標題: Minimizing machine assignment costs over Delta-approximate solutions of the scheduling problem P parallel to C-max
作者: Kononov, A. V.
Kovalyov, M. Y.
Lin, B. M. T.
資訊管理與財務金融系 註:原資管所+財金所
Department of Information Management and Finance
關鍵字: Scheduling;Bicriteria optimization;Approximation;Computational complexity;Fixed parameter tractability
公開日期: 12-Nov-2019
摘要: Bi-criteria lexicographical minimization problems with the makespan as the primary objective and the total machine assignment costs as the secondary objective have been recently introduced to the scheduling research, and polynomial time (r + 1, 1)-approximation algorithms have been suggested for their solution, where 1 < r < 2 is the performance ratio of an approximation algorithm for P parallel to C-max. We improve these results by presenting a polynomial time (1.5r - 1, 1)-approximation algorithm for the additive cost type. Then, we introduce a problem of minimizing the total machine assignment cost over the Delta-approximate solutions of the makespan minimization problem. We prove that this new problem is strongly NP-hard and pseudo-polynomially non-approximable in general. A polynomial time approximation algorithm with a guaranteed approximation ratio is presented for the additive cost type and bounded ratio between the maximal and minimal machine costs. An O (mn(2k)) time dynamic programming algorithm is also presented, where k is the fixed number of distinct job processing times. (C) 2019 Elsevier B.V. All rights reserved.
URI: http://dx.doi.org/10.1016/j.tcs.2019.05.024
http://hdl.handle.net/11536/153046
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2019.05.024
期刊: THEORETICAL COMPUTER SCIENCE
Volume: 793
起始頁: 70
結束頁: 78
Appears in Collections:Articles