摘要:

AbstractMultiechelon repairable‐item provisioning systems are considered under a time‐varying environment. Such conditions could arise, for example, in a military context where a shift from peacetime operation to wartime operation takes place; or, in a civilian setting where a public transit system decides to increase its hours of operation or frequency of service. Exact Markovian models, incorporating afinitepopulation of repairable components andlimitedrepair capacity (nonample service), are treated, with transient solutions obtained using the randomization technique. The exact models are compared with the approximate Dyna‐METRIC model which assumes aninfinitepopulation of components andamplerepair cap

ISSN:0028-1441    

DOI:10.1002/nav.3800310302

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY

摘要:

AbstractThe fundamental stochastic duel considers two opponents who fire at each other at either random continuous or fixed‐time intervals with a constant hit probability on each round fired. Each starts with an unloaded weapon, unlimited ammunition, and unlimited time. The first to hit wins. In this article we extend the theory to the case where hit probabilities are functions of the time since the duel began. First, the marksman firing at a passive target is considered and the characteristic function of the time to a hit is developed. Then, the probability of a given side winning the duel is derived. General solutions for a wide class of hit probability functions are derived. Specific examples of both the marksman and the duel problem are give

ISSN:0028-1441    

DOI:10.1002/nav.3800310303

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY

摘要:

AbstractThe coverageCof area targets by salvos of weapons generally varies randomly, because of random target location and weapon impact point fluctuations. A third source of variation appears when, instead of an area target, a multiple‐element target is considered, consisting ofmpoint targets distributed randomly and independently of one another around the target center. A multiple‐integral expression is derived for the probabilitypkof killing exactlyktarget elements. It is shown thatpkis a linear function of the higher moments, of the orderktom, of the area coverageC.More explicit expressions are derived for the case of two weapons and for circular‐symmetric functions. Similar to well‐known results for the expectation and variance of coverage of area targets, these expressions can be evaluated by numerical quadrature. Furthermore, the coverage problem in which all underlying functions are Gaussian can be completely solved in closed form. For such a problem, with two weapons, numerical results are presented. They show that the distribution ofkcan be approximated by a binomial distribution only if the target center and weapon impact point fluctuations ar

ISSN:0028-1441    

DOI:10.1002/nav.3800310304

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY

摘要:

AbstractThis article examines a version of the machine repair problem where failures may be irreparable. Since the number of machines in the system keeps decreasing, we impose a fixed state‐dependent ordering policy of the type often encountered in inventory models. Although the system is Markovian, the number of states becomes very large. The emphasis of the article, therefore, is on deriving computationally tractable formulas for the steady‐state probabilities, the long‐run average cost per unit time, and the vector of expected discounted costs. When the state space is so large that exact computations may be infeasible, we propose approximations which are relatively quick and simple to compute and which yield very accurate results for the test problems exa

ISSN:0028-1441    

DOI:10.1002/nav.3800310305

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY

摘要:

AbstractTo locationLiwe are to allocate a “generator” andni“machines” fori= 1, …,k, wheren1…n1≧ … ≧nk. Although the generators and machines function independently of one another, a machine is operable only if it and the generator at its location are functioning. The problem we consider is that of finding the arrangement or allocation optimizing the number of operable machines. We show that if the objective is to maximize the expected number of operable machines at some future time, then it is best to allocate the best generator and then1best machines to locationL1, the second‐best generator and then2‐next‐best machines to locationL2, etc. However, this arrangement is not always stochastically optimal. For the case of two generators we give a necessary and sufficient condition that this arrangement is stochastically best, and illustrate the resul

ISSN:0028-1441    

DOI:10.1002/nav.3800310306

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY

摘要:

AbstractThis article presents a simple proof of Hu's algorithm for scheduling in minimum time a set of tasks constrained by precedence tree constraints, each task requiring a unit time to complete, and wheremprocessors are available.

ISSN:0028-1441    

DOI:10.1002/nav.3800310307

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY

摘要:

AbstractIt is proposed to describe multiple air‐to‐air combat having a moderate number of participants with the aid of a stochastic process based on end‐game duels. A simple model describing the dominant features of air combat leads to a continuous time discrete‐state Markov process. Solution of the forward Kolmogorov equations enables one to investigate the influence of initial force levels and performance parameters on the outcome probabilities of the multiple engagement. As is illustrated, such results may be useful in the decision‐making process for aircraft and weapon system development planning. Some comparisons are made with Lanchester models as well as with a semi‐M

ISSN:0028-1441    

DOI:10.1002/nav.3800310308

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY

摘要:

AbstractA set of n spare components whose life lengths are exponentially distributed with rates μ1, …,μnare available to keep a two‐component parallel system in operation. We derive the optimal order of replacement of failed components in order to maximize the system life l

ISSN:0028-1441    

DOI:10.1002/nav.3800310309

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY

摘要:

AbstractLet X denote a random vector with a spherically symmetric distribution. The density of U = X'X, called a “generalized chi‐square,” is derived for the noncentral case, when μ = E(X) ≠ 0. Explicit series representations are found in certain special cases including the “generalized spherical gamma,” the “generalized” Laplace and the Pearson type VII distributions. A simple geometrical representation of U is shown to be useful in generating random U variates. Expressions for moments and characteristic functions are also given. These densities occur in offset hitti

ISSN:0028-1441    

DOI:10.1002/nav.3800310310

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY

摘要:

AbstractThis article treats the problem of determining optimal and approximately optimal order quantities for a multiple‐item inventory system subject to a single constraint on space or budget. Although this problem can be solved by the usual method of Lagrange multipliers, we wish to consider a more efficient scheme that requires fewer computations. We provide calculations that compare and contrast four approximation techniques. In particular, we have discovered a method that yields a direct algebraic expression of the problem parameters for allocation and achieves an expected profit within 90% of the optimal in about 90% of the cases teste

ISSN:0028-1441    

DOI:10.1002/nav.3800310311

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1984

数据来源: WILEY