Consider the following preemptive variant of the Load Balancing problem: There are m identical machines, and n jobs with processing times t1, t2, ..... tn respectively. Each machine can process at most one job at a time. Each job can run on more than one machines but must run on at most one machine at any time. Let T = max{max1<=j<=n tj ,1/ m Σ 1<=j<=n tj } : (a) Prove that the optimal makespan is at least T. (b) Give a linear-time algorithm which produces a preemptive schedule with makespan exactly T.

Consider the following preemptive variant of the Load Balancing problem: There are m identical machines, and n jobs with processing times t1, t2, ..... tn respectively. Each machine can process at most one job at a time. Each job can run on more than one machines but must run on at most one machine at any time. Let T = max{max1<=j<=n tj ,1/ m Σ 1<=j<=n tj } : (a) Prove that the optimal makespan is at least T. (b) Give a linear-time algorithm which produces a preemptive schedule with makespan exactly T.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter9: Integer Programming

Section9.6: Solving Combinatorial Optimization Problems By The Branch-and-bound Method

Problem 2P

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