Modelling and an improved NSGA-II algorithm for sustainable manufacturing systems with energy conservation under environmental uncertainties: a case study

This study addresses a flexible job shop scheduling problem considering the energy tax regulations. We introduce two strategies as reactive scheduling to deal with two different kinds of uncertainty. The first uncertainty is about the start and processing times of the jobs with a known probability distribution. The second kind is related to machine breakdowns, modification or cancellation of the orders, and receive new orders without any known probability distribution. Two conflict objective functions are considered as minimising tax cost on surplus energy consumption and minimising total cost of jobs lateness based on soft time-windows. A bi-objective mathematical model is developed to formulate the problem. Since the problem is well-known strongly NP-hard, a new solution approach is introduced based on the NSGA-II algorithm to solve the problem in a reasonable computational time. Some test problems based on a real case study are used to evaluate the performance of the proposed solution approach. The result analysis confirms the effectiveness of the proposed algorithm and its superiority comparing with another algorithm based on the classic NSGA-II. Moreover, sensitivity analysis is done on the main parameters to provide proper managerial suggestions based on the obtained Pareto front solutions.