Makespan minimization for multiple uniform machines

Authors:
Chien-Hung Lin;Ching-Jong Liao
Affiliations:
Department of International Trade, Jinwen University of Science and Technology, 99 An-Chung Road, Hsin-Tien, Taipei County 231, Taiwan;Department of Industrial Management, National Taiwan University of Science and Technology, Taipei, Taiwan
Venue:
Computers and Industrial Engineering
Year:
2008

Citing 6
Cited 1

Scheduling independent tasks on uniform processors

SIAM Journal on Computing
Tighter bounds for LPT scheduling on uniform processors

SIAM Journal on Computing
A polynomial approximation scheme for scheduling on uniform processors: Using the dual approximation approach

SIAM Journal on Computing
Scheduling identical jobs with unequal ready times on uniform parallel machines to minimize the maximum lateness

Computers and Industrial Engineering
Exact and Approximate Algorithms for Scheduling Nonidentical Processors

Journal of the ACM (JACM)
Makespan minimization subject to flowtime optimality on identical parallel machines

Computers and Operations Research

Minimizing the normalized sum of square for workload deviations on m parallel processors

Computers and Industrial Engineering

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Abstract

We consider a classical scheduling problem with makespan minimization on uniform parallel machines. From the viewpoint of workload, instead of completion time, two important theorems are developed for the problem. The first theorem provides an improved lower bound as the starting point for the search, and the second theorem further accelerates the search speed in the algorithm. Incorporating the two useful theorems, an algorithm is developed for obtaining the optimal solution. Although the developed algorithm has an exponential time complexity, extensive computational experiments demonstrate that it is quite efficient for various sizes of the problem. With the optimal algorithm, we also examine the effectiveness of the popular LPT heuristic.