Mathematical Models of Energy-Conscious Bi-Objective Unrelated Parallel Machine Scheduling

Abstract

The industrialization has led to the prosperity of human life. However, it causes the side effect that harms the environment. Moreover, the source of energy used to drive the industrialization comes from non-renewable resources that can be extinct. As the extensive energy user, the manufacturing sector can use energy efficiently by scheduling and planning. A scheduling system that incorporates environmental and the energy consumption is one of the initiatives to reduce energy consumption and reduce environmental effects. Therefore, this study addresses bi-objective unrelated parallel machine scheduling to minimize the total tardiness and energy consumption. The energy consumption follows the Time-Of-Use (TOU) tariffs price scheme. The problem is formulated as two mixed-integer programming (MIP) models, using the time-indexed and disjunctive formulation, and solved using the weighted sum method. We perform complexity and computational analysis to evaluate the performance of models. Numerical experiments show that the time-indexed formulation is more efficient than the disjunctive formulation. The results provide useful insights for decision-makers in the manufacturing sectors to be energy-conscious without neglecting the production efficiency.