A branch and bound algorithm to minimise the total tardiness in the two-machine permutation flowshop scheduling problem with minimal time lags

In this paper, we consider the two‐machine permutation flowshop scheduling problem with minimal time lags and the objective of minimising total tardiness. Dominance criteria are developed to establish precedence constraints between jobs in an optimal schedule and a lower bound on the total tardiness of the problem is derived. A branch and bound algorithm for this problem is developed to reach an optimal solution using lower bound and dominance criteria. Also, computationally efficient heuristics are proposed. Results of computational experiments on randomly generated problems are reported.