Combination of genetic algorithm with Lagrange multipliers for lot-size determination in multi-stage production scheduling problems

In this paper a meta-heuristic approach for lot-size determination problems in a complex multi-stage production scheduling problems with production capacity constraint has been developed. This type of problem has multiple products with sequential production processes which are manufactured in different periods to meet customer’s demand. By determining the decision variables, machinery production capacity and customer’s demand, an integer linear program with the objective function of minimization of total costs of set-up, inventory and production is has been provided. In the first step, the original problem is converted to several individual problems using a heuristic approach based on the limited resource Lagrange multiplier. Thus, each individual problem can be solved using one of the easier methods. In the second step, through combining the genetic algorithm with one of the neighborhood search techniques, a new approach has been developed for the individual problems. In the third step, to obtain a better result, resource leveling is performed for the smaller problems using a heuristic algorithm. Using this method, each product’s lot-size is determined through several steps. We have verified our results through several empirical experiments.