Time lag size in multiple operations flow shop scheduling heuristics

This paper considers a multistage flow shop where jobs require multiple operations at each stage and a finish-to-start time lag between any two consecutive operations of a job: the next operation of a job cannot start until the time lag after the former operation of that job has elapsed. The effect of the size of this time lag is considered when studying the effectiveness of solution approaches for this problem. Since the problem of minimizing the makespan is shown to be NP-hard even for the two-stage case, we present a lower bound based heuristic approach that is used to construct several heuristic procedures. These heuristics use lower bounds on the minimum makespan to solve the problem. The effectiveness of these heuristics is empirically evaluated for various time lag sizes by solving a large number of randomly generated problems. We show that the relative performance of the heuristics depends on the size of the time lag. If the ratio of mean time lag and mean processing time is 20% or more, heuristics that construct an active schedule perform less well than heuristics that construct a non-delay schedule. The opposite holds true if this ratio is smaller. The performance of the widely used Shortest Processing Time heuristic (SPT) deteriorates quickly if the size of the time lags increases. We propose instead to use the Earliest Finish Time heuristic (EFT) in case time lags are present. EFT performs much better in this case and is identical to SPT if all time lags are zero. The use of the lower bound based heuristics results in an improvement of the makespan performance of up to 50% as compared with the performance of some simple dispatching heuristics that take the presence of multiple operations and time lags into account. This effect increases with the size of the time lags.