Journal of the Operations Research Society of Japan

[title in Japanese]

Article type: Cover
1989 Volume 32 Issue 1 Pages Cover1-
Published: 1989
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.32.Cover1

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[title in Japanese]

Article type: Appendix
1989 Volume 32 Issue 1 Pages App1-
Published: 1989
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.32.App1

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AN ANALYSIS OF A STOCHASTIC RESOURCE ALLOCATION MODEL WITH VARIOUS UTILITY FUNCTIONS

Tohru Nitta

Article type: Article
1989 Volume 32 Issue 1 Pages 1-15
Published: 1989
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.32.1

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This paper deals with stochastic models of an optimal sequential allocation of resources between consumption and production. We obtain the following results by means of the theory of martingales. For a model of resource allocation we establish the dynamic programming equation and show that a supermartingale characterizes the composition of the model and clear the composition of the optimality, representing the sufficient condition for an allocation to be optimal via a martingale. Further, we show the following three results as the application of the above result. (1) For the Kennedy's model we give another proof for the fact on an optimal allocation. (2) For a model with a convex utility function, we represent an optimal allocation via a supelmartingale. (3) For a model with a logarithmic utility function, we obtain an explicit optimal allocation.

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ALGORITHMS USING A BRANCH AND BOUND METHOD FOR FINDING ALL REAL SOLUTIONS TO AN EQUATION OF ONE VARIABLE

Shinji MIZUNO

Article type: Article
1989 Volume 32 Issue 1 Pages 16-33
Published: 1989
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.32.16

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In this paper, we propose algorithms using a branch and bound method for finding all real solutions to an equation f(x)=0 of one variable x on an interval [a,b]. We denote by P([c,d]) the subproblem in which we find all approximate solutions to f(x)=0 on [c,d]⊂ [a,b]. The algorithms repeat the following procedure for each subproblem P([c,d]) (the first subproblem is P([a,b])) until we terminate all the subproblems: If we solve the subproblem P([c,d]) then we terminate it, otherwise we split it into two new subproblems P([c,e]) and P([e,d]) for e=(c+d)/2. Here we can solve the subproblem P([c,d]) when there is no solution of f(x)=0 on [c,d] or when there exists a solution of f(x)=0 on [c,d] and the width d-c is sufficiently small. We assume that there are two functions g(x) and h(x) such that f(x) = g(x)-h(x) and one of the following conditions holds: (1) The functions g(x) and h(x) are continuous and monotone increasing. (2) The first derivatives g'(x) and h'(x) are continuous and monotone increasing. (3) The second derivatives g"(x) and h"(x) are continuous and monotone increasing . Then we present new sufficient conditions that the equation f(x)=0 has no solution on [c,d]. Those conditions are used in the algorithms for solving subproblems. We also show that if the function f(x) is a sum of elementary functions then there exist the functions g(x) and h(x) which satisfy the above as sumption. Furthermore we present sufficient conditions that the equation f(x)=0 has exactly one solution on [c,d]. We propose two algorithms which solve the subproblem P([c,d]) efficiently when the conditions hold.

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OPTIMIZATION IN PRODUCTION SYSTEMS: A SURVEY ON QUEUING APPROACHES

Tadayoshi Shioyama, Hiroshi Kise

Article type: Article
1989 Volume 32 Issue 1 Pages 34-55
Published: 1989
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.32.34

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This paper surveys recent works on queuing approaches to a number of optimization problems in production systems, especially modern jobbing production systems (or multi-item small lot production systems) represented by flexible manufacturing systems (FMS). This paper outlines optimization problems concerning with such aspects of the system design and control as workloading, job selection, production rate control, production/inventory control and system configuration.

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OPTIMAL WEIGHING PROBLEMS

Sumio HIROKAWA, Kazuyoshi WAKUTA

Article type: Article
1989 Volume 32 Issue 1 Pages 56-74
Published: 1989
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.32.56

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The false coin problem is stated as : You are given a balance and N coins (N>__=3). N-1 coins are equal in weight, but the N-th is defective, and weighs somewhat more or less than each of N-1 coins. Devise a procedure to determine, in the minimum number of weighings, which is the false coin, and whether it is lighter or heavier than the others. This problem has been studied in various approaches for the last four decades, and several methods by which the problem can be solved have been given. Almost no progress has been made, however, towards the solution of the problem of minimizing the expectation of the number of weighings in handling the false coin problem, and it has been still unsolved. In this paper we call the problem of minimizing the expectation of the number of weighings 'Optimal Weighing Problem', and solve it by a new method named 'Stochastic Skelton Method'. At first, we classify the ways of weighing coins into three types in terms of probability. Then, we present a graphical representation of a procedure of weighing and call it 'Skelton Diagram'. Next, we present an algorithm for finding an optimal procedure of weighings by means of the Skelton Diagram.

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PRACTICAL POLYNOMIAL TIME ALGORITHMS FOR LINEAR COMPLEMENTARITY PROBLEMS

Shinji Mizuno, Akiko Yoshise, Takeshi Kikuchi

Article type: Article
1989 Volume 32 Issue 1 Pages 75-92
Published: 1989
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.32.75

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In this paper, we first propose three practical algorithms for linear complementarity problems, which are based on the polynomial time method of Kojima, Mizuno and Yoshise [5] , and compare them by showing the computational complexities. Then we modify two of the algorithms in order to accelerate them. Through the computational experiments for three types of linear complementarity problems, we compare the proposed algorithms in practice and see the efficiency of the modified algorithms. We also estimate the practical computational complexity of each algorithm for each type of problems.

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UPPER BOUNDS OF A MEASURE OF DEPENDENCE AND THE RELAXATION TIME FOR FINITE STATE MARKOV CHAINS

Masaaki Kijima

Article type: Article
1989 Volume 32 Issue 1 Pages 93-102
Published: 1989
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.32.93

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In this paper, we consider a measure of dependence between X_t and X_0 where X_t is an irreducible Markov chain on a finite state space. Namely, we define d_t(X) = sup_<f,g>Cor [f(<X^^^>_0),g(<X^^^>_t)]. Here <X^^^>_t is the stationary process associated with X_t and the supreme is taken over all real functions. An upper bound of d_t(X), which is easy to calculate numerically, is derived. By showing a simple relation between d_t(X) and the relaxation time T_<REL>(X) of X_<t'> we also provide an upper bound of T_<REL>(X). The bounds are shown to be tight when the Markov chain is reversible in time.

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ON THE RELAXATION TIME FOR SINGLE SERVER QUEUES

Masaaki Kijima

Article type: Article
1989 Volume 32 Issue 1 Pages 103-111
Published: 1989
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.32.103

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This paper gives a natural definition of the relaxation time for general single server queues. First, we describe a GI/GI/1 queue as a limit of GI/GPH/1 queues. Each GI/GPH/1 queue is transferred to some equivalent bulk arrival GI^x/M/1 queue, which is formulated by a spatially homogeneous Markov chain with reflecting barrior at zero. An upper bound, which is easy to calculate, of the relaxation time of the Markov chain is derived. It will be shown that the relaxation time of the GI/GI/1 queue, defined as a limit of the relaxation times of GI/GPH/1 queues, has a particularly simple upper bound. Some particular cases are finally treated, where the upper bound obtained is shown to be tight for M/M/1 and M/D/1 queues.

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[title in Japanese]

Article type: Appendix
1989 Volume 32 Issue 1 Pages 112-113
Published: 1989
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.32.112

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[title in Japanese]

Article type: Appendix
1989 Volume 32 Issue 1 Pages App2-
Published: 1989
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.32.App2

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[title in Japanese]

Article type: Cover
1989 Volume 32 Issue 1 Pages Cover2-
Published: 1989
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.32.Cover2

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[title in Japanese]

Article type: Cover
1989 Volume 32 Issue 1 Pages Cover3-
Published: 1989
Released on J-STAGE: June 27, 2017

DOIhttps://doi.org/10.15807/jorsj.32.Cover3

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