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Mathematical Problems in Engineering
Volume 2011, Article ID 151563, 19 pages
Research Article

Due-Window Assignment and Scheduling with Multiple Rate-Modifying Activities under the Effects of Deterioration and Learning

1School of Management, State Key Laboratory for Mechanical Manufacturing Systems Engineering and the Key Laboratory of the Ministry of Education for Process Control and Efficiency Engineering, Xi’an Jiaotong University, Shaanxi Province, Xi'an 710049, China
2Institut Charles Delaunay, Université de Technologie de Troyes and FRE CNRS 2848, Laboratoire d'Optimisation des Systémes Industriels (LOSI), 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex, France
3Laboratoire d'Informatique, Biologie Intégrative et Systèmes Complexes (IBISC), FRE CNRS 3190, Université d’Evry Val d’Essonne, 40 rue du Pelvoux, CE1455 Courcouronnes, 91020 Evry Cedex, France
4School of Economics and Management, Tongji University, Shanghai 200092, China

Received 3 September 2010; Accepted 31 January 2011

Academic Editor: Paulo Batista Gonçalves

Copyright © 2011 Zhanguo Zhu 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 discusses due-window assignment and scheduling with multiple rate-modifying activities. Multiple types of rate-modifying activities are allowed to perform on a single machine. The learning effect and job deterioration are also integrated concurrently into the problem which makes the problem more realistic. The objective is to find jointly the optimal location to perform multiple rate-modifying activities, the optimal job sequence, and the optimal location and size of the due window to minimize the total earliness, tardiness, and due-window-related costs. We propose polynomial time algorithms for all the cases of the problem under study.