In recent years, it has become very important to build mathematical models for uncertain situations of systems in the field of industrial engineering. In general, uncertainty is considered to be random characteristics and is treated by the methods of probability theory. But in real situations the major source of uncertainty is not only the presence of random variables, but the imprecision of the meaning of real objects in f given problem such ajs the constraints and objectives. This type of imprecision is called fuzziness which is expressed by fuzzy sets. Some attempts to explain about the concepts of fuzziness and their applications are described.

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It is well known that the fluctuation in stochastic demand often produce the inventory fluctuation which has an effect on service ration and mean stock in an ordering system. The key point of inventory management is a problem how to make the inventory fluctuation as small as possible. H.J.Vassian introduced a reorder rule which minimized it on an assumption, and then the author developed Vassians's model into a fixed-cycle ordering system under proportional control, and tried to analyze the feedback function in the system. The author obtained the conclusion that the inventory fluctuation by the new reorder rule is smaller than that by Vassian's rule.

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The purpose of this paper is to present decision rules based on internal rate of return that can be used to find an optimal subset under limited funds from a proposed compound set of investment altermatives in which there exist mutually exclusive or independent relationships. It has been said that for accepting or rejecting investment alternatives the internal rate of return method can only be applied to a limited class of investment alternatives. The paper discusses the general properties of the compound set of investment alternatives to which the rule based on internal rate of return can be applicable and expands the limit of applicability of the method by defining a concept of relevant and irrelevant internal rate of return and normal investment project.

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N-stage Series type Inventory Model with reference to Model proposed by Bryan et al. is considered. We present and algorithm for determining optimal inventory level by using the concept of marginal profit function. In this model, the demand during a unit time is assumed to follow a given distribution. And the cost of ordering, holding stocks, transportation, liquidation loss and opportunity loss are included. The model gives the optimal inventory level distributed at each stage which maximizes the profit. Furthermore, we examine the relations between various estimated values of opportunity loss and inventory level, expected profit and expected service ratio.

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There are many difficulties in comparing Fixed-Interval Ordering Systems with Fixed-Size Ordering Systems which are representative of ordering systems. The purpose of this paper is to discuss how we choose and adapt these two systems to circumstances. The author proposes a way to compare these two systems by focusing attention on the level of safety stock. The main result in this paper is as follows; The level of safety stock can be lowered by the Fixed-Interval Ordering System when the forecasting error is small, and reverse is the case when the forecasting error is large.

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The multiplicative data are often treated as additive ones after logarithmic or power transformation. So far as the time series data are concerned, however, there has been few research on the transformation. In this paper, the power transformation of time series data is used for fitting the data to Henshaw's[4]multiple regressional equation which contains seasonal and trend bariations. A computer simulation explains that the estimation by likelihood function gives more correct transformation parameter value than other methods by multiple correlation coefficient.

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A heuristic synthesis method of network systems is proposed using Fuzzy utomata. In order to realize the method, a computational algorithm is given by virtue of a successive substitution. Further, a necessary condition for the convergence of algorithm is given on the basis of Fuzzy Transition Matrix and the initial condition of the state of network. A few examples are illustrated to show how the proposed method works.

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A decision must be made as to the desired precision (or accuracy) that is to be used in determining the required number of observations in work measurement. In this paper, a statistical interpretation of the characteristics of the precision is suggested. After the discussion on practical usage of the desired precision, we propose a graphical method for determining it.

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This paper discusses the application of servo theory to the analysis of the effectiveness of parts-oriented production management system, using the simplest model as an example. A closedloop system is given as a basic inventory model, which consists of such four departments as planning, parts production, assembly, and inventory. On this basis, characteristics of each department are obtained and the static and dynamic characteristics of the system accompanied by the change in the level of standardization for parts are clarified by the numerical analysis. The results of the numerical analysis show the effects that the system stability increases and the inventory decreases inproportion to the shortness of the planning cycle which results in increasing the service ratio.

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This report gives an example of our recent developments of production system (from selection of orders to delivery) using a micro-computer in the production of products on orders of individual specifications in the metal mold production shop. We developed two simulators; One (Sim I) is used to give answers of exact date of delivery when inquiries are received and the other (Sim II) is used to make a practicable and efficient shop floor scheduling system, keeping the delivery date answered. For the efficient operation of the system centering on Sim I and II, the following methods were adopted. 1) To prevent business fixation through systematizations, interactive man-machine system with control variables was adopted for use by manager and foremen. 2) Aside from the idea of using larger-size domputer, a handy micro-computer was installed on the shop floor for the effective use of information.

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