Economic lot sizing with constant capacities and concave inventory costs

This article studies the classical single‐item economic lot‐sizing problem with constant capacities, fixed‐plus‐linear order costs, and concave inventory costs, where backlogging is allowed. We propose an O(T³) optimal algorithm for the problem, which improves upon the O(T⁴) running time of the famous algorithm developed by Florian and Klein (Manage Sci18 (1971) 12–20). Instead of using the standard dynamic programming approach by predetermining the minimal cost for every possible subplan, we develop a backward dynamic programming algorithm to obtain a more efficient implementation. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Customer delays in M/M/c repair systems with spares

A service center to which customers bring failed items for repair is considered. The items are exchangeable in the sense that a customer is ready to take in return for the failed item he brought to the center any good item of the same kind. This exchangeability feature makes it possible for the service center to possess spares. The focus of the article is on customer delay in the system—the time that elapses since the arrival of a customer with a failed item and his departure with a good one—when repaired items are given to waiting customers on a FIFO basis. An algorithm is developed for the computation of the delay distribution when the item repair system operates as an M/M/c queue.     

Algorithms for the multi‐item multi‐vehicles dynamic lot sizing problem

We consider a two‐stage supply chain, in which multi‐items are shipped from a manufacturing facility or a central warehouse to a downstream retailer that faces deterministic external demand for each of the items over a finite planning horizon. The items are shipped through identical capacitated vehicles, each incurring a fixed cost per trip. In addition, there exist item‐dependent variable shipping costs and inventory holding costs at the retailer for items stored at the end of the period; these costs are constant over time. The sum of all costs must be minimized while satisfying the external demand without backlogging. In this paper we develop a search algorithm to solve the problem optimally. Our search algorithm, although exponential in the worst case, is very efficient empirically due to new properties of the optimal solution that we found, which allow us to restrict the number of solutions examined. Second, we perform a computational study that compares the empirical running time of our search methods to other available exact solution methods to the problem. Finally, we characterize the conditions under which each of the solution methods is likely to be faster than the others and suggest efficient heuristic solutions that we recommend using when the problem is large in all dimensions. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006.     

On the effectiveness of top‐down strategy for forecasting autoregressive demands

We investigate the relative effectiveness of top‐down versus bottom‐up strategies for forecasting the demand of an item that belongs to a product family. The demand for each item in the family is assumed to follow a first‐order univariate autoregressive process. Under the top‐down strategy, the aggregate demand is forecasted by using the historical data of the family demand. The demand forecast for the items is then derived by proportional allocation of the aggregate forecast. Under the bottom‐up strategy, the demand forecast for each item is directly obtained by using the historical demand data of the particular item. In both strategies, the forecasting technique used is exponential smoothing. We analytically evaluate the condition under which one forecasting strategy is preferred over the other when the lag‐1 autocorrelation of the demand time series for all the items is identical. We show that when the lag‐1 autocorrelation is smaller than or equal to 1/3, the maximum difference in the performance of the two forecasting strategies is only 1%. However, if the lag‐1 autocorrelation of the demand for at least one of the items is greater than 1/3, then the bottom‐up strategy consistently outperforms the top‐down strategy, irrespective of the items' proportion in the family and the coefficient of correlation between the item demands. A simulation study reveals that the analytical findings hold even when the lag‐1 autocorrelation of the demand processes is not identical. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007.     

A three-echelon,multi-item model for recoverable items

The main objective of this paper is to develop a mathematical model for a particular type of three-echelon inventory system. The proposed model is being used by the Air Force to evaluate inventory investment requirements for alternative logistic structures. The system we will model consists of a group of locations, called bases, and a central depot. The items of concern in our analysis are called recoverable items, that is, items that can be repaired when they fail. Furthermore, each item has a modular or hierarchical design. Briefly, the model is used to determine the stock levels at each location for each item so as to achieve optimum inventory-system performance for a given level of investment. An algorithm for the computation of stock levels for each item and location is developed and illustrated. Some of the ways the model can be used are illustrated with Air Force data.     

Locational tying of complementary retail items

We study a selling practice that we refer to as locational tying (LT), which seems to be gaining wide popularity among retailers. Under this strategy, a retailer “locationally ties” two complementary items that we denote by “primary” and “secondary.” The retailer sells the primary item in an appropriate “department” of his or her store. To stimulate demand, the secondary item is offered in the primary item's department, where it is displayed in very close proximity to the primary item. We consider two variations of LT: In the multilocation tying strategy (LT‐M), the secondary item is offered in its appropriate department in addition to the primary item's department, whereas in the single‐location tying strategy (LT‐S), it is offered only in the primary item's location. We compare these LT strategies to the traditional independent components (IC) strategy, in which the two items are sold independently (each in its own department), but the pricing/inventory decisions can be centralized (IC‐C) or decentralized (IC‐D). Assuming ample inventory, we compare and provide a ranking of the optimal prices of the four strategies. The main insight from this comparison is that relative to IC‐D, LT decreases the price of the primary item and adjusts the price of the secondary item up or down depending on its popularity in the primary item's department. We also perform a comparative statics analysis on the effect of demand and cost parameters on the optimal prices of various strategies, and identify the conditions that favor one strategy over others in terms of profitability. Then we study inventory decisions in LT under exogenous pricing by developing a model that accounts for the effect of the primary item's stock‐outs on the secondary item's demand. We find that, relative to IC‐D, LT increases the inventory level of the primary item. We also link the profitability of different strategies to the trade‐off between the increase in demand volume of the secondary item as a result of LT and the potential increase in inventory costs due to decentralizing the inventory of the secondary item. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Minimum cost sampling plans using bayesian methods

This article considers a general method for acceptance/rejection decisions in lot-by-lot sampling situations. Given arbitrary cost functions for sampling, accepting, and rejecting (where the cost can depend on the quality of the item) and a prior distribution on supplier quality, formulas are derived that lead to the minimal cost single-staged inspection plan. For the Bernoulli case, where each item is classified as acceptable or defective, the formulas simplify immensely. A computer code for solving the Bernoulli case is given.     

Queueing models for spares provisioning

A population of items which break down at random times and require repair is studied (the classic “machine repair problem with spares”). It is desired to determine the number of repair channels and spares required over a multiyear planning horizon in which population size and component reliability varies, and a service level constraint is imposed. When an item fails, a spare (if available) is immediately dispatched to replace the failed item. The failed item is removed, transported to the repair depot, repaired, and then placed in the spares pool (which is constrained to be empty not more than 10% of the time) unless there is a backlog of requests for spares, in which case it is dispatched immediately. The first model considered treats removal, transportation, and repair as one service operation. The second model is a series queue which allows for the separate treatment of removal, transportation, and repair. Breakdowns are assumed Poisson and repair times exponential.     

Selecting review periods for a coordinated multi‐item inventory model with staggered deliveries

Consider an N‐item, periodic review, infinite‐horizon, undiscounted, inventory model with stochastic demands, proportional holding and shortage costs, and full backlogging. For 1 ≤ j ≤ N, orders for item j can arrive in every period, and the cost of receiving them is negligible (as in a JIT setting). Every T_j periods, one reviews the current stock level of item j and decides on deliveries for each of the next T_j periods, thus incurring an item‐by‐item fixed cost k_j. There is also a joint fixed cost whenever any item is reviewed. The problem is to find review periods T₁, T₂, …, T_N and an ordering policy satisfying the average cost criterion. The current article builds on earlier results for the single‐item case. We prove an optimal policy exists, give conditions where it has a simple form, and develop a branch and bound algorithm for its computation. We also provide two heuristic policies with O(N) computational requirements. Computational experiments indicate that the branch and bound algorithm can handle normal demand problems with N ≤ 10 and that both heuristics do well for a wide variety of problems with N ranging from 2 to 200; moreover, the performance of our heuristics seems insensitive to N. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:430–449, 2001     

Inventory rotation policies for slow moving items

In this article we present a stochastic model for determining inventory rotation policies for a retail firm which must stock many hundreds of distinctive items having uncertain heterogeneous sales patterns. The model develops explicit decision rules for determining (1) the length of time that an item should remain in inventory before the decision is made on whether or not to rotate the item out of inventory and (2) the minimum sales level necessary for retaining the item in inventory. Two inventory rotation policies are developed, the first of which maximizes cumulative expected sales over a finite planning horizon and the second of which maximizes cumulative expected profit. We also consider the statistical behavior of items having uncertain, discrete, and heterogeneous sales patterns using a two-period prediction methodology where period 1 is used to accumulate information on individual sales rates and this knowledge is then used, in a Bayesian context, to make sales predictions for period 2. This methodology assumes that over an arbitrary time interval sales for each item are Poisson with unknown but stationary mean sales rates and the mean sales rates are distributed gamma across all items. We also report the application of the model to a retail firm which stocks many hundreds of distinctive unframed poster art titles. The application provides some useful insights into the behavior of the model as well as some interesting aspects pertaining to the implementation of the results in a “real-world” situation.     

Optimal block replacement policies with multiple choice at failure

In this article we consider block replacement policies where the operating item is replaced by a new one at times kT, k = 1, 2, …, independently of its failure history. At failure the item is either replaced by a new or a used one or remains inactive until the next planned replacement. The mathematical model is defined and general analytical results are obtained. Computations are carried out for the case where the underlying life distribution is gamma or Weibull.     

Cyclical schedules for the joint replenishment problem with dynamic demands

The Joint Replenishment Problem (JRP) involves production planning for a family of items. The items have a coordinated cost structure whereby a major setup cost is incurred whenever any item in the family is produced, and an item-specific minor setup cost is incurred whenever that item is produced. This paper investigates the performance of two types of cyclical production schedules for the JRP with dynamic demands over a finite planning horizon. The cyclical schedules considered are: (1) general cyclical schedules—schedules where the number of periods between successive production runs for any item is constant over the planning horizon—and (2) power-of-two schedules—a subset of cyclical schedules for which the number of periods between successive setups must be a power of 2. The paper evaluates the additional cost incurred by requiring schedules to be cyclical, and identifies problem characteristics that have a significant effect on this additional cost. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 577–589, 1997.     

Insurance type item provisioning guidelines

Policy decisions for insurance type items, where zero or one unit is maintained at the depot, are more difficult and more critical than decisions for common supply items. This report presents results of developing initial provisioning guidelines for insurance type items. The guidelines are based on examination of lifetime costs and benefits. Costs of stocking an item as compared with not stocking are developed through a sinking fund annual payment formulation. Benefits of stocking are developed as stationary reduction in time weighted backorders experienced. A resource allocation formulation yields an optimal policy for allocating a fixed budget. The guideline is presented with refinements based on a sample of items. A figure of merit is calculated for each item, and if it is large the item is stocked while if small it is not stocked. Empirical definitions for large and small are developed based on sample data. Estimation techniques are discussed for deriving all of an item's parameters needed to compute its figure of merit. A Bayes procedure is suggested based on family group Experienced Demand Replacement Factors. This and other techniques are discussed.     

A deterministic inventory model for reparable items

A reparable inventory system has two distinct inventories within it—the inventory of items ready-for-issue and the inventory of carcasses available for repair. A reparable item is usually rebuilt upon failure, but the scrap rate in the repair process is generally positive. Consequently, new items must be procured from time to time to replace those item: which were scrapped. The ready-for-issue inventory has two input sources—procurement and repair, This paper develops a deterministic inbentory model for the reparable inventory system, and determines the optimal procurement and repair quantities.     

Multivariate age-dependent imperfect repair

In this article we consider models of systems whose components have dependent life lengths with specific multivariate distributions. Upon failure, components are repaired. Two types of repair are distinguished. After perfect repair, a unit has the same life distribution as a new item. After imperfect repair, a unit has the life distribution of an item which is of the same age but has never failed. We study a model in which the mechanism for determining the nature of the repair is age dependent.     

Economic screening procedures using a correlated variable with multidecision alternatives

Economic screening procedures using a correlated variable are developed for selecting markets in situations when there are several markets with different profit/ cost structures. It is assumed that the performance variable and the screening variable are jointly normally distributed. Profit models are constructed which involve three profit/cost components: profit from a conforming item, cost from an accepted nonconforming item, and screening inspection cost. Methods of finding the optimal screening procedures are presented and numerical examples are given.     

Multiple subset sum with inclusive assignment set restrictions

In a traditional multiple subset sum problem (MSSP), there is a given set of items and a given set of bins (or knapsacks) with identical capacities. The objective is to select a subset of the items and pack them into the bins such that the total weight of the selected items is maximized. However, in many applications of the MSSP, the bins have assignment restrictions. In this article, we study the subset sum problem with inclusive assignment set restrictions, in which the assignment set of one item (i.e., the set of bins that the item may be assigned to) must be either a subset or a superset of the assignment set of another item. We develop an efficient 0.6492‐approximation algorithm and test its effectiveness via computational experiments. We also develop a polynomial time approximation scheme for this problem. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Estimation for a weibull accelerated life testing model

It is sometimes reasonable to assume that the lifetime distribution of an item belongs to a certain parametric family, and that actual parameter values depend upon the testing environment of the item. In the two-parameter Weibull family setting, suppose both the shape and scale parameters are expressible as functions of the testing environment. For various models of functional dependency on environment, maximum likelihood methods are used to estimate characteristics of interest at specified environmental levels. The methodology presented handles exact, censored, and grouped data. A detailed accelerated life testing analysis of stress-rupture data for Kevlar/epoxy composites is given.     

后方油库整体生存概率分析计算

针对我军后方油库特点,探讨了油库整体生存概率计算的基本思路和方法,分析了各类分项目标生存概率的计算方法,采用层次分析对后方油库各分项目标权值进行了详细分析计算,可为后方油库伪装防护效能评估提供依据。     

一种新的对违法青少年的心理训练项目的分类模式

在美国,对违法青少年的心理训练项目(即心理治疗矫正,这里用心理训练的新概念代替心理治疗矫正更符合现代心理学的道德、尊重、人性的原则)与其违法青少年的类型和特点是紧密联系、不可截然分开的。美国对违法青少年的心理训练项目的分类方法主要有:心理评价分类法、I-level分类制度和行为分类体系等。