Analysis of an EOQ inventory model with partial backordering and non-linear unit holding cost

In this paper, an economic order quantity inventory model is analyzed, considering that the unit cumulative holding cost has two significant components: a fixed cost which represents the cost of accommodating the item in the warehouse and a variable cost given by a potential function of the length of time over which the item is held in stock. Shortages are allowed and, during the stockout period, only a fraction of demand is partially backordered. The backordering cost includes a fixed cost and a cost linearly dependent on the length of time for which backorder exists. A solution procedure is developed for determining the optimal inventory policy. Moreover, to illustrate the effects of some parameters on the optimal policy and the minimum total inventory cost, a numerical study is developed.     

An Entropy‐Based Methodology for Valuation of Demand Uncertainty Reduction

We propose a distribution‐free entropy‐based methodology to calculate the expected value of an uncertainty reduction effort and present our results within the context of reducing demand uncertainty. In contrast to existing techniques, the methodology does not require a priori assumptions regarding the underlying demand distribution, does not require sampled observations to be the mechanism by which uncertainty is reduced, and provides an expectation of information value as opposed to an upper bound. In our methodology, a decision maker uses his existing knowledge combined with the maximum entropy principle to model both his present and potential future states of uncertainty as probability densities over all possible demand distributions. Modeling uncertainty in this way provides for a theoretically justified and intuitively satisfying method of valuing an uncertainty reduction effort without knowing the information to be revealed. We demonstrate the methodology's use in three different settings: (i) a newsvendor valuing knowledge of expected demand, (ii) a short life cycle product supply manager considering the adoption of a quick response strategy, and (iii) a revenue manager making a pricing decision with limited knowledge of the market potential for his product.     

我国零售业的供应商管理库存实施策略研究

针对我国零售行业库存方面普遍存在的问题，零售业采取比较先进的供应商管理库存（VMI）管理模式，通过实施VMI降低企业的运营成本，提高企业的经营效益与效率。本土零售企业在借鉴外国的先进经验的基础上，结合实际情况来发展供应商管理库存，从而促进了我国零售企业快速发展，提高了市场竞争力。     

基于提前期的通用件库存模型研究

通用件正作为企业在市场上提供更高的产品多样化,而在企业内部保持零部件低多样化的优化技术而被广泛研究和应用。本文在考虑提前期影响的前提下,建立无通用件和有通用件的库存模型,并以风神汽车有限公司有关数据进行案例研究分析,通过数据分析揭示通用件应用的一些管理启示,并修正了一些理论界的原有观点。     

Models and Methods to Support a New Type of Inventory Performance Measure: The ESWSO

When analyzing a reorder point, order quantity (r, Q) inventory systems, one important question that often gets very little, if any, attention is: When a stockout occurs, how large is it? This paper is directed at researchers and practicing inventory planners with two objectives. First, we provide several models and algorithms to compute the Expected Shortages When a Stockout Occurs (ESWSO) for a variety of stochastic environments. We show that when ESWSO, is used in conjunction with the traditional fill rate measures it greatly enhances a planners ability to plan for shortages. Second, we develop two cost‐minimizing inventory models—one addressing the backorder and the other the shortage scenario—to show how the ESWSO can be seamlessly integrated into an inventory‐cost framework to specify lot sizes and safety stocks.     

The Impact of Imperfect Processes on Production Run Times

This paper investigates the interaction between the economics of production and imperfections in the production process. Specifically, this paper is the first to devise a model in an attempt to provide managers with guidelines to choose the appropriate production run times to buffer against both the production of defective items and stoppages occurring due to machine breakdowns. In addition to providing several structural properties of the model, we show that a manager will always incur a cost penalty when (s)he uses the results of two oft‐cited models‐the EMQ (Economic Order/Manufacturing Quantity) and the NR‐E (No‐Resumption, Exponential machine breakdown)‐to determine production run times.     

Some Analytical Results for a Two-Product Newsboy Problem

A recent Decision Sciences paper considered maximizing the probability of achieving a profit target in a two-product newsboy problem. Numerical solutions to this problem revealed some intriguing properties, but the authors were unable to analytically explain many of their results. This paper presents an analytical solution procedure to this problem for the case of uniformly distributed demands. The analytical structure reveals more intriguing properties and these properties are proven and explained.     

Optimal Purchase and Transportation Cost Lot Sizing for a Single Item

A review of the literature indicates that the traditional approach for evaluating quantity discount offerings for purchased items has not adequately considered the effect that transportation costs may have on the optimal order quantity; despite the general fact that purchased materials must bear transportation charges. The transportation cost structure for less-than-truckload (LTL) shipments reflects sizable reductions in freight rates when the shipment size exceeds one of the nominal rate breakpoints. However, the shipper must also be aware of the opportunity to reduce total freight costs by artificially inflating the actual shipping weight to the next rate breakpoint, in order that a lower marginal tariff is achieved for the entire shipment. Such over-declared shipments result in an effective freight rate schedule that is characterized by constant fixed charge segments in addition to the nominal marginal rates. Over-declared shipments are economical when the shipment volume is less than the rate breakpoint, but greater than a cost indifference point between the two adjacent marginal rates. This paper presents a simple analytical procedure for finding the order quantity that minimizes total purchase costs which reflect both transportation economies and quantity discounts. After first solving for the series of indifference points that apply to a particular freight rate schedule, a total purchase cost expression is presented that properly accounts for the actual transportation cost structure. The optimal purchase order quantity will be one of the four following possibilities: (1) the valid economic order quantity (EOQ), QC; (2) a purchase price breakpoint in excess of QC; (3) a transportation rate breakpoint in excess of QC; and (4) a modified EOQ which provides an over-declared shipment in excess of QC. Finally, an algorithm which systematically explores these four possibilities is presented and illustrated with a numerical example.     

On Extending Russell and Krajewski's Algorithm for Economic Purchase Order Quantities*

Russell and Krajewski presented an optimal purchase order quantity algorithm that considered the effect of the transportation rate structure for less-than-truckload (LTL) shipments. The authors applied the Russell and Krajewski algorithm to a variety of freight classes and lengths-of-haul. Anomalous cases were found in which the freight rate schedule, when used with the suggested algorithm, resulted in incorrect order size decisions. In this comment, the authors consider the impact of these anomalies on the optimal order quantity and associated total costs. A procedure is presented to adjust the Russell and Krajewski algorithm to arrive at the optimal purchase order quantity and the lowest total annual cost.     

The Value of Supplier Information to Improve Management of a Retailer's Inventory

The distribution of lead time demand is essential for determining reorder points in inventory systems. Usually, the distribution of lead time demand is approximated directly. However, in some cases it may be worthwhile to take the demand per unit time and lead time into account, particularly when specific information is available. This paper deals with the situation where a supplier, who produces on order in fixed production cycles, provides information on the status of the coming production run. The retailer can use this information to gain insight into the lead-time process. A fixed order (s_vQ) strategy is presented, with a set of reorder points s_v depending on the time t until the first possible delivery, which is determined by the information of the supplier. A Markov model that analyzes a given (s_vQ) strategy is used to quantify the value of the information provided by the supplier. Some numerical examples show that the approach may lead to considerable cost savings compared to the traditional approach that uses only one single reorder point, based on a two-moments approximation. Using this numerical insight, the pros and cons of a more frequent exchange of information between retailers and suppliers can be balanced.