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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 837910, 5 pages
http://dx.doi.org/10.1155/2014/837910
Research Article

Stochastic Machine Scheduling to Minimize Waiting Time Related Objectives with Emergency Jobs

1School of Management and Engineering, Nanjing University, Nanjing 210093, China
2School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China
3Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong

Received 14 March 2014; Accepted 24 April 2014; Published 11 May 2014

Academic Editor: Xiaolin Xu

Copyright © 2014 Lianmin Zhang 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.

Abstract

We consider a new scheduling model where emergency jobs appear during the processing of current jobs and must be processed immediately after the present job is completed. All jobs have random processing times and should be completed on a single machine. The most common case of the model is the surgery scheduling problem, where some elective surgeries are to be arranged in an operation room when emergency cases are coming during the operating procedure of the elective surgeries. Two objective functions are proposed to display this practice in machine scheduling problem. One is the weighted sum of the waiting times and the other is the weighted discounted cost function of the waiting times. We address some optimal policies to minimize these objectives.