Vol.5 No.2 2012

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Research paper : Toward the integrated optimization of steel plate production process (K. Nishioka et al.)−102−Synthesiology - English edition Vol.5 No.2 (2012) that determines the efficiency of rolling processes as a whole particular to each product group, by properly extracting the factors of each process that affect efficiency, classifying them into product groups where these affecting factors have significant differences, calculating statistically the efficiency by each product group and comparing the efficiency of each process by each product group, and thus identifying the bottleneck processes contained in the sub-processes installed in tandem and connected directly. Once the sizes of product groups are properly adjusted, the difference between the actual records of integrated efficiency and the integrated efficiency specific to each product group is balanced out for the rolling processes as a whole, and irrespective of the changes caused by production permutation, it becomes possible to estimate the rolling efficiency with high accuracy (see NOTE 1). With this rolling efficiency model, it is also possible to estimate the rate of occurrence of processes that occur in the downstream processes for each product type.The efficiency model’s objective is to determine the efficiency and the load of each process, but by applying this model as indicated above, it achieved a substantial enhancement of rolling efficiency in the rolling processes.5.4 Development of manufacturing lead time modelWe achieved a substantial improvement in the efficiency of rolling processes, which, however, resulted in more pronounced characteristics of the push-type structure and in the increase of requirement fluctuation (fluctuation in the amount to be processed) of the finishing processes caused by the larger size of lots. In other words, this raised the issue pertaining to the necessity of optimization in pursuing simultaneously the enlargement of the lot size for the upstream processes of steelmaking to rolling processes and the leveling of the loads of the downstream processes of finishing.The total amount of intermediate in-process product stock nearly equals the product of the production volume per day and the manufacturing lead time (number of days), and the correct amount of product stock is determined by the variation of manufacturing lead time and the targeted rate of deliveries made within the due date. However, in the past, it was difficult to say that the factors affecting these two items and their relationship were quantitatively grasped and the production scheduling for accurate and optimal control was implemented. Therefore, to shorten the manufacturing lead time and realize a lower stock level, it is necessary to determine the relationship between the lead time variation and the targeted rate of deliveries made within the due date, but at the same time, to develop a model that is capable of describing comprehensively and quantitatively the consequences that are generated by the order mix of product types and manufacturing lot sizes in each process and in the integrated manufacturing lead time and stock volume.The manufacturing lead time is a variable that is the shorter the better, and is never in the negative, but the average of the number of days and the standard deviation show a linear relationship to some extent. The simplest model expressing this event is that the size of variation is proportional to the instantaneous value, but in this case, because the distribution of variation is a lognormal distribution, we assumed the distribution of manufacturing lead time borders on the lognormal distribution (Fig. 4). If we assume that the manufacturing lead time follows the lognormal distribution, it becomes possible to calculate in a simplified way the number of days considered necessary for achieving the targeted delivery time, which makes it very useful in developing or evaluating the manufacturing lead time model. The lognormal distribution is expressed by the following formula, where is the logarithmic mean of x, and is the logarithmic standard deviation of x. 0> 022exp21 ( )= < 0xx2(ln( )− )xxxfσσThe past records of the spare days of the manufacturing completion against the delivery due date are distributed almost normally and if their average value and standard deviation are determined, the probability that the delivery achievement ratio, i.e., the number of spare days against the delivery due date (manufacturing completion until delivery), is recorded as more than zero can be calculated easily by using the cumulative probability distribution function given below:Ratio achieving delivery due date: expd22221( − )( > 0; , )= 1−σσσxptt where x = spare days until delivery, = average of spare days, = standard deviation of spare daysNext, we studied the factors contributing to the variation of the number of spare delivery days. The order specifies the delivery due date and based on the transportation facilities and the specification of each product type, the timing to start rolling is decided, at which time, because the ordered diversified products are grouped in a lot for delivering, the spare delivery days and the individual manufacturing lead time become independent. Furthermore, the rolling start timing is affected by the fluctuation of production in the upper stream process of steelmaking. The variation of spare delivery days is affected by the variation of rolling start timing (spare days for starting rolling against delivery day: rolling start until delivery day) and the variation of

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