Heuristics for scheduling jobs in a permutation flow shop to minimize total earliness and tardiness with unforced idle time allowed

•Scheduling a permutation flow shop to minimize earliness and tardiness is addressed.•The use of unforced idle time is considered.•It is shown that unforced idle time only needs to be scheduled on the last machine.•Several dispatching heuristics are tested.•Several procedures are developed that result in improved solutions. This paper considers the problem of scheduling jobs in a permutation flow shop with the objective of minimizing total earliness and tardiness. Unforced idle time is considered in order to reduce the earliness of jobs. It is shown how unforced idle time can be inserted on the final machine. Several dispatching heuristics that have been used for the problem without unforced idle time were modified and tested. Several procedures were also developed that conduct a second pass to develop a sequence using dispatching rules. These procedures were also tested and were found to result in better solutions.