In this paper, we use event graphs, a paricular type of Petri nets, to evaluate job-shops when manufacturing times are random variables and the control is defined as the sequence of product types at the entrance of each machine. Under very general assumptions, we prove that the cycle time of the system converges in probability to a constant and asymptotically tends in distribution to a normal distribution whose standard deviation tends to zero. We also provide a lower bound of the main cycle time. We finally derive from the previous results a heuristic algorithm which leads to a near optimal solution of the problem (an optimal solution being the minimal work-in-process which allows the maximal productivity, i.e. the minimal cycle time, knowing the control).
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