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Mathematical Problems in Engineering
Volume 2017, Article ID 5791796, 8 pages
Research Article

A Single-Machine Scheduling Problem with Uncertainty in Processing Times and Outsourcing Costs

1Department of Industrial and Management Systems Engineering, Kyung Hee University, 1732 Deogyeong-daero, Giheung-gu, Yongin-si, Kyunggi-do 17104, Republic of Korea
2Department of Business Administration, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea

Correspondence should be addressed to Byung-Cheon Choi;

Received 13 December 2016; Accepted 22 February 2017; Published 5 March 2017

Academic Editor: Sabri Arik

Copyright © 2017 Myoung-Ju Park and Byung-Cheon Choi. 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.


We consider a single-machine scheduling problem with an outsourcing option in an environment where the processing time and outsourcing cost are uncertain. The performance measure is the total cost of processing some jobs in-house and outsourcing the rest. The cost of processing in-house jobs is measured as the total weighted completion time, which can be considered the operating cost. The uncertainty is described through either an interval or a discrete scenario. The objective is to minimize the maximum deviation from the optimal cost of each scenario. Since the deterministic version is known to be NP-hard, we focus on two special cases, one in which all jobs have identical weights and the other in which all jobs have identical processing times. We analyze the computational complexity of each case and present the conditions that make them polynomially solvable.