Convex quadratic and semidefinite programming relaxations in scheduling
Journal of the ACM (JACM)
Designing PTASs for MIN-SUM Scheduling Problems
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Lower bounds for on-line single-machine scheduling
Theoretical Computer Science
Journal of Global Optimization
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Management Science
Designing PTASs for MIN-SUM scheduling problems
Discrete Applied Mathematics - Special issue: Efficient algorithms
On the relationship between combinatorial and LP-based lower bounds for NP-hard scheduling problems
Theoretical Computer Science - Approximation and online algorithms
An Experimental Study of LP-Based Approximation Algorithms for Scheduling Problems
INFORMS Journal on Computing
Computation of approximate α-points for large scale single machine scheduling problem
Computers and Operations Research
Proceedings of the 2007 Summer Computer Simulation Conference
A global constraint for total weighted completion time for cumulative resources
Engineering Applications of Artificial Intelligence
A Global Constraint for Total Weighted Completion Time
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Stochastic Online Scheduling Revisited
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Encouraging Cooperation in Sharing Supermodular Costs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Designing PTASs for MIN-SUM scheduling problems
Discrete Applied Mathematics - Special issue: Efficient algorithms
Mechanism Design for Decentralized Online Machine Scheduling
Operations Research
Operations Research
LP-based online scheduling: from single to parallel machines
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
List scheduling in order of α-points on a single machine
Efficient Approximation and Online Algorithms
Efficient algorithms for average completion time scheduling
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
On-line scheduling to minimize average completion time revisited
Operations Research Letters
Computers and Operations Research
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We consider the scheduling problem of minimizing the average weighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on a time-indexed formulation, the other on a completion-time formulation. We show their equivalence by proving that a O(n log n) greedy algorithm leads to optimal solutions to both relaxations. The proof relies on the notion of mean busy times of jobs, a concept which enhances our understanding of these LP relaxations. Based on the greedy solution, we describe two simple randomized approximation algorithms, which are guaranteed to deliver feasible schedules with expected objective function value within factors of 1.7451 and 1.6853, respectively, of the optimum. They are based on the concept of common and independent $\alpha$-points, respectively. The analysis implies in particular that the worst-case relative error of the LP relaxations is at most 1.6853, and we provide instances showing that it is at least $e/(e-1) \approx 1.5819$. Both algorithms may be derandomized; their deterministic versions run in O(n2) time. The randomized algorithms also apply to the on-line setting, in which jobs arrive dynamically over time and one must decide which job to process without knowledge of jobs that will be released afterwards.