摘要:

AbstractThe design of a system with many locations, each with many items which may fail while in use, is considered. When items fail, they require repair; the particular type of repair being governed by a probability distribution. As repairs may be lengthy, spares are kept on hand to replace failed items. System ineffectiveness is measured by expected weighted shortages over all items and locations, in steady state. This can be reduced by either having more spares or shorter expected repair times. Design consists of a provisioning of the number of spares for each item, by location; and specifying the expected repair times for each type of repair, by item and location. The optimal design minimizes expected shortages within a budget constraint, which covers both (i) procurement of spares and (ii) procurement of equipment and manning levels for the repair facilities. All costs are assumed to be separable so that a Lagrangian approach is fruitful, yielding an implementable algorithm with outputs useful for sensitivity analysis. A numerical example is presented.

ISSN:0028-1441    

DOI:10.1002/nav.3800210202

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

年代:1974

数据来源: WILEY

摘要:

AbstractRecent efforts in the field of dynamic programming have explored the feasibility of solving certain classes of integer programming problems by recursive algorithms. Special recursive algorithms have been shown to be particularly effective for problems possessing a 0–1 attribute matrix displaying the “nesting property” studied by, Ignall and Veinott in inventory theory and by Glover in network flows.This paper extends the class of problem structures that has been shown amenable to recursive exploitation by providing an efficient dynamic programming approach for a general transportation scheduling problem. In particular, we provide alternative formulations lor the scheduling problem and show how the most general of these formulations can be readily solved vis a vis recursive techn

ISSN:0028-1441    

DOI:10.1002/nav.3800210203

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

年代:1974

数据来源: WILEY

摘要:

AbstractThis paper describes a procedure for determining if constrained transportation problems (i.e., transportation problems with additional linear constraints) can be transformed into equivalent pure transportation problems by a linear transformation involving the node constraints and the extra constraints. Our results extend procedures for problems in which the extra constraints consist of bounding certain partial sums of variables.

ISSN:0028-1441    

DOI:10.1002/nav.3800210204

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

年代:1974

数据来源: WILEY

摘要:

AbstractComputerized Scheduling of Seagoing Tankers The tanker scheduling problem considered in this paper is that of the Defense Fuel Supply Center (DFSC) and the Military Sealift Command (MSC) in the worldwide distribution of bulk petroleum products. Routes and cargoes which meet delivery schedule dates for a multiplicity of product requirements at minimum cost are to be determined for a fleet of tankers. A general mathematical programming model is presented, and then a mixed integer model is developed which attempts to reflect the true scheduling task of DFSC and MSC as closely as possible. The problem is kept to within a workable size by the systematic construction of a set of tanker routes which does not contain many possible routes that can be judged unacceptable from practical considerations alone.

ISSN:0028-1441    

DOI:10.1002/nav.3800210205

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

年代:1974

数据来源: WILEY

摘要:

AbstractA cutting plane method for solving concave minimization problems with linear constraints has been advanced by Tui. The principle behind this cutting plane has been applied to integer programming by Balas, Young, Glover, and others under the name of convexity cuts.This paper relates the question of finiteness of Tui's method to the so‐called generalized lattice point problem of mathematical programming and gives a sufficient condition for terminating Tui's method.The paper then presents several branch‐and‐bound algorithms for solving concave minimization problems with linear constraints with the Tui cut as the basis for the algorithm. Finally, some computational experience is reported for the fixed‐charge transportation

ISSN:0028-1441    

DOI:10.1002/nav.3800210206

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

年代:1974

数据来源: WILEY

摘要:

AbstractThe search for an optimal point in a mixed‐integer space with a single linear bound may be significantly reduced by a procedure resembling the Lagrangian technique. This procedure uses the coefficients of the linear bound to generate a set of necessary conditions that may eliminate most of the space from further consideration. Enumerative or other techniques can then locate the optimum with greater efficiency. Several methods are presented for applying this theory to separable and quadratic objectives. In the maximization of a separable concave function, the resulting average range of the variables is approximately equal to the maximum (integer) coefficient of the constraint equatio

ISSN:0028-1441    

DOI:10.1002/nav.3800210207

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

年代:1974

数据来源: WILEY

摘要:

AbstractThis paper provides a method for solving mixed integer quadratic programs with the help of cutting‐plane techniqu

ISSN:0028-1441    

DOI:10.1002/nav.3800210208

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

年代:1974

数据来源: WILEY

摘要:

AbstractIn this paper, the existence of a saddle point for two‐person zero‐sum infinite games of a special type is proved. The games have continuous bilinear payoff functions and strategy sets which are convex, noncompact subsets of an infinite‐dimensional vector space. The closures of the strategy sets are, however, compact. The payoff functions satisfy conditions which allow the use of dominance arguments to show that points in the closure of a strategy set are dominated by or are strategically equivalent to points in the strategy set itself. Combining the dominance arguments with a well‐known existence theorem produces the main result of the paper.The class of games treated is an extension of a class studied by J. D. Matheson, who obtained explicit solutions for the saddle points by using necessary con

ISSN:0028-1441    

DOI:10.1002/nav.3800210209

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

年代:1974

数据来源: WILEY

摘要:

AbstractThis work considers a class of bimatrix games to which some well‐known structure theorems of 0‐sum matrix games can be made to generalize. It is additionally shown how to construct such games and how to generate the equilibrium points defining a given game as a member of that cl

ISSN:0028-1441    

DOI:10.1002/nav.3800210210

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

年代:1974

数据来源: WILEY

摘要:

AbstractThe appropriate size for a piece of fixed capital equipment (measured in units of capacity) depends on the anticipated demand for its services and on its cost. Using several models developed in the study of optimal inventory policy we derive the contribution to cost reduction that additional storage space makes under each of these models. Comparison of the sum of the discounted benefits (ie., reduced operating cost) with construction costs for additional storage space then yields the optimal size of the storage facility.

ISSN:0028-1441    

DOI:10.1002/nav.3800210211

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

年代:1974

数据来源: WILEY