Heuristics for Flow Shop Scheduling with Multiple Operations and Time Lags

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. Since the problem of minimizing the make span is shown to be NP-hard even for the two-stage case, we present a lowerbound based heuristic approach that is used to construct several heuristic procedures. These heuristics use lowerbounds on the minimum make span to solve the problem. The effectiveness of these heuristics is empirically evaluated by solving a large number of randomly generated problems. The use of these lowerbounds in the construction of heuristics results in an improvement of the make span 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. Furthermore, 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.