A balancing problem for mixed model assembly lines with a paced moving conveyor

We state a balancing problem for mixed model assembly lines with a paced moving conveyor as: Given the daily assembling sequence of the models, the tasks of each model, the precedence relations among the tasks, and the operations parameters of the assembly line, assign the tasks of the models to the workstations so as to minimize the total overload time. Several characteristics of the problem are investigated. A line‐balancing heuristic is proposed based on a lower bound of the total overload time. A practical procedure is provided for estimating the deviation of any given line‐balance solution from the theoretical optimum. Numerical examples are given to illustrate the methodology. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Stochastic allocation of inspection capacity to competitive processes

Optimal allocation and control of limited inspection capacity for multiple production processes are considered. The production processes, which operate independently but share inspection capacity, are subject to random failures and are partially observed through inspection. This study proposes an approach of stochastic allocation, using a Markov decision process, to minimize expected total discounted cost over an infinite time horizon. Both an optimal model and a disaggregate approximation model are introduced. The study provides some structural results and establishes that the control policy is of a threshold type. Numerical experiments demonstrate a significantly decreased amount of computational time required for the disaggregate approach when compared to the optimal solution, while generating very good control policies. © 2002 John Wiley & Sons, Inc. Naval Research Logistics, 49: 78–94, 2002; DOI 10.1002/nav.1049     

动态武器目标分配问题的马尔可夫性

动态武器目标分配(weapon target assignment,WTA)问题是军事运筹学研究的重要理论问题,也是作战指挥决策中迫切需要解决的现实问题。在对动态WTA问题进行描述分析的基础上,运用随机过程理论证明了动态WTA过程的马尔可夫性;给出了该马尔可夫决策过程的状态转移概率的解析表达式,并对其状态特点进行了简要分析。研究结果可以为动态WTA及相关问题的研究提供理论和方法依据。     

A Lanchester-type model of combat with stochastic rates

The effects of environmental stochasticity in a Lanchester-type model of combat are investigated. The methodology is based on a study of stochastic differential equations with random parameters characterized by dichotomous Markov processes. Exact expressions for the Laplace transforms of the time evolution of the first- and second-order moments of the system are obtained. A special case when the fluctuations in the parameters occur with great rapidity in comparison with the natural time scale of the system is also analyzed. The stochastic stability in the mean-square sense is discussed by using the Routh–Hurwitz criterion and it is found that the stochastic perturbations tend to destabilize the system.     

Predictability of operational processes over finite horizon

Operational processes are usually studied in terms of stochastic processes. The main information measure used for predictability of stochastic processes is the entropy rate, which is asymptotic conditional entropy, thus not suitable for application over a finite horizon. We use the conditional entropy to study the predictability of stochastic processes over the finite horizon. It is well‐known that the conditional entropies of stationary processes decrease as the processes evolve, implying that, on average, their pasts become more informative about prediction of their future outcomes. Some important operational processes such as martingale, models for maintenance policies, nonhomogeneous Poisson, and mixed Poisson processes are nonstationary. We show that as a nonstationary process evolves, it may provide more information or less information about the future state of the system. We develop results for comparing the predictability of stochastic processes. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Performance evaluation of a production/inventory system with periodic review and endogenous lead times

This paper considers a discrete time, single item production/inventory system with random period demands. Inventory levels are reviewed periodically and managed using a base‐stock policy. Replenishment orders are placed with the production system which is capacitated in the sense that there is a single server that sequentially processes the items one at a time with stochastic unit processing times. In this setting the variability in demand determines the arrival pattern of production orders at the queue, influencing supply lead times. In addition, the inventory behavior is impacted by the correlation between demand and lead times: a large demand size corresponds to a long lead time, depleting the inventory longer. The contribution of this paper is threefold. First, we present an exact procedure based on matrix‐analytic techniques for computing the replenishment lead time distribution given an arbitrary discrete demand distribution. Second, we numerically characterize the distribution of inventory levels, and various other performance measures such as fill rate, base‐stock levels and optimal safety stocks, taking the correlation between demand and lead times into account. Third, we develop an algorithm to fit the first two moments of the demand and service time distribution to a discrete phase‐type distribution with a minimal number of phases. This provides a practical tool to analyze the effect of demand variability, as measured by its coefficient of variation, on system performance. We also show that our model is more appropriate than some existing models of capacitated systems in discrete time. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

动态贝叶斯网络的无人机炮火校射

动态贝叶斯网络(Dynamic Bayesian Networks-DBNs),是对具有随机过程性质的不确定性问题进行建模和处理的一个有力工具.提出将隐马尔可夫模型(Hidden Markov Models-HMMs)图形模式与贝叶斯网络结合起来构成DBN,将其用于无人机照相侦察情报的推理分析,决定炮火优先打击区域.首先建立动态贝叶斯网络的战场态势变化模型,而后应用HMM的推理算法获得当前隐含序列最优估计,且可预测出未来战场态势.最后应用模糊推理获得优先打击的区域号.仿真结果表明了模型的可行性.该方法有效解决了贝叶斯网络对于瞬间变化战场态势推理的不足的缺陷,为炮兵指挥员更好地运用火力,分出主次奠定了基础.     

Dynamic order acceptance and capacity planning on a single bottleneck resource

We present a tactical decision model for order acceptance and capacity planning that maximizes the expected profits from accepted orders, allowing for aggregate regular as well as nonregular capacity. The stream of incoming order arrivals is the main source of uncertainty in dynamic order acceptance and the company only has forecasts of the main properties of the future incoming projects. Project proposals arrive sequentially with deterministic interarrival times and a decision on order acceptance and capacity planning needs to be made each time a proposal arrives and its project characteristics are revealed. We apply stochastic dynamic programming to determine a profit threshold for the accept/reject decision as well as to deterministically allocate a single bottleneck resource to the accepted projects, both with an eye on maximizing the expected revenues within the problem horizon. We derive a number of managerial insights based on an analysis of the influence of project and environmental characteristics on optimal project selection and aggregate capacity usage. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Limiting behavior of the stochastic sequential assignment problem

The stochastic sequential assignment problem (SSAP) considers how to allocate available distinct workers to sequentially arriving tasks with stochastic parameters such that the expected total reward obtained from the sequential assignments is maximized. Implementing the optimal assignment policy for the SSAP involves calculating a new set of breakpoints upon the arrival of each task (i.e., for every time period), which is impractical for large‐scale problems. This article studies two problems that are concerned with obtaining stationary policies, which achieve the optimal expected reward per task as the number of tasks approaches infinity. The first problem considers independent and identically distributed (IID) tasks with a known distribution function, whereas in the second problem tasks are derived from r different unobservable distributions governed by an ergodic Markov chain. The convergence rate of the expected reward per task to the optimal value is also obtained for both problems. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

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.     

Inspection policies and processes for deteriorating systems subject to catastrophic failure

Deteriorating reliability systems that are subject to catastrophic failure are analyzed in order to propose and evaluate some deterministic and stochastic inspection models. The underlying deterioration process is assumed to be an increasing Markov renewal process where the true state of the system can not be determined by simple observations. Instead, some tests can be done in order to detect if the system has positive deterioration or not. The results of the tests, however, are not perfect so that the probability of true and false detections depend on the unobserved state of the system. The system is inspected either deterministically at prespecified points in time, or stochastically at random points in time. Both types of models are considered to present explicit computational expressions for various performance measures like the expected number of inspections with different results and the probability of detection. Some practical applications of the results are also included.     

Monotone optimal preventive maintenance policies for stochastically failing equipment

This paper examines various models for maintenance of a machine operating subject to stochastic deterioration. Three alternative models are presented for the deterioration process. For each model, in addition to the replacement decision, the option exists of performing preventive maintenance. The effect of this maintenance is to “slow” the deterioration process. With an appropriate reward structure imposed on the processes, the models are formulated as continuous time Markov decision processes. the optimality criterion being the maximization of expected discounted reward earned over an infinite time horizon. For each model conditions are presented under which the optimal maintenance policy exhibits the following monotonic structure. First, there exists a control limit rule for replacement. That is, there exists a number i* such that if the state of machine deterioration exceeds i* the optimal policy replaces the machine by a new machine. Secondly, prior to replacement the optimal level of preventive maintenance is a nonincreasing function of the state of machine deterioration. The conditions which guarantee this result have a cost/benefit interpretation.     

A continuous review inventory model with compound poisson demand process and stochastic lead time

Using Markov renewal theory, we derive analytic expressions for the expected average cost associated with (s, S) policies for a continuous review inventory model with a compound Poisson demand process and stochastic lead time, under the (restrictive) assumption that only one order can be outstanding.     

Structured maintenance policies on interior sample paths

We examine the problem of adaptively scheduling perfect observations and preventive replacements for a multi‐state, Markovian deterioration system with silent failures such that total expected discounted cost is minimized. We model this problem as a partially observed Markov decision process and show that the structural properties of the optimal policy hold for certain non‐extreme sample paths. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Heuristic solution to a discrete collection model

A discrete time Collection Model is formulated, involving the completion of a touring objective on a network with stochastic node states. Heuristic touring strategies are constructed, there being as yet inadequate analytic results for its optimal solution. Effectiveness of the heuristics is assessed by comparing expected tour times under the heuristics with expected tour times given perfect information. A branch and bound algorithm is presented for computing the perfect information tour times.     

The stochastic U‐line balancing problem

A U‐line arranges tasks around a U‐shaped production line and organizes them into stations that can cross from one side of the line to the other. In addition to improving visibility and communication between operators on the line, which facilitates problem‐solving and quality improvement, U‐lines can reduce the total number of operators required on the line and make rebalancing the line easier compared to the traditional, straight production line. This paper studies the (type 1) U‐line balancing problem when task completion times are stochastic. Stochastic completion times occur when differences between operators cause completion times to vary somewhat and when machine processing times vary. A recursive algorithm is presented for finding the optimal solution when completion times have any distribution function. An equivalent shortest path network is also presented. An improvement for the special case of normally distributed task completion times is given. A computational study to determine the characteristics of instances that can be solved by the algorithms shows that they are able to solve instances of practical size (like the 114 Japanese and U.S. U‐lines studied in a literature review paper). © 2002 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

State information lag markov decision process with control limit rule

In the framework of a discrete Markov decision process with state information lag, this article suggests a way for selecting an optimal policy using the control limit rule. The properties sufficient for an optimal decision rule to be contained in the class of control limit rules are also studied. The degradation in expected reward from that of the perfect information process provides a measure of the potential value of improving the information system.     

On the availability of R out of N repairable systems

An R out of N repairable system consisting of N components and operates if at least R components are functioning. Repairable means that failed components are repaired, and upon repair completion they are as good as new. We derive formulas for the expected up‐time, expected down‐time, and the availability of the system, using Markov renewal processes. We assume that either the repair times of the components are generally distributed and the components' lifetimes are exponential or vice versa. The analysis is done for systems with either cold or warm stand‐by. Numerical examples are given for several life time and repair time distributions. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 483–498, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10025     

Evaluation of base-stock policies in multiechelon inventory systems with compound-poisson demands

This article analyzes a model of a multiechelon inventory system: The exogenous demands form independent compound-Poisson processes. Each location follows a base-stock policy. The transit times between locations may be stochastic. Instead of assuming independent transit times, we follow an approach closer to the standard treatment of single-location models. We develop procedures to compute steady-state performance measures, including average backorders and average inventories. The model and the analysis generalize those of Svoronos and Zipkin, who treat the case of pure Poisson demands.     

Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty

We propose a novel simulation‐based approach for solving two‐stage stochastic programs with recourse and endogenous (decision dependent) uncertainty. The proposed augmented nested sampling approach recasts the stochastic optimization problem as a simulation problem by treating the decision variables as random. The optimal decision is obtained via the mode of the augmented probability model. We illustrate our methodology on a newsvendor problem with stock‐dependent uncertain demand both in single and multi‐item (news‐stand) cases. We provide performance comparisons with Markov chain Monte Carlo and traditional Monte Carlo simulation‐based optimization schemes. Finally, we conclude with directions for future research.