摘要:

AbstractWe consider the transportation problem of determining nonnegative shipments from a set ofmwarehouses with given availabilities to a set ofnmarkets with given requirements. Three objectives are defined for each solution: (i) total cost,TC, (ii) bottleneck time,BT(i.e., maximum transportation time for a positive shipment), and (iii) bottleneck shipment,SB(i.e., total shipment over routes with bottleneck time). An algorithm is given for determining all efficient (pareto‐optimal or nondominated) (TC, BT) solution pairs. The special case of this algorithm when all the unit cost coefficients are zero is shown to be the same as the algorithms for minimizingBT.provided by Szwarc and Hammer. This algorithm for minimizingBTis shown to be computationally superior. Transportation or assignment problems withm=n=100 average about a second on the UNIVAC 1108 computer (FORTRAN V)) to the threshold algorithm for minimizingBT.The algorithm is then extended to provide not only all the efficient (TC, BT) solution pairs but also, for each suchBT, all the efficient (TC, SB) solution pairs. The algorithms are based on the cost operator theory of parametric programming for the transportation problem developed by the author

ISSN:0028-1441    

DOI:10.1002/nav.3800230402

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

年代:1976

数据来源: WILEY

摘要:

AbstractWe consider a class of network flow problems with pure quadratic costs and demonstrate that the conjugate gradient technique is highly effective for large‐scale versions. It is shown that finding a saddle point for the Lagrangian of anmconstraint,nvariable network problem requires only the solution of an unconstrained quadratic programming problem with onlymvariables. It is demonstrated that the number of iterations for the conjugate gradient algorithm is substantially smaller than the number of variables or constraints in the (primal) network problem. Forty quadratic minimum‐cost flow problems of various sizes up to 100 nodes are solved. Solution time for the largest problems (4,950 variables and 99 linear constraints) averaged 4 seconds on the CBC Cyber 70 Model 72 compu

ISSN:0028-1441    

DOI:10.1002/nav.3800230403

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

年代:1976

数据来源: WILEY

摘要:

AbstractMixed integer programming problems arising in practice often contain special structures such as imbedded networks and multiple choice constraints. Easily derived inequalities are given that can be used to reduce the range of admissible solutions for such problems.

ISSN:0028-1441    

DOI:10.1002/nav.3800230404

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

年代:1976

数据来源: WILEY

摘要:

AbstractA mathematical programming problem with an objective function containing the square root of a positive semidefinite quadratic form has been considered by Mond. In order to use a transposition theorem of Eisenberg, Mond introduces a complicated constraint qualification. In this note we give a simple geometric characterization to this constraint qualification and show that it is implied by the generalized Slater constraint qualification.

ISSN:0028-1441    

DOI:10.1002/nav.3800230405

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

年代:1976

数据来源: WILEY

摘要:

AbstractThis paper investigates a class of two‐person zero‐sum multiple payoff games in which each component is deterministic. The problem of minimizing a player's total underachievement of a fixed set of goals is shown to reduce to a linear programming problem. Applications are discussed and illustrative examples are presen

ISSN:0028-1441    

DOI:10.1002/nav.3800230406

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

年代:1976

数据来源: WILEY

摘要:

AbstractThe problem considered involves the assignment ofnfacilities tonspecified locations. Each facility has a given nonnegative flow from each of the other facilities. The objective is to minimize the sum of transportation costs.Assume thesenlocations are given as points on a two‐dimensional plane and transportation costs are proportional to weighted rectangular distances. Then the problem is formulated as a binary mixed integer program. The number of integer variables (all binary) involved equals the number of facilities squared. Without increasing the number of integer variables, the formulation is extended to include “site costs” Computational results of the formulation are pres

ISSN:0028-1441    

DOI:10.1002/nav.3800230407

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

年代:1976

数据来源: WILEY

摘要:

AbstractA sample is taken from a continuous multivariate distribution. The problem is to test the hypothesis that the unknown joint cumulative distribution function is equal to a completely specified function. The observed data are transformed so that the hypothesis being tested is that the distribution is uniform over a unit hypercube. If only neighboring alternatives are considered, it is shown that the numbers of observations falling in a gradually increasing number of subcubes are asymptotically sufficient. It is shown that for all asymptotic probability calculations, we can assume that the joint distribution of the numbers of observations can be considered to be the distribution of slightly rounded off normal random variables. Tests based on these facts are constructed.

ISSN:0028-1441    

DOI:10.1002/nav.3800230408

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

年代:1976

数据来源: WILEY

摘要:

AbstractA stochastically constrained optimal replacement model for capital equipment is constructed. Each piece of capital equipment, or machine, is characterized by its age and “utility” or “readiness” class. The readiness of a machine at any age is a stochastic function of its initial utility class and its age.The total discounted replacement cost of several replacement streams, each commencing with an initial machine, is minimized with respect to the replacement age and initial utility class of each machine, subject to a readiness constraint stating the lower bound on the expected number of machines in each utility class at any time. A general solution procedure is outlined and a specific case is solved in

ISSN:0028-1441    

DOI:10.1002/nav.3800230409

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

年代:1976

数据来源: WILEY

摘要:

AbstractThis paper considers a traffic problem in which vehicles queue up according to a Poisson process on a single‐lane entrance ramp prior to merging into a major stream of vehicular traffic. In order to then prevent the ramp queue from becoming too large, a model is proposed which considers a lowering of the critical gap as the ramp queue size increases. With the critical gap assumed to be a nonincreasing function of the number of vehicles on the ramp at instances that correspond to departure times of lead vehicles from the ramp queue, the resultant model is an M/G/1 queue with state‐dependent service times. Some general results are obtained for this model and a specific case discussed in moderate det

ISSN:0028-1441    

DOI:10.1002/nav.3800230410

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

年代:1976

数据来源: WILEY

摘要:

AbstractIn this study we deal with the determination of optimal service rate in an M/M/1 queue. The arrival rate is unknown and assumed to be a random variable with a known distribution function. Holding and operating costs are considered and service rate is determined to minimize total expected discounted costs for infinite horizon. The effects of the arrival rate's distribution properties on the characteristics of the system are examined.

ISSN:0028-1441    

DOI:10.1002/nav.3800230411

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

年代:1976

数据来源: WILEY