Permutation flowshop scheduling to minimize the total tardiness with learning effects

Scheduling with learning effects has received considerable attention recently. Often, numbers of operations have to be done on every job in many manufacturing and assembly facilities. However, it is seldom discussed in the general multiple‐machine setting, especially without the assumptions of identical processing time on all the machines or dominant machines. With the current emphasis of customer service and meeting the promised delivery dates, we consider a permutation flowshop scheduling problem with learning effects where the objective is to minimize the total tardiness. A branch‐and‐bound algorithm and two heuristic algorithms are established to search for the optimal and near‐optimal solutions. Computational experiments are also given to evaluate the performance of the algorithms.