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Summary: Improved Bicriteria Existence Theorems for Scheduling
Javed Aslam # April Rasala + Cli# Stein # Neal Young §
Dartmouth College
Two common objectives for evaluating a schedule
are the makespan, or schedule length, and the average
completion time. In this note, we give improved bounds
on the existence of schedules that simultaneously opti
mize both criteria.
In a scheduling problem, we are given n jobs and
m machines. With each job j we associate a non
negative weight w j . A schedule is an assignment of
jobs to machines over time, and yields a completion
time C j for each job j. We then define the average
completion time as # n
j=1 w j C j and the makespan as
Cmax = max j C j . We use C opt
max and
# w j C #
j to denote
the optimal makespan and average completion time.
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