摘要:

AbstractStructured finite action‐finite state space discounted Markovian decision problems are analyzed. Any problem of a general class is shown to be equivalent to a “separated” problem with decomposable problem structure. A modified policy iteration approach is developed for this decomposable reformulation. Both analytic and computer evaluations of the decomposition algorithm's effectiveness are pres

ISSN:0028-1441    

DOI:10.1002/nav.3800200102

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

年代:1973

数据来源: WILEY

摘要:

AbstractThis paper presents a generalization, calledpolaroid, of the concept ofpolarsetsA list of properties satisfied by polaroids is established indicating that the new concept nay be fruitfully used in an area of non‐convex (called here polar) programming as well as in integer programming, by means of polaroid cuts; this class of new cuts contains the ones defined by Tuy for concave programming (a special case of polar programming) and by Balas integer programming; it furthermore provides for new degrees of freedom in the construction of algorithms in the above‐mentioned areas of mathematical programm

ISSN:0028-1441    

DOI:10.1002/nav.3800200103

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

年代:1973

数据来源: WILEY

摘要:

AbstractWe show that the well‐known necessary and sufficient conditions for a relative maximum of a nonlinear differentiable objective function with nonnegative variables constrained by nonlinear differentiable inequalities may be derived using the classical theory of equality constrained optimization problems with unrestricted variables. To do this we transform the original inequality‐constrained problem to an equivalent equality‐constrained problem by means of a well‐known squared‐variable transformation. Our major result is to show that second order conditions must be used to obtain the Kuhn‐Tucker conditions by this approach. Our nonlinear programming results are motivated by the development of some well‐known linear programming results by

ISSN:0028-1441    

DOI:10.1002/nav.3800200104

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

年代:1973

数据来源: WILEY

ISSN:0028-1441    

DOI:10.1002/nav.3800200105

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

年代:1973

数据来源: WILEY

摘要:

AbstractRecent efforts to improve lower bounds in implicit enumeration algorithms for the general (n/m/G/Fmax) sequencing problem have been directed to the solution of an auxiliary single machine problem that results from the relaxation of some of the interference constraints. We develop an algorithm that obtains optimal and near optimal solutions for this relaxed problem with relatively little computational effort. We report on computational results achieved when this method is used to obtain lower bounds for the general problem. Finally, we show the equivalence of this problem to a single machine sequencing problem with earliest start and due date constraints where the objective is to minimize the maximum lateness.

ISSN:0028-1441    

DOI:10.1002/nav.3800200106

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

年代:1973

数据来源: WILEY

摘要:

AbstractThis paper treats the problem of sequencing n jobs on two machines in a “flow shop.” (That is, each job in the shop is required to flow through the same sequence of the machines.) The processing time of a given job on a given machine is assumed to be distributed exponentially, with a known mean. The objective is to minimize the expected job completion time. This paper proves an optimal ordering rule, previously conjectured by Talwar [10]. A formula is also derived through Markov Chain analysis, which evaluates the expected job completion time for any given sequence of the jobs. In addition, the performance of a heuristic rule is discussed in the light of the optimal solut

ISSN:0028-1441    

DOI:10.1002/nav.3800200107

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

年代:1973

数据来源: WILEY

摘要:

AbstractLinear programming problems with upper bounded variables can be solved by regular simplex method by considering upper bounding constraints as explicit constraints of the problem. However, more efficient methods exist which consider these upper bound constraints implicitly. When parametric analysis for problems with upper bounds is to be carried out, one can use the regular parameter analysis by considering the upper bound constraints explicitly. This paper develops formulas for parametric analysis where upper bound constraints are used implicitly, thus reducing the size of the basic matrix.

ISSN:0028-1441    

DOI:10.1002/nav.3800200108

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

年代:1973

数据来源: WILEY

摘要:

AbstractA comparison of the complementary pivot method of Lemke‐Howson and the more commonly used primal‐simplex method for solving linear programming problems in symmetric dual form has been made. In our tests the complementary pivot method shows a definite superiority over the simplex method both with regard to the number of iterations and computation t

ISSN:0028-1441    

DOI:10.1002/nav.3800200109

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

年代:1973

数据来源: WILEY

摘要:

AbstractUsing Mills Differential a game value function ϕ, used in the Kemeny‐Morgenstern‐Thompson growth model to show the existence of solutions, is discussed. In doing so, several proofs become shorter, in addition known results are seen in a new context. Finally connections between the existence of a so‐called economic solution and the differentiability or non‐differentiability of function ϕ are

ISSN:0028-1441    

DOI:10.1002/nav.3800200110

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

年代:1973

数据来源: WILEY

摘要:

AbstractThis paper introduces an efficient heuristic procedure for a special class of mixed integer programming problems called the uncapacitated warehouse (plant) location problem. This procedure is derived from the branching decision rules proposed for the branch and bound algorithm by the author in an earlier paper. It can be viewed as tracing a single path of the branch and bound tree (from the initial node to the terminal node), the path being determined by the particular branching decision rule used. Unlike branch and bound the computational efficiency of this procedure is substantially less than linearly related to the number of potential warehouse locations (integer variables) in the problem. Its computational efficiency is tested on problems found in the literature.

ISSN:0028-1441    

DOI:10.1002/nav.3800200111

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

年代:1973

数据来源: WILEY