On computing the expected discounted return in a markov chain

The discounted return associated with a finite state Markov chain X₁, X₂… is given by g(X₁)+ αg(X₂) + α²g(X₃) + …, where g(x) represents the immediate return from state x. Knowing the transition matrix of the chain, it is desired to compute the expected discounted return (present worth) given the initial state. This type of problem arises in inventory theory, dynamic programming, and elsewhere. Usually the solution is approximated by solving the system of linear equations characterizing the expected return. These equations can be solved by a variety of well-known methods. This paper describes yet another method, which is a slight modification of the classical iterative scheme. The method gives sequences of upper and lower bounds which converge mono-tonely to the solution. Hence, the method is relatively free of error control problems. Computational experiments were conducted which suggest that for problems with a large number of states, the method is quite efficient. The amount of computation required to obtain the solution increases much slower with an increase in the number of states, N, than with the conventional methods. In fact, computational time is more nearly proportional to N², than to N³.     

A perfect lot-tree procedure for the discounted dynamic lot-size problem with speculation

This article considers the dynamic lot-size problem under discounting, allowing a speculative motive for holding inventory. A forward procedure is developed that determines the first lot-size decision in a rolling horizon environment by using forecast data of the minimum possible number of future periods. © 1992 John Wiley & Sons, Inc.     

TTT transforms and age replacements with discounted costs

The ordinary age replacement problem consists of finding an optimal age at which a unit, needed in a continuous production process, should be replaced in order to minimize the average long-run cost per unit time. Bergman introduced a graphical procedure based on the total-time-on-test (TTT) concept for the analysis of the age replacement problem. In this article, that idea is generalized to the situation of discounted costs. We also study a more general age replacement problem in which we have a form of imperfect repair.     

Inference on a future reliability parameter with the weibull process model

An inferential procedure is presented which provides confidence intervals for a future reliability parameter when reliability growth testing is only partially completed. Hypothesis tests based on this method are uniformly most powerful unbiased. These results are applicable if (1) the system failure rate can be modeled as the intensity function of a Weibull process and (2) efforts to improve reliability are assumed to continue at a steady rate throughout the intervening period of testing. The usefulness of this methodology is illustrated by evaluating the risk of not reaching some future reliability milestone. If such risk is unacceptably high, program management may have time to identify problem areas and take corrective action before testing has ended. As a consequence, a more reliable system may be developed without incurring overruns in the scheduling or cost of the development program.     

A methodology for estimating expected usage of repair parts with application to parts with no usage history

In this paper a model is presented which focuses on the difficult problem of predicting demands for items with extremely low usage rates. These form the bulk of repair parts in military systems. The basic notion underlying the model is the pooling of usage data for common design items with movement for the purpose of estimating usage rates for similar items which have shown no movement. A unique feature of the model is that it also makes possible the estimation of usage rates for items newly introduced into a system for which no previous usage history is available.     

A single-machine replacement model with learning

The replacement or upgrade of productive resources over time is an important decision for a manufacturing organization. The type of technology used in the productive resources determines how effectively the manufacturing operations can support the product and marketing strategy of the organization. Increasing operating costs (cost of maintenance, labor, and depreciation) over time force manufacturing organizations to periodically consider replacement or upgrade of their existing productive resources. We assume that there is a setup cost associated with the replacement of a machine, and that the setup cost is a nonincreasing function of the number of replacements made so far due to learning in setups. The operating cost of a newer machine is assumed to be lower than the operating cost of an older machine in any given period, except perhaps in the first period of operation of the new machine when the cost could be unusually high due to higher initial depreciation. A forward dynamic programming algorithm is developed which can be used to solve finite-horizon problems. We develop procedures to find decision and forecast horizons such that choices made during the decision horizon based only on information over the forecast horizon are also optimal for any longer horizon problem. Thus, we are able to obtain optimal results for what is effectively an infinite-horizon problem while only requiring data over a finite period of time. We present a numerical example to illustrate the decision/forecast horizon procedure, as well as a study of the effects of considering learning in making a series of machine replacement decisions. © 1993 John Wiley & Sons. Inc.     

A network reformulation of an electric utility expansion planning model

We reformulate a multiperiod capacity expansion model of electric utilities as a network model. We show how to reconstruct the dual solution of the original mathematical program from the network model solution. To formulate the network model, we use information about the properties of the optimal solution of the mathematical program to reduce the number of constraints. The remaining constraints are then readily converted into network constraints. © 1993 John Wiley & Sons. Inc.     

A multiechelon inventory model with multiple failures

This article presents a recoverable spares model for performance evaluation in a multiechelon inventory environment. This model explicitly incorporates the phenomenon known as multiple failures, in which more than one part can require replacement or repair when an end-item reaches a maintenance base. The model is shown to be computationally intractable, and an approximation scheme is presented to estimate system performance. © 1993 John Wiley & Sons, Inc.     

A replacement model with overhauls and repairs

This article generalizes the classical periodical replacement model with minimal repair by considering the effect of the overhaul, which is assumed to be able to rejuvenate the system. The generalization is based on the notion of the virtual age of a system introduced by Kijima, Morimura, and Suzuki [“Periodical Replacement Problem without Assuming Minimal Repair,” European Journal of Operational Research, 37 , 194–203 (1988)]. © 1995 John Wiley & Sons, Inc.     

A reliability model with states of partial operation

This article generalizes the classical dichotomic reliability model to include states of partial operation. The generalized model can be considered as a special case of a general jump process. Both continuous and discrete state spaces are included. The relationship to cumulative damage shock models is discussed. Properties of the model are investigated and these are illustrated via examples. The equivalence of three forms of component independence is proved, but this equivalence does not generalize to the property of zero covariance. Alternative forms of series and parallel connections and the effect of component replacement are discussed.     

A two-machine repair model with variable repair rate

A two-unit cold standby production system with one repairman is considered. After inspection of a failed unit the repairman chooses either a slow or a fast repair rate to carry out the corresponding amount of work. At system breakdown the repairman has an additional opportunity to switch to the fast rate. If there are no fixed costs associated with system breakdowns, then the policy which minimizes longrun average costs is shown to be a two-dimensional control limit rule. If fixed costs are incurred every time the system breaks down, then the optimal policy is not necessarily of control limit type. This is illustrated by a counterexample. Furthermore, we present several performance measures for this maintenance system controlled by a two-dimensional control limit rule. © 1993 John Wiley & Sons, Inc.     

A multi-item EOQ model with inventory cycle balancing

This article concerns a multi-item, infinite-horizon, lot-sizing problem, where the objective is to minimize a total cost function made up of reordering cost, holding cost, and a cost determined by peak inventory levels. By spreading inventory replenishments over the reordering cycle, the peak inventory level can be reduced. The model permits the derivation of simultaneously optimal solutions for the length of the cycle and the individual item replenishment times within the cycle. An alternative formulation, in which total storage capacity is modeled as a constraint, is also solved.     

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.     

A general age replacement model with minimal repair

A general age replacement is introduced which incorporates minimal repair, planned and unplanned replacements, and costs which depend on time. Finite and infinite horizon results are obtained. Various special cases are considered. Furthermore, a shock model with general cost structure is considered.     

The United States and Latin America: Shaping an elusive future

This article presents a regional overview of US‐Latin American security relations, focusing on those countries where US national security interests are most likely to be endangered over the next two decades. The author examines the current US strategy of ‘shaping’ the Latin security environment, with a view to assessing the strength and weaknesses of this approach. The article presents some policy recommendations, including the recommendation that the US do more to redress the historical imbalance in Latin American civil‐military relations by strengthening civilian institutions. It also argues that at the regional level a major effort be made to recapture momentum toward the creation of a Free Trade Association of the Americas.     

A cumulative damage shock model with imperfect preventive maintenance

In this article we consider a cumulative damage shock model under a periodic preventive maintenance (PM) policy. The PM is imperfect in the sense that each PM reduces the damage level by 100(1 – b)%, 0 < b < 1. A system suffers damage due to shocks and fails when the damage level exceeds some threshold. We derive a sufficient condition for the time to failure to have an IFR distribution. We also discuss the associated problem of finding the number of PM's that minimizes the expected cost rate.     

具有模糊偏好认知的两层递阶超对策模型

针对一类具有模糊结局偏好认知的两层冲突环境,建立了一个两层模糊递阶超对策模型。在决策者给定的置信水平λ下,基于模糊数截集以及模糊数之间的相对距离测度,将模糊递阶超对策模型清晰化,进而给出了模型λ递阶超纳什均衡的定义和具体的求解方法。最后,通过实例验证了该模型方法的有效性。     

基于Agent的"信息路由"通信模型

针对一种基于Agent的信息收集系统,提出了一个具备"信息路由"模块的通信模型.依据该通信模型,定义了一种用作消息传送的通信语言,并给出了该语言XML的描述.     

Optimal lot sizing and inspection policy for an EMQ model with imperfect inspections

An EMQ model with a production process subject to random deterioration is considered. The process can be monitored through inspections, and both the lot size and the inspection schedule are subject to control. The “in-control” periods are assumed to be generally distributed and the inspections are imperfect, i.e., the true state of the process is not necessarily revealed through an inspection. The objective is the joint determination of the lot size and the inspection schedule, minimizing the long-run expected average cost per unit time. Both discrete and continuous cases are examined. A dynamic programming formulation is considered in the case where the inspections can be performed only at discrete times, which is typical for the parts industry. In the continuous case, an optimum inspection schedule is obtained for a given production time and given number of inspections by solving a nonlinear programming problem. A two-dimensional search procedure can be used to find the optimal policy. In the exponential case, the structure of the optimal inspection policy is established using Lagrange's method, and it is shown that the optimal inspection times can be found by solving a nonlinear equation. Numerical studies indicate that the optimal policy performs much better than the optimal policy with periodic inspections considered previously in the literature. The case of perfect inspections is discussed, and an extension of the results obtained previously in the literature is presented. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 165–186, 1998