The Single Machine Problem with Quadratic Penalty Function of Completion Times: A Branch-and-Bound Solution

1978 ◽  
Vol 24 (5) ◽  
pp. 530-534 ◽  
Author(s):  
W. Townsend
Keyword(s):  
Branch And Bound ◽  
Single Machine ◽  
Penalty Function ◽  
Bound Solution ◽  
Completion Times ◽  
Quadratic Penalty Function ◽  
Machine Problem

The Single Machine Problem with a Quadratic Cost Function of Completion Times

1988 ◽  
Vol 34 (12) ◽  
pp. 1480-1488 ◽  
Author(s):  
Wlodzimierz Szwarc ◽  
Marc E. Posner ◽  
John J. Liu
Keyword(s):  
Cost Function ◽  
Single Machine ◽  
Quadratic Cost ◽  
Quadratic Cost Function ◽  
Completion Times ◽  
Machine Problem

scholarly journals AN EXACT APPROACH FOR THE SINGLE MACHINE SCHEDULING PROBLEM WITH LINEAR EARLY AND QUADRATIC TARDY PENALTIES

2008 ◽  
Vol 25 (02) ◽  
pp. 169-186 ◽  
Author(s):  
JORGE M. S. VALENTE
Keyword(s):  
Branch And Bound ◽  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Dominance Test ◽  
Branch And Bound Algorithms ◽  
Exact Approach ◽  
Lower Bounding ◽  
Completion Times

In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We propose a lower bounding procedure based on the relaxation of the jobs' completion times. Optimal branch-and-bound algorithms are then presented. These algorithms incorporate the proposed lower bound, as well as an insertion-based dominance test. The branch-and-bound procedures are tested on a wide set of randomly generated problems. The computational results show that the branch-and-bound algorithms are capable of optimally solving, within reasonable computation times, instances with up to 20 jobs.

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