Open AccessA mathematical formulation and an NSGA-II algorithm for minimizing the makespan and energy cost under time-of-use electricity price in an unrelated parallel machine scheduling
Author(s) -
Marcelo Ferreira Rego,
Julio Cesar Pinto,
Luciano Perdig�ão Cota,
Marcone Jamilson Freitas Souza
Publication year - 2022
Publication title -
peerj. computer science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.806
H-Index - 24
ISSN - 2376-5992
DOI - 10.7717/peerj-cs.844
Subject(s) - mathematical optimization , job shop scheduling , computer science , multi objective optimization , scheduling (production processes) , pareto optimal , single machine scheduling , algorithm , mathematics , routing (electronic design automation) , computer network
In many countries, there is an energy pricing policy that varies according to the time-of-use. In this context, it is financially advantageous for the industries to plan their production considering this policy. This article introduces a new bi-objective unrelated parallel machine scheduling problem with sequence-dependent setup times, in which the objectives are to minimize the makespan and the total energy cost. We propose a mixed-integer linear programming formulation based on the weighted sum method to obtain the Pareto front. We also developed an NSGA-II method to address large instances of the problem since the formulation cannot solve it in an acceptable computational time for decision-making. The results showed that the proposed NSGA-II is able to find a good approximation for the Pareto front when compared with the weighted sum method in small instances. Besides, in large instances, NSGA-II outperforms, with 95% confidence level, the MOGA and NSGA-I multi-objective techniques concerning the hypervolume and hierarchical cluster counting metrics. Thus, the proposed algorithm finds non-dominated solutions with good convergence, diversity, uniformity, and amplitude.