A multi-objective mathematical model and genetic algorithm solution approach for flexible job shop cell scheduling problems

In today's highly competitive business environment, customers desire to buy various products with higher quality at lower costs. Manufacturing firms require a high degree of product variety and small manufacturing lot sizes to meet the demand variability. The product variations in manufacturing cause many problems such as lengthy setup and transportation times, complex scheduling. Cellular Manufacturing Systems contain the characteristics, which will respond to the needs of manufacturers, even though Conventional Manufacturing Systems are not flexible enough to respond to changes. In addition, in most real life manufacturing problems, some or all operations of a part can be processed on more than one machine, and sometimes operations may visit a machine or work center more than once. It is necessary to use resources effectively in order to run such a complex production system successfully. In this study, a mathematical model and a solution approach that deals with a flexible job shop scheduling problem in cellular manufacturing environment is proposed by taking into consideration exceptional parts, intercellular moves, intercellular transportation times, sequence-dependent family setup times, and recirculation. To the best of our knowledge, this is the first attempt to use multi-objective mathematical model and meta-heuristic approach for a Flexible Job Shop Cell Scheduling Problem (FJCSP). However, in the real-life applications, the scalarization method considered is highly important in terms of theoretical research and practical application because the FJCSP process is not easy because of many conflicting objectives. The proposed mixed integer non-linear model can be used for solving small and middle scaled problems. Solution of large scaled problems is not possible in reasonable time or takes too long time, so a Genetic Algorithm (GA) meta-heuristic approach that uses a multi-objective mathematical model with conic scalarization has been presented. An experimental design was used to determine the best combination of parameters which are affected performance of genetic algorithm to achieve optimum or sub-optimum solution. In this thesis study, a case study was conducted in Tülomsaş Locomotive and Engine Factory in Eskişehir. This study was solved by using both conic scalarization GA approach and weighted sum scalarization GA approach with six different weights of objective. It is emphasized that the multi-objective conic scalarization GA approach has better quality than other approach for five different weights of objective. In addition, it has been shown that the multi-objective model could also obtain optimum results in reasonable time for the real-world problems.