Speed scaling in two-machine lot-streaming flow shops with consistent sublots

Abstract

We consider a single-job model lot streaming problem in two-machine flow shops with speed scaling, in which the job can be splitted into n consistent sublots, and each sublot can be processed at varying continuous speeds on each machine. The aim is to find an optimal schedule that determines both the sizes and the processing speeds of sublots so that the job can be finished before a given deadline and the total energy consumption is minimized. To solve this problem, we investigate the structural properties of the optimal schedules and show that it can be obtained within a no-wait environment. Then, we show that the problem is in fact a convex optimization problem, and can be solved by existing convex programming techniques.

Keywords:

• Lot streaming
• Flow shop
• Speed scaling
• Energy consumption

Additional information

Funding

The authors would like to express their gratitude to the three anonymous referees for their constructive suggestions and comments. This work was supported by the National Science Foundation of China (NSFC) under projects 71701144, 11971252, 71528002 and 91646118 and the Fundamental Research Funds for the Central Universities. Luo was also supported by the Humanities and Social Sciences Planning Foundation of the Ministry of Education (Grant No. 18YJA630077), Zhejiang Provincial Natural Science Foundation of China (Grant No. LY19A010005) and Ningbo Natural Science Foundation (2018A610198).