This paper deals with a discrete time replacement model for a system with minimal repair. The system consists of n components under Markovian deterioration. The transition probability of its component is not independent each other and the cost of replacing several components jointly is less than the sum of the costs of separate replacements. Then we investigate the structural properties of the optimal replacement policy which minimizes the expected total discounted cost, and propose the simple replacement policy which lets easily implementable policy. Also a numerical example is presented.

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Some of the results of a computer simulation on the effects of a desirable. adjustment of the Japanese industrial structure are described. The simulation model is based on an LP calculation under certain constraints of energy consumption, using the abbreviated industrial input-output table for 1979. The objective function of this LP model, which the author refers to as a welfare function, is selected to be maximized by the output vector of domestic industries under some possible constraints.

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This paper provides an approximate analysis for an on-line network system consisting of a CPU and a large number of terminals located in many service stations. Customers arrive at each station for CPU service via a Poisson process. The CPU processes jobs from terminals according to the processor sharing discipline. The CPU processing rate is dependent on the number of customers receiving the CPU service simultaneously and decreases when this number increases beyond the CPU capacity. The approximate analysis in this paper is performed by dividing the entire system into a computer subsystem and queueing subsystems. The computer subsystem is formulated as a closed queueing network and each queueing subsystem as an M/G/m queue. Our results are simple and can be applied easily to decide on the optimal number of terminals that minimizes mean total system time. Key Words: on-line network system; closed queueing network; M/G/m queue; terminal control policy.

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A combinatorial characterization of the rigidity of plane link systems was first established by Laman[9] (he used the term 'skeletal structure' instead of 'link system' of this paper). This paper presents a combinatorial analysis method for the structures of plane link systems. More precisely, the proposed method affords a representation of the family of all the rigid sub-systems of a plane link system.

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[numerical formula] In this paper, we give a proof that the coordinatewise minimization (CM) procedure for the above problem converges to the optimal solution. D'ESopo gave a proof for a special class of Q with the property (A) that f(x) has a unique minimizing argument in each coordinate direction (but need not strictly convex). This paper is the extention of his proof to the more general case that f(x) is differentiable and convex but does not necessarily have the above property. Problem Q is not only a special class of convex programming problem with only upper and lower bounded constraints, but also a dual of the more general concave programming problem with strictly concave objective function. The Lagrangian dual function with respect to all primal constraints has the above property (A), but the function with respect to only part of the constraints (Lagrange relaxation) does not necessarily have the property. This paper also gives a proof that the CM method for the latter case converges to the optimal solution as well as for the former case.

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This paper studies an infinitely-many server queue which has Markov renewal inputs and hypere-xponential service times. The stationary distributions of the number of busy servers both immediately before an arrival epoch and at an arbitrary time are obtained. These results can be applied to engineering telephone networks.

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This paper extends Newton and quasi-Newton methods to systems of PC^1 equations and establishes the quadratic convergence property of the extended Newton method and the Q-superlinear convergence property of the extended quasi-Newton method.

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This survey article is intended to present a bird's-eye view of the current status of the re_searches on systems theory which have been conducted these few decades from the structural and/or qualitative point of view. Samuelson's work on comparative static analysis of a model of national economy [38] may be quoted as an origin of this kind of study, where he raised a problem of finding the direction of change in economic equilibrium induced by a small change of exogenous variables based solely on qualitative information. In engineering field, Lin's work on structural controllability [2l] of dynamic systems has been quite influential. Following these pioneering works, a variety of researches have been done by economists and engineers, as well as by mathematicians. They include refinements and extensions of the earlier results, and also formulation and solution of new problems. A few examples are: structural decouplability and sign-stability of dynamic systems, and structural solvability and decomposability of linear and nonlinear systems of equations. Especially, the structural analysis of systems of equations has emerged as a new direction of research, as we become more and more frequently involved with large-scale systems. The rapid progress of hardware technology in computing is of course a blessing, but the structural analysis is expected to provide an equally powerful software techniques in such a situation. This paper therefore surveys the known results in structural and/or qualitative analysis of systems. A11 these results will be described purely in graph-theoretic terms, with explaining examples. By doing so, it is hoped that this paper serves to introduce OR researchers with some new ideas and viewpoints, and encourage them toward the new applications and possibilities of graph theory.

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M. Minoux considered the maximum balanced flow problem, which is a maximum flow problem with an additional constraint described in terms of a balancing rate function. In this paper, we propose an algorithm for the maximum balanced flow problem which is practically fast and simple. When the balancing rate function is constant, the proposed algorithm requires O(mT(n,m)) time, where T(n,m) is the time for the maximum flow computation for a network with n vertices and m arcs.

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