Vol.5 No.2 2012

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Research paper : Toward the integrated optimization of steel plate production process (K. Nishioka et al.)−105−Synthesiology - English edition Vol.5 No.2 (2012) If the occurrence and processing frequency in every hour changes in the general distribution pattern, and if the frequency of stops and time caused by equipment failures, etc. changes, the required time and in-process stock of a certain process is derived as in the following formula using the queuing theory [22]: B = ρX (1 +ρY) < 1ρY = 1 − ρLρX==111 −1+1+1+ SX21212X1 −BXY1+YY2 X+1+ SY2 Y1+1+ SX21212X1+YYY2 X+1+ SY2 Y=PWN CCCCEEEEWρρρρρρρρρρYρhowever, the requirements for waiting time W and in-process stock N to stabilize are B = ρX (1 +ρY) < 1ρY = 1 − ρLρX==111 −1+1+1+ SX21212X1 −BXY1+YY2 X+1+ SY2 Y1+1+ SX21212X1+YYY2 X+1+ SY2 Y=PWN CCCCEEEEWρρρρρρρρρρYρwhere, W: average waiting time, N: average number of lots in stock in the process, EX: average processing time, EY: average equipment stop timeCSX: proportion of the standard deviation of processing time and average processing time, CSY: proportion of the standard deviation of stop time and average stop timePB: total utilization ratio, X: utilization ratio, Y: stop ratio, 1-Y: operation rate,: average occurrence rate, L: operation rate of preceding processesWe applied this required time/ in-process stock model to the plate finishing processes and estimated the required time and stock level. It was revealed that both the required time and the in-process stock level agreed well with the past records even in the cases where there was variation in the frequency of occurrence, processing and stops, and the validity of this model based on the queuing theory was confirmed.6 Toward the systemization of manufacturing knowledge6.1 Proposal of a multi-scale hierarchically structured model for production controlIn the preceding chapter, we explained, in a time-series schedule, how the support system was developed for solving individual problems of production control, taking examples from the Plate Mill of Kimistu Works. In this chapter, we now consider how and from which viewpoint the realized production control system can be converted into a conceptual model, so that a deeper understanding of the integrated optimization in the process industry can be acquired. We synthesize the knowledge we acquired from our problem solving efforts to solve the individual technical issues we experienced, and propose the following conceptual model.In the lean production system outlined in this paper as an already existing system, the time-wise process structure of a manufacturing line operating on the second time scale/ production plan of monthly scale/ very long manufacturing lead time/ stock, which is common knowledge in the conventional production control, synchronizes the flow of stock with the flow of the manufacturing line (just-in-time), which then synchronizes the time scale in the production control with that of the mainline. In contrast, an examination of the time process structure of the production control for manufacturing plates reveals that it is established as a time-wise multi-scale hierarchical structure of the processing (second time scale), lot planning (hour time scale), daily plan (day time scale), weekly plan (week time scale) and monthly plan (month time scale), and that the shop floor operation and the production control by the staff in charge have been implemented on the basis of such given hierarchical structure. In the past, a macroscopic capacity model calculated the capacity of each process using a spreadsheet based on the product mix forecast in the monthly plan. However, in the course of realizing the integrated optimization of plate manufacturing we developed the following three models: efficiency model, required time/ in-process stock model and manufacturing lead time model. These models meet the time-wise multi-scale hierarchical structure in plate manufacturing; namely, the efficiency model is for the second (processing) hour (lot) plan day plan; the required time/ in-process stock model is for the hour (lot) plan day plan weekly plan; and the manufacturing lead time model is for the day plan weekly plan monthly plan; and these three models are mutually inclusive. The efficiency model shows the efficiency and the load to be processed, but it also gives the occurrence rate of processes that products complete in the downstream processes for each product type (process occurrence rate for each product type). By inputting this processing load and process occurrence rate for each product type together with the day/ weekly plan into the required time/ in-process stock model, the required time of the process and the in-process stock volume can be obtained. For the product type determined by the daily/ weekly plan and monthly plan, if the process occurrence rate of the product type obtained from the efficiency model and the required time obtained from the required time/ in-process stock model are input to the manufacturing lead time model, the manufacturing lead time can be calculated (see Fig. 6).As described in the preceding chapter, trial and error on the shop floor resulted in the establishment of a production control system of plate manufacturing that has complex processes and product specifications and that ensures different time scales (hierarchy) are covered without contradiction, of both the required accuracy of plan and the responsiveness to the fluctuation of production/ orders. We propose to identify this system from the viewpoint of multi-

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