Minimizing total tardiness in the permutation flowshop scheduling problem with minimal and maximal time lags

In this research, we study permutation flowshop scheduling problem with minimal and maximal time lags while minimizing the total tardiness. The time lags are defined between couples of successive operations of jobs. Each time lag is greater than or equal to a prescribed value called minimal time lag and smaller than or equal to a prescribed value called maximal time lag. A new mathematical formulation is proposed. Upper bounds are provided by applying heuristic procedures based on known and new rules. Then, new lower bounds are derived by applying different methods where the main one is the Lagrangian relaxation. In order to make the last technique a viable approach to the considered problem, an auxiliary formulation is adopted and the Lagrangian multipliers are updated using the subgradient algorithm. Then, results of computational experiments are reported.