Question
Consider the following job scheduling problem. m machines, all identical. There are n jobs, and job j has processing time (or size) tj . Each
Consider the following job scheduling problem. m machines, all identical. There are n jobs, and job j has processing time (or size) tj . Each job must be assigned to exactly one machine. The load of a machine is the sum of the sizes of the jobs that get assigned to it. The makespan of an assignment of jobs is the maximum load over all the machines; this is the quantity that we want to minimize.
(a) (6 points) Suppose we have an instance where there are two machines and 4 jobs with sizes 7, 8, 5, and 6.
i. If we assign the first two jobs to the first machine and the last two jobs to the second machine, what will the load be on each machine?
ii. What will the makespan be?
iii. How can the assignment be modified to yield the optimal makespan?
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started