green scheduling of permutation flow shop with tool deterioration and constrained tool replacement

Recently, there has been a growing scientific and political concern about global warming and its effects on the environment. since the industrial sector is the number one world-wide contributor to this phenomenon with its huge discharge of carbon dioxide (co2), researchers are looking for effective way to improve carbon efficiency in manufacturing plants by investigating scheduling strategies aiming at reducing the greenhouse effect of production processes. in this paper, we consider a permutation flowshop scheduling problem with constrained tool replacement activities where the tools needed for processing jobs are susceptible to deterioration and need to be replaced with new ones supplied from outside the system at prescheduled moments. the objectives of the scheduling problem are to simultaneously minimize the total carbon emission and the maximum completion time. a non-linear mixed integer programming formulation for the problem is developed. to obtain approximate non-dominated solution sets in reasonable time, an enhanced non dominated sorting genetic algorithm ii (nsga-ii) combined with a simulated annealing algorithm (sa) is adopted. computational results show the effectiveness of the proposed algorithm to solve the problem.