Evaluation of base-stock policies in multiechelon inventory systems with state-dependent demands part I: State-independent policies

This article analyzes a model of a multiechelon inventory system. The exogenous demands form Markov-modulated Poisson processes. That is, the demand rates are functions of an underlying Markov chain. Each location follows a base-stock policy which is independent of the state of the underlying Markov chain. We employ the exogenous transit mechanism introduced by Zipkin [7] and Svoronos and Zipkin [6]. The transit times between locations have phase-type distributions. An exact procedure to compute steady-state performance measures is presented. © 1992 John Wiley & Sons, Inc.     

Integrating decisions with advance supply information in an assemble-to-order system

We study a periodic-review assemble-to-order (ATO) system with multiple components and multiple products, in which the inventory replenishment for each component follows an independent base-stock policy and stochastic product demands are satisfied according to a First-Come-First-Served rule. We assume that the replenishment for various component suffers from lead time uncertainty. However, the decision maker has the so-called advance supply information (ASI) associated with the lead times and thus can take advantage of the information for system optimization. We propose a multistage stochastic integer program that incorporates ASI to address the joint optimization of inventory replenishment and component allocation. The optimal base-stock policy for the inventory replenishment is determined using the sample average approximation algorithm. Also, we provide a modified order-based component allocation (MOBCA) heuristic for the component allocation. We additionally consider a special case of the variable lead times where the resulting two-stage stochastic programming model can be characterized as a single-scenario case of the proposed multistage model. We carry out extensive computational studies to quantify the benefits of integrating ASI into joint optimization and to explore the possibility of employing the two-stage model as a relatively efficient approximation scheme for the multistage model.     

An (s,S) inventory system with rest periods to the server

We study the (s,S) inventory system in which the server takes a rest when the level of the inventory is zero. The demands are assumed to occur for one unit at a time. The interoccurrence times between successive demands, the lead times, and the rest times are assumed to follow general distributions which are mutually independent. Using renewal and convolution techniques we obtain the state transition probabilities.     

On the (S-1, S) inventory model under compound poisson demands and i.i.d. unit resupply times

We analyze an (S-1, S) inventory model with compound Poisson demands. Resupply times for individual units are independent and identically distributed. Such a model can also be characterized as an M^X/G/∞ queue. We derive expressions of performance measure such as the steady-state distribution and the expectation of the number of backlogged units. In addition, numerical examples are included to reflect the effects of i.i.d. unit resupply times. © 1996 John Wiley & Sons, Inc.     

Spares stocking policies for repairable items with dependent repair times

This paper analyzes the problem of determining desirable spares inventory levels for repairable items with dependent repair times. The problem is important for repairable products such as aircraft engines which can have very large investment in spares inventory levels. While existing models can be used to determine optimal inventory spares levels when repair times are independent, the practical considerations of limited repair shop capacity and prioritized shop dispatching rules combine to make repair times not independent of one another. In this research a simulation model of a limited capacity repair facility with prioritized scheduling is used to explore a variety of heuristic approaches to the spares stocking decision. The heuristics are also compared with use of a model requiring independent repair times (even though that assumption is not valid here). The results show that even when repair time dependencies are present, the performance of a model which assumes independent repair times is quite good.     

Minimizing the sum of weighted completion times of n-independent jobs when resource availability varies over time: Performance of a simple priority rule

In this article our objective is to evaluate the performance of a WSPT (weighted shortest processing time) rule for scheduling n independent jobs where the resources to process these jobs vary over time and a job can be processed by several processors simultaneously. This problem was raised by Baker and Nuttle [2]. A linear-programming (LP) model is formulated to obtain a lower bound on the minimum value of the weighted completion times. The purpose of the model is to provide a basis for evaluating the WSPT heuristic. 1000 experiments were performed using different resource profiles to test the performance of WSPT. Using WSPT, the weighted completion times were found to be, on the average, 0.2% away from their LP lower bounds.     

考虑需求相关的可修复系统备件配置模型

对于一个拥有多台相同设备的可修复系统来说,一种备件的需求以及其对应的备件保障方案将影响着系统的可工作设备数量,从而影响着设备其他备件的需求,故假设备件需求相互独立且与系统自身备件保障方案无关而开展备件配置研究是不合理的.在考虑备件需求相关以及备件的保障方案对备件需求的影响的前提下,利用马尔可夫理论描述了备件需求规律,针对不串件拼修和串件拼修两种情况分别给出了可用度的计算方法,并在此基础上以备件配置费用作为优化目标,以可用度作为约束构建备件优化配置模型,给出了边际分析求解模型的方法.通过案例分析,验证了模型的正确性.     

A (Q,R) inventory model with lost sales and erlang-distributed lead times

The exact expression is derived for the average stationary cost of a (Q,R) inventory system with lost sales, unit Poisson demands, Erlang-distributed lead times, fixed order cost, fixed cost per unit lost sale, linear holding cost per unit time, and a maximum of one order outstanding. Explicit expressions for the state probabilities and a fast method of calculating them are obtained for the case of Q greater than R. Exponential lead times are analyzed as a special case. A simple cyclic coordinate search procedure is used to locate the minimum cost policy. Examples of the effect of lead time variability on costs are given.     

Multi‐item capacitated lot‐sizing problems with setup times and pricing decisions

We study a multi‐item capacitated lot‐sizing problem with setup times and pricing (CLSTP) over a finite and discrete planning horizon. In this class of problems, the demand for each independent item in each time period is affected by pricing decisions. The corresponding demands are then satisfied through production in a single capacitated facility or from inventory, and the goal is to set prices and determine a production plan that maximizes total profit. In contrast with many traditional lot‐sizing problems with fixed demands, we cannot, without loss of generality, restrict ourselves to instances without initial inventories, which greatly complicates the analysis of the CLSTP. We develop two alternative Dantzig–Wolfe decomposition formulations of the problem, and propose to solve their relaxations using column generation and the overall problem using branch‐and‐price. The associated pricing problem is studied under both dynamic and static pricing strategies. Through a computational study, we analyze both the efficacy of our algorithms and the benefits of allowing item prices to vary over time. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Managing waiting times of backordered demands in single‐stage (Q,r) inventory systems

We present a service constrained (Q, r) model that minimizes expected holding and ordering costs subject to an upper bound on the expected waiting time of demands that are actually backordered. We show that, after optimizing over r, the average cost is quasiconvex in Q for logconcave continuous lead time demand distributions. For logconcave discrete lead time demand distributions we find a single‐pass efficient algorithm based on a novel search stopping criterion. The algorithm also allows for bounds on the variability of the service measure. A brief numerical study indicates how the bounds on service impact the optimal average cost and the optimal (Q, r) choice. The discrete case algorithm can be readily adapted to provide a single pass algorithm for the traditional model that bounds the expected waiting time of all demands (backordered or not). © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 557–573, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10028     

Approximation for the departure process of a queue in a network

A simple renewal process is identified to approximate the complex departure process of a queue often found in queueing network models. The arrival process to the queue is the superposition or merging of several independent component-renewal processes that are approximations of departure processes from other queues and external arrival processes; there is a single server with exponential service times, and the waiting space is infinite. The departure process of this queue is of interest because it is the arrival process to other queues in the network. The approximation proposed is a hybrid; the mean and variance of the approximating departure intervals is a weighted average of those determined by basic methods in Whitt [41] with the weighting function empirically determined using simulation. Tandem queueing systems with superposition arrival processes and exponential service times are used to evaluate the approximation. The departure process of the first queue in the tandem is approximated by a renewal process, the tandem system is replaced by two independent queues, and the second queue is solved analytically. When compared to simulation estimates, the average absolute error in hybrid approximations of the expected number in the second queue is 6%, a significant improvement over 22–41% in the basic methods.     

攻击直升机编队火力分配方式及其毁伤效果评估

从联合作战的实际需求出发,根据作战理论以及攻击直升机编队作战指挥特点,将直升机和目标抽象为系统要素及其作用对象,运用系统科学、系统结构分析、作战运筹与系统工程等理论,论证了统一、自主、混合和平行等火力分配方式下空中攻击编队毁伤效果评估模型。通过实例仿真计算和结果对比分析,得到了基于不同火力分配方式的编队毁伤效果的变化特点与规律,以及一系列具有普遍意义的、潜在的、实用的编队火力分配要求与规则。     

Compound distributions with efficient computation in inventory model applications

In an inventory model, the distribution of total units demanded can be considered as a compound distribution arising from the distributions of demand occurrence and individual demand size. Three such compound distributions are considered, where the number of demands is Poisson distributed. The demand size distribution will depend on the observed or desired variance-to-mean ratio. An approximation using the gamma distribution is given in terms of the cumulants of the compound distribution for both fixed and stochastic lead times.     

Strategic investment to reduce setup times in the economic lot scheduling problem

This article considers the Economic Lot Scheduling Problem where setup times and costs can be reduced by an initial investment that is amortized over time. The objective is to determine a multiple-item single facility cyclic schedule to minimize the long run average holding and setup costs plus the amortized investment. We develop a lower bound on the long run average inventory carrying and setup costs as a function of the setup times, and show that this lower bound is increasing concave on the setup times when the out-of-pocket setup costs are zero or proportional to the setup times. We then develop a model that may be helpful in deciding the magnitude and the distribution of a one-time investment in reducing the setup times when the investment is amortized over time. Numerical results based on randomly generated problems, and on Bomberger's ten item problem indicate that significant overall savings are possible for highly utilized facilities. Most of the savings are due to a significant reduction in the long run average holding cost. © 1995 John Wiley & Sons, Inc.     

An analysis of single item inventory systems with returns

Inventory systems with returns are systems in which there are units returned in a repairable state, as well as demands for units in a serviceable state, where the return and demand processes are independent. We begin by examining the control of a single item at a single location in which the stationary return rate is less than the stationary demand rate. This necessitates an occasional procurement of units from an outside source. We present a cost model of this system, which we assume is managed under a continuous review procurement policy, and develop a solution method for finding the policy parameter values. The key to the analysis is the use of a normally distributed random variable to approximate the steady-state distribution of net inventory. Next, we study a single item, two echelon system in which a warehouse (the upper echelon) supports N(N ? 1) retailers (the lower echelon). In this case, customers return units in a repairable state as well as demand units in a serviceable state at the retailer level only. We assume the constant system return rate is less than the constant system demand rate so that a procurement is required at certain times from an outside supplier. We develop a cost model of this two echelon system assuming that each location follows a continuous review procurement policy. We also present an algorithm for finding the policy parameter values at each location that is based on the method used to solve the single location problem.     

Production planning with resources subject to congestion

A fundamental difficulty in developing effective production planning models has been accurately reflecting the nonlinear dependency between workload and lead times. We develop a mathematical programming model for production planning in multiproduct, single stage systems that captures the nonlinear dependency between workload and lead times. We then use outer linearization of this nonlinear model to obtain a linear programming formulation and extend it to multistage systems. Extensive computational experiments validate the approach and compare its results to conventional models that assume workload‐independent planning lead times. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

基于状态的检查与修理综合决策模型

分析了单部件系统退化过程的特点,建立了基于状态的检查与修理决策模型。该模型根据系统的当前状态来决定检查与修理,通过分析计算系统在一个更新周期内平均检查次数、预防性维修及修复性故障的概率,建立维修费用与检查问隔及预防性维修阈值的关系,以平均维修费用最小为目标,优化检查间隔及预防性维修阈值。最后运用Matlab对模型进行数值计算,结果表明,模型能有效地降低维修费用。     

Analysis of the finite‐source multiclass priority queue with an unreliable server and setup time

In this article, we study a queueing system serving multiple classes of customers. Each class has a finite‐calling population. The customers are served according to the preemptive‐resume priority policy. We assume general distributions for the service times. For each priority class, we derive the steady‐state system size distributions at departure/arrival and arbitrary time epochs. We introduce the residual augmented process completion times conditioned on the number of customers in the system to obtain the system time distribution. We then extend the model by assuming that the server is subject to operation‐independent failures upon which a repair process with random duration starts immediately. We also demonstrate how setup times, which may be required before resuming interrupted service or picking up a new customer, can be incorporated in the model. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

The individual station technique for the analysis of cyclic polling systems

Polling systems are used to model a wide variety of real-world applications, for example, telecommunication and material handling systems. Consequently, there is continued interest in developing efficient algorithms to analyze the performance of polling systems. Recent interest in the optimization of these systems has brought up the need for developing very efficient techniques for analyzing their waiting times. This article presents the Individual Station technique for cyclic polling systems. The technique possesses the following features: (a) it allows the user to compute the mean waiting time at a selected station independent of the mean waiting time computations at other stations, and (b) its complexity is low and independent of the system utilization. In addition the technique provides explicit closed-form expressions for (i) the mean waiting times in a system with 3 stations, and (ii) the second moment of the waiting times in a system with 2 stations, for an exhaustive service system. © 1996 John Wiley & Sons, Inc.     

Approximation methods for the analysis of a multicomponent,multiproduct assemble‐to‐order system

In this article, we consider the performance evaluation of a multicomponent, multiproduct assemble‐to‐order (ATO) system. Each component is managed independently using a base‐stock policy at a supply facility with limited production capacity and an infinite buffer. The arrivals of demands follow a multivariate Poisson process and unfilled demands are backlogged. Because exact analysis of the proposed system is not feasible, we propose two approximation methods which provide upper and lower bounds for various performance measures such as fill rate, average waiting time, and average number of backorders of the proposed system. Our computational experiments demonstrate the effectiveness of the two approximation methods under various system settings. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011