Minimizing total carbon footprint and total late work criterion in flexible job shop scheduling by using an improved multi-objective genetic algorithm

Abstract

In scheduling, previous research attention has been directed towards classical-based objective functions, while ignoring environmental-based objective functions. The purpose of this research is to present a multi-objective flexible job shop scheduling problem with the objectives of minimizing total carbon footprint and total late work criterion, simultaneously, as sustainability-based and classical-based objective functions, respectively. In order to solve the presented problem effectively, an improved multi-objective genetic algorithm is proposed to obtain high quality non-dominated schedules. This work has three main scientific contributions that are: (1) This is a novel and pioneer research that addresses carbon footprint reduction in flexible job shop scheduling, (2) This is also the first research that addresses the total late work criterion in multi-objective flexible job shop scheduling, and (3) This research proposes an improved multi-objective evolutionary algorithm for solving the newly extended bi-objective problem. Stepwise delineation of the proposed algorithm is provided and fifteen newly extended test instances are solved by the proposed approach. Computational outcomes of the proposed algorithm are compared with two most representative and well-known multi-objective evolutionary algorithms, namely, non-dominated sorting genetic algorithm II and strength Pareto evolutionary algorithm 2. The principal results show that: (1) The proposed algorithm is superior in finding high quality non-dominated schedules, (2) It performs better in four averaged comparison metrics as compared to the other algorithms, and (3) Carbon footprint has an impact on the optimum solutions. As conclusions, the proposed algorithm is useful for production managers to schedule their operations in a way that can reduce carbon emission while minimizing late work. Production managers will also have the flexibility in selecting a schedule from amongst a set of non-dominated schedules.