Journal of the Operations Research Society of Japan

[title in Japanese]

Article type: Cover
1977 Volume 20 Issue 1 Pages Cover1-
Published: 1977
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.20.Cover1

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[title in Japanese]

Article type: Appendix
1977 Volume 20 Issue 1 Pages App1-
Published: 1977
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.20.App1

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A PRIMAL APPROACH TO THE INDEPENDENT ASSIGNMENT PROBLEM

SATORU FUJISHIGE

Article type: Article
1977 Volume 20 Issue 1 Pages 1-15
Published: 1977
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.20.1

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We show a theorem which characterizes optimal independent assignments. Based on the theorem, we propose an algorithm for finding an optimal independent assignment, which is of a primal type in that we start from a maximum independent matching and that we get maximum independent matchings having smaller total weights than the old ones as the computation proceeds.

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ON THE COMPUTATIONAL EFFICIENCY OF BRANCH-AND-BOUND ALGORITHMS

TOSHIHIDE IBARAKI

Article type: Article
1977 Volume 20 Issue 1 Pages 16-35
Published: 1977
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.20.16

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The behavior of the number of partial problems T(A) which are decomposed in a branch-and-bound algorithm A (T(A) may be taken as a measure for the computational efficiency of A) is investigated in a fairly general setting. The first result is that the mean number T^~(n) of T(A) when A is applied to problems of size n grows at least as fast as exponentially with n, under relatively mild conditions, if A uses only the lower bound test as most of the conventional branch-and-bound algorithms do. Then it is pointed out that a possible way to avoid this exponential growth is to use the dominance test together with the lower bound test. The dominance test is also interesting from the view point of unifying a wide variety of algorithms as branch-and-bound. These points are exemplified by the well known Dijkstra algorithm for the shortest path problem and the Johnson algorithm for the two-machine flow-shop scheduling problem, for which T^~(n)<le>n-1 holds by virtue of the dominance test.

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A COMPUTATIONAL ALGORITHM FOR MINIMAX PROBLEMS WITH CONSTRAINTS

HITOSHI SASAI

Article type: Article
1977 Volume 20 Issue 1 Pages 36-41
Published: 1977
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.20.36

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In this paper we propose an interior penalty method to solve a minimax problem with inequality and equality constraints. The constrained minimax problem is replaced by a sequence of unconstrained approximate minimax problems. It is shown that the sequence of solutions of unconstrained approximation problems exists and converges to the solution of original constrained minimax problem.

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TWO-PERSON ZERO-SUM GAMES WITH RANDOM PAYOFFS

TADASHI KURISU

Article type: Article
1977 Volume 20 Issue 1 Pages 42-58
Published: 1977
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.20.42

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This paper deals with two-person zero-sum rectangular games with random payoffs. It is assumed that each player knows the distribution functions of the random entries and that players must select their strategies before any observations of the random entries are made. In such a case, several models are considered and relations among the optimal values are obtained. A special case, in which these random entries are linear functions of a random variable is also treated and some properties of the optimal strategies are given. In the final section, illustrative examples are shown.

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AN ALGORITHM FOR FINDING AN OPTIMAL INDEPENDENT LINKAGE

SATORU FUJISHIGE

Article type: Article
1977 Volume 20 Issue 1 Pages 59-75
Published: 1977
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.20.59

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This paper considers the weighted independent linkage problem which is a natural extension of the independent assignment problem recently treated by M. Iri and N. Tomizawa. Given a directed graph with two specified vertex subsets V_1 and V_2 on which matroidal structures are defined respectively, an independent linkage is a set of pairwise-arc-disjoint paths from V_1 to V_2 such that the set of the initial vertices (resp. terminal vertices) of those paths is an independent set on V_1 ・(resp. V_2). The problem is to find an optimal independent linkage, i.e., a maximum independent linkage having the smallest total weight among all maximum independent linkages, where a weight is given to each arc. We present an algorithm for finding an optimal independent linkage.

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[title in Japanese]

Article type: Appendix
1977 Volume 20 Issue 1 Pages App2-
Published: 1977
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.20.App2

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[title in Japanese]

Article type: Cover
1977 Volume 20 Issue 1 Pages Cover2-
Published: 1977
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.20.Cover2

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[title in Japanese]

Article type: Cover
1977 Volume 20 Issue 1 Pages Cover3-
Published: 1977
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.20.Cover3

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