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Research paper : Toward the integrated optimization of steel plate production process (K. Nishioka et al.)−104−Synthesiology - English edition Vol.5 No.2 (2012) completion time of each process. The standard deviation of all the plate manufacturing processes and that of the rolling + shearing + finishing calculated by the following formula, assuming that the required completion time of each one of the finishing processes is determined independently, are nearly equal and the validity of the assumption that the required completion time of each process is independent was confirmed. Therefore, if the following formula is used, the impact of the fluctuation of the required time and of the capacity of each process on the manufacturing lead time of the entire plate manufacturing can be easily estimated.rolling + shearing + finishing = (rolling + shearing2+∑each finishing process2)1/2where, rolling + shearing + finishing: standard deviation of rolling + shearing + finishing lead time rolling + shearing: standard deviation of rolling + shearing lead timeeach finishing process: standard deviation of required completion time of each finishing process (surface grinding, CL, OL, gas cutting, coating, UST, weld repair, marking, shot blasting, normalizing, quenching, tempering)As a result of the above evaluation, the contribution of rolling + shearing to all the manufacturing lead time of all processes is no bigger than 20 % and the effect of the enhanced rolling efficiency on the shortening of manufacturing lead time is limited. In contrast, where the lead time of finishing processes is concerned, most of the time spent was on waiting, and their contribution to necessary work time was no bigger than 5 %. In other words, if the variation of rolling start against the delivery due date is reduced and appropriate lot sizes are assured, realizing at the same time operation where the required time of each process and the in-process stock level is minimized, it is highly possible that the manufacturing lead time will be substantially shortened.The number of processes for each product type to pass and the manufacturing lead time are shown in Fig. 5, which indicates that the number of processes to be passed and the manufacturing lead time differ greatly depending on the product type, and that the manufacturing lead time is dependent almost entirely on the number of processes to be passed. Therefore, it is observed that for leveling the load of each process, it is necessary to maintain the input of each product type at an even level, and for preventing the input volume from being in spasm, it is important to control the lot sizes.We adopted a method to identify the distribution of manufacturing lead time for each manufacturing product type by seeking the distribution of manufacturing lead time for each pass pattern and by dividing it proportionally by the component percentage of pass pattern for each product type to be manufactured (see NOTE 3). We estimated the manufacturing lead time using this manufacturing lead time model, found the estimated time agreed well with the past records, and the validity of this model was thus confirmed. Therefore, if the process to be passed and the required time are known, the manufacturing lead time can be calculated.5.6 Development of a required time/ in-process stock modelIf the processes are arranged independently, and if it is possible to have enough stock between processes, the efficiency of each process is seldom affected by other processes. In contrast, if there is not enough in-process stock, there are “risks” of deteriorating efficiency such as waiting for the processing from other processes, increase in time for changing set ups, etc. Therefore, as long as the stock was within the storage yard capacity, no incentive to reduce stock was instigated, resulting in very sluggish progress in the minimization of in-process stock even after the reinforcement of the finishing processes’ equipment. The lead time of the finishing processes, as explained earlier, contributes no more than 5 % to the necessary work time, and establishment of an operation that minimizes the required time of each process and in-process stock was sought before achieving a shorter manufacturing lead time. Queuing theory is effective for analyzing waiting time, when there is variation in the occurrence frequency and its intervals and in the processing intervals, as in the case of the plate finishing processes. Therefore, to develop a model capable of describing the required time of each process, we applied the queuing theory to plate manufacturing, and developed a predictive model of the required time and the in-process stock volume of each process (required time/ in-process stock model), and then verified its validity (capable of giving a sufficiently accurate prediction of the in-process stock and required time of product in each process). Required time/ in-process stock modelIntegrated capacityEach process required time/ in-process stockStructure levelProduction controlManufacturing lead timeEach process efficiency/ processing loadProcess occurrence rate of each product typeMacroscopic capacity modelManufacturing lead time modelProcess conditionsLot planDaily planWeekly planMonthly planEfficiency modelFig. 6 Production control multi-scale hierarchically structured model

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