A new deterministic production and inventory system model is studied. The model differs from earlier well-known models involving minimum shutdown time, startup cost and constraints for production level. A branch-and-bound algorithm for the optimal schdule of this model and some computational results are stated. And an application to a power apparatus model system constructed with three thermal generators and one pumped storage hydro is also considered.

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The solution for the traveling salesman problem is of importance because of its many application in the fields of engineering. Although many good solutions have been previously proposed for the traveling salesman problem, they are difficult to apply to practical large scale problems. In this paper we propose a new solution which can solve large scale problems covering more than 100 cities in high speed computation. In experiments using a computer (HITAC 8800 at TOKYO University Computing Center) the solution proposed in this paper succeeded in succeeded in solving 300-city problems in less than ten minutes. In this paper it will be shown that the success of this solution lies in effectively applying the branch and bound technique.

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In the first place, the author gives an example of the formulation of the optimization of the railway track capacity in a special case. Next, he shows a subject and a plan of the optimization in the general case. And lastly, he discusses on indeterminancy and uncertainty associated with optimization and decision making of the railway diagram and capacity.

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This paper attempts to explore the algorithm of a new method for solving non-linear optimization problems. The study focuses on the method for obtaining maximum or minimum value for one variable multi-modal function. It is shown that the algorithm developed here can be applied to solving the problem to optimize any objective function defined on a bounded closed interval which satisfies the Lipschitz's condition . The traditional optimizing methods deal primarily with the uni-modal objective function for obtaining optimum value. This paper studies the method to obtain the global solution for multi-modal objective function. This algorithm, through using the Lipschitz's constant, can determine the upper limit of the obtained solution and evaluate the relative error to the true optimum value. This algorithm makes use of the relative error stopping rule. The accuracy of the solution, therefore, does not depend on the form of the objective function. This method can also be applied to some of the separable objective functions in the fixed charge problem. Numerical tests with the algorithm produced fairly satisfactory results.

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As the interactions among urban activities have increased and complicated, it is urgently demanded to analyze the effects which might be caused by urban policies. The aim of this model is to analyze not only direct effects but also repercussions of urban policies upon citizens' welfare and to assist decision-makers in evaluating policy alternatives and in detecting urban problems in advance. One of the new ideas in this model is that urban activities are grasped from two principal viewpoints of system theory (feedback and hierarchy), and the simulation model is formulated on the basis of this framework. (1) feedback system; Urban activities can be considered as such a feedback system as to maximize citizens' utility (output) by satisfying various demands of citizens (input) Herein exist two main feedback loops, one is with equipment or services (process). administrative control and the other is the influence of the benefit level on the demand pattern. (2) hierarchical system; Urban activities can be considered as a hierarchical system. From the hierarchical points of view, urban activities were categorized into four levels and the relationships between a higher level and a lower level are identified. The met-hod used to build the simulation model was System Dynamics and the method applied to analyze and formulate urban activities was Scenario. Some of model parameters which are highly sociological and psychological were defined on the result of the enquete investigation for administrative officials of Hiroshima city. Concerning Hiroshima city, the long range simulation (20 years) was carried out on this model with regard to several alternative urban policies.

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As the interactions among urban activities have increased and complicated, it is urgently demanded to analyze the effects which might be caused by urban policies. The aim of this model is to analyze not only direct effects but also repercussions of urban policies upon citizens' welfare and to assist decision-makers in evaluating policy alternatives and in detecting urban problems in advance. One of the new ideas in this model is that urban activities are grasped from two principal viewpoints of system theory (feedback and hierarchy), and the simulation model is formulated on the basis of this framework. (1) feedback system; Urban activities can be considered as such a feedback system as to maximize citizens' utility (output) by satisfying various demands of citizens (input) Herein exist two main feedback loops, one is with equipment or services (process). administrative control and the other is the influence of the benefit level on the demand pattern. (2) hierarchical system; Urban activities can be considered as a hierarchical system. From the hierarchical points of view, urban activities were categorized into four levels and the relationships between a higher level and a lower level are identified. The met-hod used to build the simulation model was System Dynamics and the method applied to analyze and formulate urban activities was Scenario. Some of model parameters which are highly sociological and psychological were defined on the result of the enquete investigation for administrative officials of Hiroshima city. Concerning Hiroshima city, the long range simulation (20 years) was carried out on this model with regard to several alternative urban policies.

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