Augmented ε-constraint method in multi-objective flowshop problem with past sequence set-up times and a modified learning effect

This article addresses a general tri-objective non-permutation flowshop problem to minimise the makespan, the sum of flow time and maximum tardiness simultaneously. In order to enhance the applicability of the model, some practical assumptions are included. These are release dates, past sequence-dependent set-up times, a truncated generalisation of Dejong’s learning effect and predetermined machine availability constraints. First, the problem is formulated as a mixed-integer linear programming model. Second, the true Pareto front is achieved with augmented ε-constraint method for small-sized problems. Third, due to the high complexity of the model and the impractical computational times of larger instances, a heuristic algorithm based on the ε-constraint method is also proposed. Finally, the algorithms are tested to gauge their effectiveness, and the results are compared with other methods.