Non-permutation flow shop scheduling problems with unavailability constraints to Minimize Total Energy Consumption

Nowadays, energy demand has grown rapidly and remarkably in the different sector. More particularly the industry currently consumes about half of the world's energy. Furthermore, there has been a growing concern over the environmental impact of traditional manufacturing, especially in terms of energy consumption and related emissions of carbon dioxide. Besides the adoption of new equipment, production scheduling could play a key role in reducing the total energy consumption of a manufacturing plant. This article deals with the non-permutation flow shop scheduling problems with non-availability intervals to minimize the total energy consumption (TEC) and makespan (Cmax). Specifically, two kinds of unavailability constraints are investigated and the jobs are non-resumable in both cases. In the first case, the non- availability intervals are periodically fixed and known in advance. In the second case, the intervals are flexible and the machines' continuous working time cannot exceed a maximum allowed time. The mixed binary integer programming model is provided for deriving the optimal schedules. The problems of minimising makespan in such flow shops are proved Non-deterministic Polynomial-time hard in strong sense. To the best of our knowledge, no papers considering both production scheduling and unavailability constraints with minimizing the total of energy consumption and makespan in flow shop. The gap between theory and practice prevents the satisfying performance of the schedules in industry. The purpose of this paper is to establish a joint model for integrating the production and unavailability constraints to optimize the bi-objective of the total energy consumption and makespan simultaneously; and to make the theory applied in practice more efficaciously.