Bi-objective optimization of a reentrant flow shop scheduling with exact time lag considering energy cost

Abstract : — In this paper, we study a bi-objective optimization of the two-machine reentrant flow shop scheduling problem with an exact time lag considering energy consumption cost. This problem is proposed by Amrouche et al. (2016), in which each job must be operated from the first machine M1 to the second machine M2 and then back to the first machine M1 with an exact time lag lj between the two operations on the first machine. The two objectives are: (1) minimization of the total energy consumption cost and (2) makespan. To describe the problem precisely, we propose a bi-objective mixed integer programming formulation. An-constraint method and NSGA-II approach are proposed to obtain the optimal Pareto front and approximate Pareto solutions for the problem. The frameworks of the proposed methods are presented in this paper.