A Mathematical Programming Approach for Online Hierarchical Scheduling

Authors:
Zhiyi Tan;An Zhang
Affiliations:
Department of Mathematics, State Key Lab of CAD & CG, Zhejiang University, China 310027;Department of Mathematics, State Key Lab of CAD & CG, Zhejiang University, China 310027
Venue:
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Year:
2009

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Abstract

This paper considers an online hierarchical scheduling problem on parallel identical machines. We are given a set of m machines and a sequence of jobs. Each machine has a different hierarchy, and each job also has a hierarchy associated with it. A job can be assigned to a machine only if its hierarchy is no less than that of the machine. The objective is to minimize makespan. Two models are studied in the paper. For the fractional model, we present an improved algorithm and lower bounds. Both algorithm and lower bounds are based on solutions of mathematical programming. For any given m , our algorithm is optimal by numerical calculation. For the integral model, we present both a general algorithm for any m , and an improved algorithm with better competitive ratios of 2.333 and 2.610 for m = 4 and 5, respectively.