摘要:

AbstractThe first problem considered in this paper is concerned with the assembly of independent components into parallel systems so as to maximize the expected number of systems that perform satisfactorily. Associated with each component is a probability of it performing successfully. It is shown that an optimal assembly is obtained if the reliability of each assembled system can be made equal. If such equality is not attainable, then bounds are given so that the maximum expected number of systems that perform satisfactorily will lie within these stated bounds; the bounds being a function of an arbitrarily chosen assembly. An improvement algorithm is also presented.A second problem treated is concerned with the optimal design of a system. Instead of assembling given units, there is an opportunity to “control” their quality, i.e., the manufacturer is able to fix the probability,p, of a unit performing successfully. However, his resources, are limited so that a constraint is imposed on these probabilities. For (1) series systems, (2) parallel systems, and (3)kout ofnsystems, results are obtained for finding the optimalp's which maximize the reliability of a single system, and which maximize the expected number of systems that perform satisfactorily out of a total assembly ofJsyst

ISSN:0028-1441    

DOI:10.1002/nav.3800210102

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

年代:1974

数据来源: WILEY

摘要:

AbstractA significant problem in electronic system design is that of partitioning the functional elements of an equipment schematic into subsets which may be regarded as modules. The collection of all such subsets generated by a particular partitioning forms a potential modular design. The specific problem is to determine that partitioning of the schematic that minimizes a cost function defined on the subsets subject to specified hardware, design, packaging, and inventory constraints. This problem is termed the modularization problem. This paper presents a method for obtaining restricted solutions to the modularization problem by employing some recent developments in linear graph theory obtained by one of the coauthors. Numerical results from the solution of several typical problems are presented.

ISSN:0028-1441    

DOI:10.1002/nav.3800210103

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

年代:1974

数据来源: WILEY

ISSN:0028-1441    

DOI:10.1002/nav.3800210104

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

年代:1974

数据来源: WILEY

摘要:

AbstractThis paper investigates the problem of choosing between two simple hypothesis,H0andH1, in terms of independent, identically distributed random variables, when observations can be taken in groups. At any stage in the decision process it must be decided whether to stop and take action now or to continue, in which case the size of the next group of observations must be decided upon. The problem is to find an optimal procedure incorporating a stopping, group size (batch) and terminal action rule.It is proven, in general, that the optimal stopping and terminal action rule is of the sequential probability ratio type (SPRT). Fixed stopping rules of the SPRT type are studied and an iterative procedure of the policy improvement type, both with and without a value determination step, is developed. It is shown, for the general situation, that both the average risk and scheduling rule converge to the optima. Also, six suboptimal scheduling rules are considered with respect to the average risks they achieve. Numerical results are presented to illustrate the effectiveness of the procedures.

ISSN:0028-1441    

DOI:10.1002/nav.3800210105

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

年代:1974

数据来源: WILEY

摘要:

AbstractThis paper considers the problem of defending a set of point targets of differing values. The defense is proportional in that it forces the offense to pay a price, in terms of reentry vehicles expended, that is proportional to the value of the target. The objective of the defense is to balance its resources so that no matter what attack is launched, the offense will have to pay a price greater than or equal to some fixed value for every unit of damage inflicted. The analysis determines which targets should be defended and determines the optimal firing doctrine for interceptors at defended targets. A numerical example is included showing the relationship between the total target damage and the size of the interceptor force for different values ofp, the interceptor single shot kill probability. Some generalizations are discussed.

ISSN:0028-1441    

DOI:10.1002/nav.3800210106

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

年代:1974

数据来源: WILEY

摘要:

AbstractThe optimization of the dynamics of combat (optimal distribution of fire over enemy target types) is studied through a sequence of idealized models by use of the mathematical theory of optimal control. The models are for combat over a period of time described by Lanchester‐type equations with a choice of tactics available to one side and subject to change with time. The structure of optimal fire distribution policies is discussed with reference to the influence of combatant objectives, termination conditions of the conflict, type of attrition process, and variable attrition‐rate coefficients. Implications for intelligence, command and control systems, and human decision making are pointed out. The use of such optimal control models for guiding extensions to differential games is discus

ISSN:0028-1441    

DOI:10.1002/nav.3800210107

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

年代:1974

数据来源: WILEY

ISSN:0028-1441    

DOI:10.1002/nav.3800210108

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

年代:1974

数据来源: WILEY

摘要:

AbstractThis paper investigates a new procedure for solving the general‐variable pure integer linear programming problem. A simple transformation converts the problem to one of constructing nonnegative integer solutions to a system of linear diophantine equations. Rubin's sequential algorithm, an extension of the classic Euclidean algorithm, is used to find an integer solution to this system of equations. Two new theorems are proved on the properties of integer solutions to linear systems. This permits a modified Fourier‐Motzkin elimination method to be used to construct a nonnegative integer solution. An experimental computer code was developed for the algorithm to solve some test problems selected from the literature. The computational results, though limited, are encouraging when compared with the Gomory all‐integer algo

ISSN:0028-1441    

DOI:10.1002/nav.3800210109

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

年代:1974

数据来源: WILEY

摘要:

AbstractThe paper discusses mathematical properties of the well‐known Bellman‐Johnson 3 ×nsequencing problem. Optimal rules for some special cases are developed. For the case min Bi≥ maxAjwe find an optimal sequence of the 2 ×nproblem for machinesBandCand move one item to the front of the sequence to minimize (7); when minBi≥ maxCjwe solve a 2 ×nproblem for machinesAandBand move one item to the end of the optimal sequence so as to minimize (9).There is also given a sufficient optimality condition for a solution obtained by Johnson's approximate method. This explains why this method so often produces an optima

ISSN:0028-1441    

DOI:10.1002/nav.3800210110

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

年代:1974

数据来源: WILEY

摘要:

AbstractA cost‐based composite scheduling rule is developed and evaluated in comparison with three other well‐researched scheduling rules—SPT, S/OPN, and SST. This cost rule permits the optimization of more than one performance measure at a time. The priority number that is used for scheduling operations through each machine group is based on four separate performance measures—(1) In‐process Inventory, (2) Facilities Utilization, (3) Lateness, and (4) Mean Setup Time. The factorial experimental design involved three factor levels of loads, three factor levels of cost, and three factor levels of mean time. Analysis of variance was performed on each of the five output measures to study the effects of each of the three factors on each individual rule. Rank‐order comparisons between rules were also made; and, finally, general conclusions with regard to the effectiveness and flexibility of the Cost Rule

ISSN:0028-1441    

DOI:10.1002/nav.3800210111

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

年代:1974

数据来源: WILEY