Lot-sizing and scheduling optimization using genetic algorithm

Abstract: Simultaneous lot-sizing and scheduling problem is the problem to decide what products to be produced on which machine and in which order, as well as the quantity of each product. Problems of this type are hard to solve. Therefore, they were studied for years, and a considerable number of papers is published to solve different lotsizing and scheduling problems, specifically real-case problems. This work proposes a Real-Coded Genetic Algorithm (RCGA) with a new chromosome representation to solve a non-identical parallel machine capacitated lot-sizing and scheduling problem with sequence dependent setup times and costs, machine cost and backlogging. Such a problem can be found in real world production line at furniture manufacturer in Sweden. Backlogging is an important concept in this problem, and it is often ignored in the literature. This study implements three different types of crossover; one of them has been chosen based on numerical experiments. Four mutation operators have been combined together to allow the genetic algorithm to scan the search area and maintain genetic diversity. Other steps like initializing of the population and a reinitializing process have been designed carefully to achieve the best performance and to prevent the algorithm from trapped into the local optimum. The proposed algorithm is implemented and coded in MATLAB and tested for a set of standard medium to large-size problems taken from the literature. A variety of problems were solved to measure the impact of different characteristics of problems such as the number of periods, machines, and products on the quality of the solution provided by the proposed RCGA. To evaluate the performance of the proposed algorithm, the average deviation from the lower bound and runtime for the proposed RCGA are compared with three other algorithms from the literature. The results show that, in addition to its high computational speed, the proposed RCGA outperforms the other algorithms for non-identical parallel machine problems, while it is outperformed by the other algorithms for problems with the more identical parallel machine. The results show that the different characteristics of problem instances, like increasing setup cost, and size of the problem influence the quality of the solutions provided by the proposed RCGA negatively.