TY - JOUR

T1 - Minimizing machine assignment costs over Δ-approximate solutions of the scheduling problem P||Cmax

AU - Kononov, A. V.

AU - Kovalyov, M. Y.

AU - Lin, Bertrand M.T.

PY - 2019/11/12

Y1 - 2019/11/12

N2 - 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 1max. 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 Δ-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(mn2k) time dynamic programming algorithm is also presented, where k is the fixed number of distinct job processing times.

AB - 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 1max. 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 Δ-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(mn2k) time dynamic programming algorithm is also presented, where k is the fixed number of distinct job processing times.

KW - Approximation

KW - Bicriteria optimization

KW - Computational complexity

KW - Fixed parameter tractability

KW - Scheduling

UR - http://www.scopus.com/inward/record.url?scp=85067263892&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2019.05.024

DO - 10.1016/j.tcs.2019.05.024

M3 - Article

AN - SCOPUS:85067263892

VL - 793

SP - 70

EP - 78

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -