A novel mathematical model and multi-objective method for the low-carbon flexible job shop scheduling problem

Most conventional scheduling problems use production efficiency, cost and quality as their preeminent optimization objectives. However, because of increasing costs of energy and environmental pollution, “low-carbon scheduling” as a novel scheduling model has received increasing attention from scholars and engineers. This scheduling model focuses on reducing energy consumption and environmental pollution at the workshop level. In this paper, a new low-carbon mathematical scheduling model is proposed for the flexible job-shop environment that optimizes productivity, energy efficiency and noise reduction. In this model, the machining spindle speed — which affects production time, power and noise — is flexible and is treated as an independent decision-making variable. The methods of evaluation of productivity, energy consumption and noise are presented. A multi-objective genetic algorithm based on a simplex lattice design is proposed to solve this mixed-integer programming model effectively. The corresponding encoding/decoding method, fitness function, and crossover/mutation operators are designed specifically for the features of this problem. Three example problem instances with different scales and one Engineering case study illustrate and evaluate the performance of this method. The results demonstrate the effectiveness of the proposed model and method for the low-carbon job shop scheduling problem.