Robust identical parallel machine scheduling with two-stage time-of-use tariff and not-all-machine option

Abstract

Time-of-use (TOU) tariff has been implemented in the manufacturing industry to improve energy efficiency by regulating the electricity imbalance between supply and demand. Besides, not-all-machine (NAM) option is another way of energy-saving by using only a subset of all the available machines. This study investigates a robust identical parallel machine scheduling problem with a two-stage TOU tariff and NAM option. Only interval bounds on job processing times are known. The problem is first formulated into a min–max regret model to maximise the robustness. Based on problem properties, both an iterative relaxation-based exact algorithm and a memetic differential evolution-based heuristic are developed to solve the problem. Computational experiments on 240 randomly generated instances with up to 20 jobs are conducted to evaluate the performance of the developed methods. Besides, 900 large-sized randomly generated instances with up to 150 jobs are tested for sensitivity analysis and to identify managerial insights for achieving energy-efficient schedules.

Keywords:

• Energy-efficient scheduling
• identical parallel machine
• robust optimisation
• memetic algorithm
• min–max regret

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [Grant Number 71701048].

Notes on contributors

Xin Feng

Xin Feng received the B.S. degree in industrial engineering in 2011 and the Ph.D. degree in management science in 2016 both from Xi'an Jiaotong University, Xi'an, China. He is currently a Professor at College of Economics and Management, Nanjing Forestry University, Nanjing, China. Meanwhile, he was supported by the China Scholarship Council to work as a Postdoctoral, from 2018 to 2019 with the Laboratory IBISC, Université d'Evry, University of Paris-Saclay, France. His current research interests include combinatorial optimisation, scheduling and supply chain management.

Hongjun Peng

Hongjun Peng received the B.S. degree in probability statistics in 2002 from Anhui University, Hefei, China, and the M.S. degree in quantitative economics in 2007 and the Ph.D. degree in Management Science and Engineering in 2011 both from China University of Mining and Technology, Xuzhou, China. He worked as a Postdoctoral from 2014 to 2017 in Nanjing Forestry University, Nanjing, China. He is currently a Professor at college of Economics and Management, Nanjing Forestry University, Nanjing, China. Meanwhile, he conducted an academic visit to North Carolina State University, Raleigh, U.S.A. as a visiting scholar in 2016. His current research interests include operations research and management science, agricultural and forestry economic management, green supply chain, supply chain finance and carbon finance.