摘要:

AbstractThis paper investigates the effect on the optimum solution of a (capacitated) transportation problem when the data of the problem (the rim conditions‐i. e., the warehouse supplies and market demands‐the per unit transportation costs and the upper bounds) are continuously varied as a (linear) function of a single parameter. An operator theory is developed and algorithms provided for applying rim and cost operators that effect the transformation of optimum solution associated with changes in rim conditions and unit costs. Bound operators that effect changes in upper bounds are shown to be equivalent to rim operators. The discussion in this paper is limited to basis preserving operators for which the changes in the data are such that the optimum basis structures are preser

ISSN:0028-1441    

DOI:10.1002/nav.3800190202

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

年代:1972

数据来源: WILEY

摘要:

AbstractThis paper investigates the effect on the optimum solution of a (capacitated) transportation problem when the data of the problem (the rim conditions‐i. e., the warehouse supplies and market demands‐, the per unit transportation costs and the upper bounds) are continuously varied as a (linear) function of a single parameter. Operators that effect the transformation of optimum solution associated with such data changes, are shown to be a product of basis preserving operators (described in the earlier paper) that operate on a sequence of adjacent basis structures. Algorithms are provided for both rim and cost operators. The paper concludes with a discussion of the economic and managerial interpretations of the operat

ISSN:0028-1441    

DOI:10.1002/nav.3800190203

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

年代:1972

数据来源: WILEY

摘要:

AbstractA program with a quadratic objective function and quadratic constraints is considered. Two duals to such programs are provided, and an algorithm is presented based upon approximations to the duals. The algorithm consists of a sequence of linear programs and programs involving the optimization of a quadratic function either unconstrained or constrained to the nonnegative orthant. An example involving production planning is presented.

ISSN:0028-1441    

DOI:10.1002/nav.3800190204

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

年代:1972

数据来源: WILEY

摘要:

AbstractIn this paper we consider a major assembly composed of two or more subassemblies. The failure of any subassembly causes the major assembly to not function. Every failed subassembly is repaired or replaced. A total investment in stocks of spare components is to be distributed among the various subassemblies and the major assembly so as to provide the best possible customer service. This is a complicated problem: relevant factors are the failure rates, unit costs, and repair times of the various components. For the case of Poisson failures, a heuristic solution is developed which is a compromise between theoretical optimality and practical usefulness.

ISSN:0028-1441    

DOI:10.1002/nav.3800190205

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

年代:1972

数据来源: WILEY

摘要:

AbstractThe purpose of this paper is to investigate and optimize policies which can be used to terminate a two‐state stochastic process with a random lifetime. Such a policy consists of a schedule of times at which termination attempts should be made. Conditions are given which reduce the difficulty of finding the optimal policy by eliminating constraints and some boundary points from consideration. Finally, a bound for the optimal policy is derived for a case where some restrictions are imposed on the mode

ISSN:0028-1441    

DOI:10.1002/nav.3800190206

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

年代:1972

数据来源: WILEY

摘要:

AbstractThree methods are used to solve the following problem: ForP, a positive constant, maximize (P. Reliability‐cost) of a system with standby redundancy. The results show that a method which rounds a noninteger solution to the nearest integer solution can lead to tremendous mistakes. However, neither a well known dynamic programming algorithm nor a previously developed branch and bound technique are able to solve large size problems. The solution of problems of large dimension thus requires the use of the noninteger solution of the first method to limit the number of possible solutions when using either the dynamic programming algorithm or a modified branch and bound technique. With this assistance, the branch and bound technique is able to solve large problems in a short amount of computational tim

ISSN:0028-1441    

DOI:10.1002/nav.3800190207

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

年代:1972

数据来源: WILEY

摘要:

AbstractA review of univariate tolerance intervals is presented from an application‐oriented point of view. Both β‐content and β‐expectation intervals are defined and considered. Standard problems are discussed for the distribution‐free case and with various distributional assumptions (normal, gamma, Poisson) which occur most frequently in practice. The determination of sample size is emphasized. A number of examples are used to illustrate the types of problems which permit solutions with the excellent tables now

ISSN:0028-1441    

DOI:10.1002/nav.3800190208

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

年代:1972

数据来源: WILEY

摘要:

AbstractThis paper considers a problem of locating new facilities in the plane with respect to existing facilities, the locations of which are known. The problem consists of finding locations of new facilities which will minimize a total cost function which consists of a sum of costs directly proportional to the Euclidian distances among the new facilities, and costs directly proportional to the Euclidian distances between new and existing facilities. It is established that the total cost function has a minimum; necessary conditions for a mimumum are obtained; necessary and sufficient conditions are obtained for the function to be strictly convex (it is always convex); when the problem is “well structured,” it is established that for a minimum cost solution the locations of the new facilities will lie in the convex hull of the locations of the existing facilities. Also, a dual to the problem is obtained and interpreted; necessary and sufficient conditions for optimum solutions to the problem, and to its dual, are developed, as well as complementary slackness conditions. Many of the properties to be presented are motivated by, based on, and extend the results of Kuhn's study of the location problem known as the General Fermat Prob

ISSN:0028-1441    

DOI:10.1002/nav.3800190209

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

年代:1972

数据来源: WILEY

摘要:

AbstractAn attacker, being one of two types, initiates an attack at some time in the interval [‐T, 0]. The a priori probabilities of each type are known. As time elapses the defender encounters false targets which occur according to a known Poisson process and which can be properly classified with known probability. The detection and classification probabilities for each type attacker are given. If the defender responds with a weapon at the time of attack, he survives with a probability which depends on the number of weapons in his possession and on attacker type. If he does not respond, his survival probability is smaller. These probabilities are known, as well as the current number of weapons in the defender's possession. They decrease as the number of weapons decreases. The payoff is the defender's survival probability.An iterative system of first‐order differential equations is derived whose unique solutionV1(t),V2(t),…,Vk(t) is shown to be the value of the game at timet, when the defender has 1, 2,…,k,… weapons, respectively. The optimal strategies are determined. Limiting results are obtained ast→‐∞, while the ratio of the number of weapons to the expected number of false targets remaining i

ISSN:0028-1441    

DOI:10.1002/nav.3800190210

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

年代:1972

数据来源: WILEY

摘要:

AbstractThe technique of probability generating functions has been applied to solve the steady state behavior of a discrete‐time, single‐channel, queueing problem wherein the arrivals to the queue at consecutive time‐marks are statistically independent, but the service is accomplished in phases which are Markov‐dependent. Special cases of importance have been discussed. In the end, mean number of phases, its special cases, the mean queue lengths, and the variances have been asce

ISSN:0028-1441    

DOI:10.1002/nav.3800190211

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

年代:1972

数据来源: WILEY