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

Abstract

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. Scope and purpose A flow shop scheduling problem involves scheduling jobs on multiple machines in series in order to optimize a given criterion. Lot-streaming scheduling allows the overlapping of operations between successive machines by splitting each job (lot) into a number of smaller sublots. The majority of research assumes that buffers between successive machines have infinite capacity, but this assumption may not be valid unless inventory costs are negligible. In the literature, the problem with infinite capacity buffers has been addressed mainly with the makespan performance measure. However, with the current interest in just-in-time production philosophy, earliness as well as tardiness should be considered. This paper presents linear programming formulations to find optimal starting and completion times for all the jobs in a given sequence considering various types of buffers and sublots. Heuristic algorithms that blend linear programming with several pairwise interchange strategies are proposed to find near-optimal solutions for multiple-job, multiple-machine lot-streaming flow shop scheduling problems.