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Mathematical Problems in Engineering
Volume 2013, Article ID 546810, 6 pages
Research Article

A Branch-and-Bound Algorithm for Minimizing the Energy Consumption in the PFS Problem

1School of Management, Guangdong University of Technology, Longdong Campus 161 Yinglong Road , Guangzhou 510520, China
2Department of Mechatronics Engineering, Guangdong University of Technology, 100 Waihuan Xi Road, Higher Education Mega Center, Guangzhou 510006, China
3Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Pokfulam, Hong Kong

Received 22 November 2012; Accepted 24 January 2013

Academic Editor: Wei-Chiang Hong

Copyright © 2013 Guo-Sheng Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper considers the energy consumption minimization in permutation flow shop (PFS) scheduling problem. The energy consumption of each machine is decomposed into two parts: useful part which completes the operation at current stage and wasted part which is consumed during idle period. The objective considered here is to minimize the total wasted energy consumption which is a weighted summation of the idle time of each machine. To solve this new problem, a branch-and-bound algorithm is developed. Two lower bounds are proposed, and an initial upper bound by using a variant of NEH heuristic algorithm is applied. Compared with the makespan minimization criterion, this model deduces more energy-saving solutions. Experimental results also validate the efficiency of the proposed algorithm for problems with job number not larger than 15.