An energy-efficient two-stage hybrid flow shop scheduling problem in a glass production

Abstract

Energy-efficient scheduling is highly necessary for energy-intensive industries, such as glass, mould or chemical production. Inspired by a real-world glass-ceramics production process, this paper investigates a bi-criteria energy-efficient two-stage hybrid flow shop scheduling problem, in which parallel machines with eligibility are at stage 1 and a batch machine is at stage 2. The performance measures considered are makespan and total energy consumption. Time-of-use (TOU) electricity prices and different states of machines (working, idle and turnoff) are integrated. To tackle this problem, a mixed integer programming (MIP) is formulated, based on which an augmented ε-constraint (AUGMECON) method is adopted to obtain the exact Pareto front. A problem-tailored constructive heuristic method with local search strategy, a bi-objective tabu search algorithm and a bi-objective ant colony optimisation algorithm are developed to deal with medium- and large-scale problems. Extensive computational experiments are conducted, and a real-world case is solved. The results show effectiveness of the proposed methods, in particular the bi-objective tabu search.

Keywords:

• two-stage hybrid flow shop
• total energy consumption
• ε-constraint method
• constructive heuristic
• bi-objective tabu search
• bi-objective ant colony optimisation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Science Foundation of China (NSFC) [grant no. 71571135]. The work was also supported by the Fundamental Research Funds for the Central Universities.