Minimizing the mean weighted absolute deviation from due dates in lot-streaming flow shop scheduling

Lot-streaming is the process of splitting a job (lot) into a number of smaller sublots so that successive operations can be overlapped in a multi-stage production system. This paper presents a procedure for minimizing the mean weighted absolute deviation from due dates when jobs are scheduled in a lot-streaming flow shop. This performance criterion has been shown to be non-regular and requires a search among schedules with inserted idle times to find an optimal solution. For a given job sequence, we present linear programming formulations to obtain optimal sublot completion times for cases where buffers between successive machines have limited or infinite capacities, and sublots have equal-size or are consistent. A no-wait flow shop problem is also considered. Sixteen pairwise interchange methods are considered to generate the best sequences. These algorithms are obtained by combining four rules to generate initial sequences with four neighborhood search mechanisms. Computational experiments are conducted on 140 test problems. The results show that the best solutions are obtained by the heuristic algorithm with a non-adjacent pairwise interchange method and the smallest overall slack time rule to generate the initial sequence.