u形生產(chǎn)線(xiàn)的分析與優(yōu)化外文翻譯-其他專(zhuān)業(yè)-在線(xiàn)瀏覽
2025-03-24 06:53本頁(yè)面
【正文】 te because of his weariness and learning effect. In Section 4, we deal with the case where the processes of operation, walking and processing times are stochastic. In particular, we discuss the case where the sequences of random variables in these processes are independent and identically distributed and there is a bottleneck machine such that the sum of processing and operation times of this machine is larger than that of any other machine with probability one. It can be shown that the worker waits for the pletion of processing at the bottleneck machine in all cycles. 2. Cycle and Waiting Times of a MultiFunction Worker In this section we consider the Ushaped production line with a single multifunction worker, which is shown in Figure 2. The worker handles machines 1 through K. The facility has enough raw material in front of machine 1. The material is processed at machines 1,2,. . . , K, sequentially, and departs from the system as a finished product. Let K = {l,. . . , K}.When the worker arrives at machine k∈ K, if the processing of the preceding item is pleted, then he removes it from machine k, sends it to machine k + 1, attaches the present item to machine k and switches it on. After the operation at machine k, he walks to machine k + 1. If the preceding item is still in process at his arrival, then he waits for the end of the processing before the operation. It is assumed as an initial condition that at time 0, there is one item on each machine, which has been already processed at this machine. That is, in the first cycle the worker operates without waiting at all machines. In this and next sections, we assume that the processing, operation and walking times are constants at each machine. This assumption is satisfied when one kind of products are produced and the worker is well experienced in the operation. We use the following notations: for k∈ K and n∈ Z^ = {l, 2, . . .}, ik: the processing time at machine k, sk: the operation time of the worker at machine k, rk: the walking time from machine k to machine k + l ( K to l, if k = K), Wk(n): the waiting time of the worker at machine k in the nth cycle, C(n): the nth cycle time, a ∨ b = max{a, b}, a ∧ b = min{a, b}, [a]+ = max{0,a} . Figure 3 illustrates the behavior of the worker and the above defined variables. The initial condition implies that Consider the nth cycle time for n 2. If the worker does not wait at any machine then thecycle time is simply the sum of all operation and walking times. Since one item is processed and operated at each machine in one cycle, the cycle time must be greater than or equal to the maximum of the sums of the processing and operation times among all the machines. If the worker starts from the machine with the maximum sum, then the cycle time will be equal to the maximum of the maximum sum and the s
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