Parallel Machine Scheduling, Linear Programming, and Parameter List Scheduling Heuristics

Authors:
Lap Mui Ann Chan;Ana Muriel;David Simchi-Levi
Affiliations:
-;-;-
Venue:
Operations Research
Year:
1998

Citing 0
Cited 4

Approximation in stochastic scheduling: the power of LP-based priority policies

Journal of the ACM (JACM)
Evaluation of mixed integer programming formulations for non-preemptive parallel machine scheduling problems

Computers and Industrial Engineering
List scheduling in order of α-points on a single machine

Efficient Approximation and Online Algorithms
An approximate algorithm for a high-multiplicity parallel machine scheduling problem

Operations Research Letters

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Abstract

In this paper we consider a class of parallel machine scheduling problems and their associated set-partitioning formulations. We show that the tightness of the linear programming relaxation of these formulations is directly related to the performance of a class of heuristics called parameter list scheduling heuristics. This makes it possible to characterize the worst possible gap between optimal solutions for the scheduling problems and the corresponding linear programming relaxations. In the case of the classical parallel machine weighted completion time model we also show that the solution to the linear programming relaxation of the set-partitioning formulation is asymptotically optimal under mild assumptions on the distribution of job weights and processing times. Finally, we extend most of the results to the time-discretized formulation of machine scheduling problems.