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(solution) Consider a stochastic counterpart of F m ǁ C max with machines that have different speeds, say...


Consider a stochastic counterpart of Fm ǁ Cmax with machines that have different speeds, say v1,...,vm. These speeds are fixed (deterministic). Job j requires an amount of work Yj , distributed according to Fj , on each one of the m machines. The amount of time it takes machine i to process job j is equal to Xij = Yj/vi. Show that if v1 ≥ v2 ≥ ··· ≥ vn (v1 ≤ v2 ≤ ··· ≤ vn) and F1 ≤lr F2 ≤lr ··· ≤lr Fn, the SEPT (LEPT) sequence minimizes the expected make span. In other words, show that if the flow shop is decelerating (accelerating) the SEPT (LEPT) sequence is optimal.

 


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Sep 13, 2020

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