Lot-Sizing and scheduling in a flexible job-shop environment considering energy efficiency

The purpose of this paper is to optimize the integrated problem of lot-sizing and scheduling in a flexible job-shop environment considering energy efficiency. The main contribution of the paper is simultaneously considering lot-sizing and scheduling decisions, while accounting for energy efficiency.  In order to achieve this objective, a mathematical model has been developed for integrated optimization of scheduling and lot-sizing problems. The developed model uses a big bucket approach and is presented as a mixed integer nonlinear problem (MINLP). The BARON solver in GAMS software has been used to solve the proposed MINLP model. By defining the relative optimality limit (OPTCR) of 0.05 for the termination criterion in BARON solver, GAMS has not been able to solve large problems at a specified time to achieve relative optimality. Therefore, due to the NP-hard nature of the problem, a new genetic-based evolutionary algorithm has been developed to solve the problem of large scale. In the developed algorithm, a different approach (instead of cross-over and mutation operators) is used to generate a new solution. By presenting and solving various problems, the efficiency of this algorithm for solving big problems is shown. Comparing the values of the objective function obtained from the genetic algorithm and the exact method shows that, especially in large problems, the genetic algorithm has been able to achieve a better solution than GAMS software in a limited time. It has also been shown that energy efficiency has a significant effect on the solution of the problem.