# American Institute of Mathematical Sciences

July  2014, 10(3): 691-700. doi: 10.3934/jimo.2014.10.691

## Single-machine scheduling and due date assignment with rejection and position-dependent processing times

 1 School of Mathematics and Systems Science, Shenyang Normal University, Shenyang, Liaoning, 110034, China 2 State Key Laboratory Breeding Base of Nuclear Resources and Environment, East China Institute of Technology, Nanchang, Jiangxi 330013, China 3 Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China 4 Department of Statistics, Feng Chia University, Taichung

Received  April 2013 Revised  June 2013 Published  November 2013

This paper considers a single-machine scheduling and due date assignment problem in which the processing time of a job depends on its position in a processing sequence and jobs can be rejected by incurring penalties. The objective is to minimize the sum of the scheduling criterion of the accepted jobs and the total penalty of the rejected jobs. We first consider the problem with the common due date assignment method where the scheduling criterion is a cost function that includes the costs of earliness, tardiness, and due date assignment. We provide a polynomial-time algorithm to solve the problem. We then provide a unified model for solving the single-machine scheduling problem with rejection and position-dependent processing times. Finally, we extend the results to the setting involving various due date assignment methods.
Citation: Chuanli Zhao, Yunqiang Yin, T. C. E. Cheng, Chin-Chia Wu. Single-machine scheduling and due date assignment with rejection and position-dependent processing times. Journal of Industrial & Management Optimization, 2014, 10 (3) : 691-700. doi: 10.3934/jimo.2014.10.691
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