In a make-to-order production system, retaining several standard products and altering them for orders with shorter due dates can reduce production lead time although some additional costs are incurred. In this paper, we consider a strategy using standard products, under which a product is manufactured individually for an order if its due date is later than or equal to a prespecified threshold, and an altered standard product is used otherwise. The standard products are assumed to be ordered according to an (s-1,s) policy. First, an average cost per unit order under this strategy is analyzed. Then an algorithm is constructed for Poisson arrival to find the optimal values of the threshold and an initial inventory quantity of the standard products that minimize the average cost.

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When partly finished goods can be obtained both by production in-house and procurement from outside vendors at each stage in a production process comprised of multiple stages, there arises a problem of finding the most economical partition of make in-house or purchase from outside vendors among a series of production stages. This paper discusses the problem of clarifying the most economical partition toward a make-or-buy decision for such a production process under the conditions that both procurement cost and in-house manufacturing cost (fixed cost and unit variable cost) for each part or product in a pocess required at each stage is given for all stages, and that once production in-house is selected at a certain stage, all succeeding stages are to be produced in-house. This paper presents a solution procedure based on the break-even point analysis of production volume at which the total cost of in-house production is equivalent to that of the procurement policy. This solution procedure can represent how the area in which in-house production is superior in terms of cost is enlarged along with the increase in production volume, thus make-or-buy decisions under uncertainty in production volume become feasible.

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Recently, the chaotic method is employed to forecast a short-term future using uncertain data. This method is feasible by restructuring the attractor of given time-series data in the multi-dimensional space through Takens' embedding theory. Nevertheless, it is hard to obtain data which comes only from a chaotic source. Ordinarily, many uncertain time-series data do not come only from a chaotic source, but also from another source. In this paper, we employ related information in order to remove the influence of the non-chaotic source from the given data. This method makes forecasting precision higher because the chaotic portion of the given data can be easily abstracted. In the end, the effectiveness and usefulness of our method are shown by application to a short-term forecasting simulation of Nikkei mean data of the Tokyo stock market.

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This paper considers a single machine scheduling problem with due time constraints, non-negative conditions of starting time and shutdown constraints on the machine. Shutdowns are disruptive events such as breaks, holidays and machine maintenance, and have prespecified periods when machine operation will be interrupted. It is necessary to schedule jobs so that the starting time of the first job is non-negative. Every job should be completed before or just on the due time when the customer requires it and leave the shop simultaneously on the due time. If a job is completed earlier than its due time, then the shop holds the job and incurs a holding cost for earliness. A heuristic scheduling algorithm with reduction in shutdown times has been developed for solving the problem approximately to minimize the sum of the holding cost for earliness and the reduction cost in shutdown times. The reduction costs in shutdown times correspond to the extra work cost, the cost for reducing the maintenance period and so on. Computational experiments are also shown for the proposed algorithm.

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This paper investigates the production planning and scheduling problems of a job shop. In general, the solution of the production planning problem is fed into a scheduling problem, and thus from the point of finding the feasible solution, it is important to consider the capacity constraints of the scheduling level when solving the production planning problem. In this paper, a heuristic solution method for the problem is proposed. The key points are to estimate the net available production time by subtracting unavoidable idle time from the maximum available production time, and the maximum production quantity for the selected products. The production planning problem is first solved considering the net available production time and maximum production quantity. The scheduling problem is then solved with the corresponding solution of the production planning problem. The last step is to revise the net available production time and add the maximum production quantity constraint. The proposed method repeats these three steps and stops if the feasible solution is obtained or the number of iterations reaches a specified maximum value. Computational experiments clarified the applicability of this method.

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In some systems which involve the interaction of human beings, such as management systems or social systems, there are cases in which the data includes human vagueness. These data are treated as fuzzy data. Furthermore, to make clear the relation between observed data and the distribution model, the x^2 test of goodness of fit has been used. But, in the case of fuzzy data, this method has to process data ignoring the vagueness, thus causing cases where we obtain incorrect results. In this paper, we propose a method to process the x^2 test of goodness of fit with consideration of the vagueness which is included in the fuzzy data. To investigate its usefulness, our method is applied to test the normality of the observed data, and its usefulness is illustrated using computer simulation.

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In this paper, we refer to the data whose boundaries of intervals are vague as fuzzy interval data ; and study the method of Bayesian discrimination using fuzzy interval data from an observation space. The states for the discrimination are fuzzy states ; and optimal discrimination rules which minimize the average error probability of discrimination are derived. We also define the entropy by fuzzy interval data, and examine the upper limit of the average error probability of discrimination. As the calculation becomes troublesome if the membership functions of fuzzy interval data are used directly, we propose the method of treating the middle points of the membership functions as the representative points of fuzzy interval data for the calculation. In realistic situations, we cannot always treat ideal symmetrical membership functions of fuzzy interval data, so computer simulation are performed under realistic circumstances in which the condition of the symmetry of membership functions is not satisfied completely. As a result, we could show the practicability of our proposed method.

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