Combination of Genetic Algorithm with Lagrange Multipliers for Lot-size Determination in Capacity Constrained Multi-period, Multi-product and Multi-stage Problems

In this paper a meta-heuristic approach has been presented to solve lotsize determination problems in a complex multi-stage production planning problems with production capacity constraint. This type of problems 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 achieved. In the first step, the original problem is decomposed to several subproblems using a heuristic approach based on the limited resource Lagrange multiplier. Thus, each sub-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 subproblems. 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. This paper’s propositions have been studied and verified through considerable empirical experiments.