On the Relationship Between Combinatorial and LP-Based Approaches to NP-Hard Scheduling Problems

@inproceedings{Uma1998OnTR,
  title={On the Relationship Between Combinatorial and LP-Based Approaches to NP-Hard Scheduling Problems},
  author={R. N. Uma and Joel Wein},
  booktitle={IPCO},
  year={1998}
}
Enumerative approaches, such as branch-and-bound, to solv- ing optimization problems require a subroutine that produces a lower bound on the value of the optimal solution. In the domain of scheduling problems the requisite lower bound has typically been derived from either the solution to a linear-programming relaxation of the problem or the solution of a combinatorial relaxation. In this paper we investigate, from both a theoretical and practical perspective, the relationship between several… 
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This paper gives a comprehensive experimental study of a number of approximation algorithms for the problem of scheduling jobs with release dates on one machine so as to minimize the average weighted completion time of the jobs scheduled, and observes that on most kinds of synthetic data used in experimental studies a simple greedy heuristic outperforms all of the LP-based heuristics.
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