Linear Program for the Problem
نویسندگان
چکیده
In this lecture, we study the topic of Job Scheduling. The problem of job scheduling is that if we have n jobs and m machines and we have a processing time pij of each machine i for each job j, the task is to find a schedule to assign the jobs to the m machines to complete all the n jobs such that the completion time of all jobs will be minimized. If each job j has the same running time pj on each of the machines, then the machines are said to be identical and a polynomial time approximation scheme (PTAS) can be derived for the problem, using the bin packing problem in Lecture 17. However, the problem we introduced here is for Unrelated Multiple Machines, which means the processing time pij of each machine i for each job j is different. This is quite natural as different processors (or different people) may have different capabilities on solving different tasks. In this lecture, we will design a 2-approximation algorithm for this problem. We first formulate this problem into a linear program.
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