Coordination of set-ups between two stages of a supply chain using multi-objective genetic algorithms

A multi-objective genetic algorithm (MOGA) solution approach for a sequencing problem to coordinate set-ups between two successive stages of a supply chain is presented in this paper. The production batches are processed according to the same sequence in both stages. Each production batch has two distinct attributes and a set-up occurs in the upstream stage every time the first attribute of the new batch is different from the previous one. In the downstream stage, there is a set-up when the second attribute of the new batch is different from that of the previous one. Two objectives need to be considered in sequencing the production batches including minimizing total set-ups and minimizing the maximum number of set-ups between the two stages. Both problems are NP-hard so attainment of an optimal solution for large problems is prohibited. The solution approach starts with an initialization stage followed by evolution of the initial solution set over generations. The MOGA makes use of non-dominated sorting and a niche mechanism to rank individuals in the population. Selected individuals taken from a given population form the succeeding generation using four genetic operators as: reproduction, crossover, mutation and inversion. Experiments in a number of test problems show that the MOGA is capable of finding Pareto-optimal solutions for small problems and near Pareto-optimal solutions for large instances in a short CPU time.