Lexicographic optimization of a permutation flow shop scheduling problem with time lag constraints

This paper considers the permutation flow shop scheduling problem with minimal and maximal time lags. Time lags are defined as intervals of time that must exist between every pair of consecutive operations of a job. The objective is to hierarchically minimize two criteria, the primary criterion is the minimization of the number of tardy jobs and the secondary one minimizes the makespan. We propose a mixed integer mathematical programming formulation which can be solved with the subroutine CPLEX. We also propose several versions of simulated annealing algorithm to heuristically solve the problem. Computational experiments to compare the proposed procedures are presented and discussed.