Relation between continuous and discrete time markovian decision problems

An associated discrete (continuous) time Markovian decision problem for any given continuous (discrete) time Markovian decision model is formulated. A relationship between the continuous and associated discrete time discounted returns is obtained. This result is used to show the existence of a deterministic stationary policy that optimizes both discounted return functions. It is also proved that the same policy optimizes the average expected return for both continuous and the associated discrete time processes. The results obtained in this paper can be used to solve the continuous time Markovian decision problem by using the discrete time algorithms or vice versa.     

Statistical decision analysis of stochastic linear programming problems

This paper presents a statistical decision analysis of a one-stage linear programming problem with deterministic constraints and stochastic criterion function. Procedures for obtaining numerical results are given which are applicable to any problem having this general form. We begin by stating the statistical decision problems to be considered, and then discuss the expected value of perfect information and the expected value of sample information. In obtaining these quantities, use is made of the distribution of the optimal value of the linear programming problem with stochastic criterion function, and so we discuss Monte Carlo and numerical integration procedures for estimating the mean of this distribution. The case in which the random criterion vector has a multivariate Normal distribution is discussed separately, and more detailed methods are offered. We discuss dual problems, including some relationships of this work with other work in probabilistic linear programming. An example is given in Appendix A showing application of the methods to a sample problem. In Appendix B we consider the accuracy of a procedure for approximating the expected value of information.     

Multiaction maintenance under markovian deterioration and incomplete state information

Much research been devoted to modeling the replacement problem under incomplete state information. Almost no work has been done on the maintenance problem under incomplete information with multiple maintenance actions that may not return the system to as good as new. We model this problem and derive structural results concerning the optimal maintenance policy. For the case where the effect of maintenance actions is state dependent, we give conditions under which the optimal policy is finitely computable. Where maintenance is state independent we show a specific structure, consisting of monotonic waiting times and constant maintenance actions, to be optimal.     

A multiserver queue with markovian arrivals and group services with thresholds

We consider a multiserver queueing system in which arrivals are governed by a Markovian arrival process. The system is attended by K identical exponential servers. Under a dynamic probabilistic service rule which depends on two threshold parameters, this model is studied as a Markov process. The steady-state probability vector is shown to be of (modified) matrix-geometric type. Efficient algorithmic procedures for the computation of the steady-state probability vector and some key performance measures of the system are developed. Some numerical examples are discussed. © 1993 John Wiley & Sons, Inc.     

Denumerable state markovian sequential control processes: On randomizations of optimal policies

We consider a denumerable state Markovian sequential control process. It is well known that when we consider the expected total discounted income as a criterion, there exists a nonrandomized stationary policy that is optimal. It is also well known that when we consider the expected average income as a criterion, an optimal nonrandomized stationary policy exists when a certain system of equations has a solution. The problem considered here is: if there exist two optimal nonrandomized stationary policies, will a randomization of these two policies be optimal? It is shown that in the discounted case the answer is always yes, but in the average income case, the answer is yes only under certain additional conditions.     

A branch and bound algorithm for allocation problems in which constraint coefficients depend upon decision variables

A branch and bound algorithm is developed for a class of allocation problems in which some constraint coefficients depend on the values of certain of the decision variables. Were it not for these dependencies, the problems could be solved by linear programming. The algorithm is developed in terms of a strategic deployment problem in which it is desired to find a least-cost transportation fleet, subject to constraints on men/materiel requirements in the event of certain hypothesized contingencies. Among the transportation vehicles available for selection are aircraft which exhibit the characteristic that the amount of goods deliverable by an aircraft on a particular route in a given time period (called aircraft productivity and measured in kilotons/aircraft/month) depends on the ratio of type 1 to type 2 aircraft used on that particular route. A model is formulated in which these relationships are first approximated by piecewise linear functions. A branch and bound algorithm for solving the resultant nonlinear problem is then presented; the algorithm solves a sequence of linear programming problems. The algorithm is illustrated by a sample problem and comments concerning its practicality are made.     

面向实体的仿真想定结构化描述方法

针对作战过程仿真模型的初始化需求,分析了仿真想定的具体内容,提出了面向实体的仿真想定结构化描述方法,即以实体的抽象和描述为核心,从实体、任务、结构、状态、行动、指挥决策6个方面来进行仿真想定内容的结构化描述,并利用XML语言在描述结构化、半结构化数据方面的突出优势,提出了基于XML的仿真想定数据存储模型,为进行作战想定的结构化和定量化提供了可行的方法,满足了由作战想定生成模型输入条件的要求。     

舰艇主机评估体系中的权重的群决策

根据舰艇主机评估体系中确定权系数的要求,提出了利用基于层次分析法的群决策方法,得到各指标的权系数.并通过调查、程序计算,定量地给出了舰艇主机评估指标体系中各指标的权重.     

Solving generalized transportation problems via pure transportation problems

This paper investigates certain issues of coefficient sensitivity in generalized network problems when such problems have small gains or losses. In these instances, it might be computationally advantageous to temporarily ignore these gains or losses and solve the resultant “pure” network problem. Subsequently, the optimal solution to the pure problem could be used to derive the optimal solution to the original generalized network problem. In this paper we focus on generalized transportation problems and consider the following question: Given an optimal solution to the pure transportation problem, under what conditions will the optimal solution to the original generalized transportation problem have the same basic variables? We study special cases of the generalized transportation problem in terms of convexity with respect to a basis. For the special case when all gains or losses are identical, we show that convexity holds. We use this result to determine conditions on the magnitude of the gains or losses such that the optimal solutions to both the generalized transportation problem and the associated pure transportation problem have the same basic variables. For more general cases, we establish sufficient conditions for convexity and feasibility. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 666–685, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10034     

Production-location problems

The joint problems of determining the optimal plant location and optimal input mix and plant size are addressed. The interrelationship between input substitutability and plant location is stressed. Conditions under which the location problem can be separated from the determination of the optimal input mix are developed for a number of problem variations. The stability of the optimal location in the face of changes in problem parameters is also discussed. It is demonstrated that consideration of input substitutability often makes the resulting problem no more difficult to solve than problem formulations in which the inherent input substitutability is ignored.     

Transportation problems with some xij negative and transshipment problems

The general solution process of the Hitchcock transportation problem resulting from the application of the method of reduced matrices may give solutions with some negative x_ij values. This paper is devoted to a review of the reduced matrices method, an examination of suitable interpretation of sets of x_ij which include some negative values, and ways of interpreting these values in useful modifications of the Hitchcock problem. Such modifications include a) the reshipment problem, b) the overshipment problem, and c) the transshipment problem. Techniques are developed for determining and eliminating c_ij which are not optimal. These techniques and results are useful in solving the problems indicated above. The natural applicability of the simple and general method of reduced matrices is emphasized.     

An analytic basis for decision support in negotiations

Mediators increase the effectiveness of negotiation processes. The art of mediation includes interpersonal skills, ability to convince, and proficiency in argumentation. The science of mediation represents an analytical approach to problem solving, a systematic analysis of the process, of players' positions, and of their goals, aspirations, and concessions. Analytical tools for mediation can be used by mediators, but these tools can also support negotiators in their analysis, verification of their positions, and choices. The knowledge of effective and safe alternatives, of sets of compromises, and the knowledge of the possible outcomes of concessions may be used to develop an effective strategy and to increase a negotiator's bargaining power. Models to analyze alternatives, to verify concessions made by the opponents, to determine effective alternatives, and to search for solutions that yield mutual gains, to aggregate opponents' proposals, to look for coalition members, and to simulate some of the actions of a mediator are discussed in the article.     

The initial provisioning decision for insurance type items

Initial provisioning decisions (inventory stocking requirements) for low demand items often have to be made without much knowledge of what future demand rates will be. When the nature of an item is such that little demand for it is expected, the problem of whether to stock initially or risk not stocking the item is most critical. This report discusses this problem and presents decision procedures which can be used to handle this aspect of initial provisioning. The procedures relate an item's provisioning desirability to its provisioning characteristics, such as expected cost, expected resupply time, current information on its likely demand rate, and to an overall operating policy or criterion. The criterion function measures the total system degredation as a function of the events of having items out of stock when demand occurs. Several different policy functions are discussed and the provisioning decision rules which apply to each are presented. Demand rate information is handled through a Bayesian type approach. The decision rules presented in this report can be utilized to either determine stocking requirements within a budgetary constraint, or determine the relative stocking desirability on an item-by-item basis.     

Approximate decision rules for continuous review inventory systems

Constrained multi-item inventory models have long presented signifcant computational problems. This article presents a general algorithm to obtain simultaneous solutions for order quantities and safety stocks for each line item in an inventory, while satisfying constraints on average inventory investment and reordering workload. Computational experience is presented that demonstrates the algorithm's efficiency in handling large-scale applications. Decision rules for several customer service objectives are developed, with a discussion of the characteristics of the inventory systems in which each objective would be most appropriate. The decision rules are approximations, based on the assumptions commonly used in practice.     

C4KISR系统决策专家系统

随着人工智能技术的不断发展,为了将基于人工智能的专家系统引入到C4KISR系统,增强系统的决策支持能力,对C4KISR系统决策专家系统进行了研究,并建立了专家系统决策模型.专家系统的建立将提高C4KISR系统的作战能力.     

Suboptimal decision rule for attacking targets of opportunity

A player having only a definite number of weapons is hunting targets. His total hunting time is also limited. Targets of opportunity with various values arrive at random, and as soon as a target arrives the player observes the target value and decides whether or not to shoot it down. The issue is what the decision rule is which guarantees him a maximum expected gain during the hunting time. Poisson arrival of the targets, uniform distribution of the target value, and the shoot-look-shoot scheme qre assumed. A decision rule is derived which is not optimal but has a very simple form and gives almost as good value as the optimal decision rule does.     

基于专家系统的消磁电流决策

分析了建立消磁电流决策的专家系统的可行性 ,从基本概念和实际应用等方面介绍了基于专家系统的消磁电流决策的状态描述、数据库的建立以及推理机的确立等