demand occurs. It is common to apply an installation stock reorder point policy. However, as the demand faced by the supplier is not Markovian, this policy can be improved by allowing placement of orders at any point in time. We develop a time delay policy for the supplier, wherein the supplier waits until time t after occurrence of the customer demand to place his next order. If the next customer demand occurs before this time delay, then the supplier places an order immediately. We develop an algorithm to determine the optimal time delay policy. We then evaluate the value of information about the customer’s inventory level. Our numerical study shows that if the supplier were to use the optimal time delay policy instead of the installation stock policy then the value of the customer’s inventory information is not very significant.