A genetic algorithm for the simultaneous lot sizing and scheduling problem in capacitated flow shop with complex setups and backlogging

In this paper the capacitated lot sizing and scheduling problem with sequence-dependent setups, setup carryover, and backlogging has been studied. The problem can be formulated as a mixed-integer program. Most lot sizing problems are hard to solve, especially in medium and large scale. In recent years, to deal with the complexity and find optimal or near-optimal results in reasonable computational time, a growing number of researchers have employed metaheuristic approaches to lot sizing problems. One of the most popular metaheuristics is genetic algorithm which has been applied to different optimization problems successfully. Therefore, we have developed a genetic algorithm to solve this model. To test the accuracy of the genetic algorithm, a lower bound is developed and compared against the genetic algorithm. In computational experiments, proposed genetic algorithm performed extremely well. It is concluded that the genetic algorithm is efficient and effective for this problem.