Let us suppose that there are n jobs (J1, J2, … Jn) each of which takes a unit of time to be processed by a machine and there is just one single machine to process the jobs. Let us suppose that (d1, d2, d3, …dn) are the deadlines in units of times to complete the jobs and (p1, p2, p3, …pn) are the profits earned if the jobs are processed within the deadline. The objective is obviously to select those jobs and complete them within their deadlines so that maximum profit is earned. Design a greedy method to obtain the optimal sequence of jobs that will earn maximum profits. Demonstrate it on the case where there are four jobs, with n = 4, deadlines given by (d1 = 2, d2 = 1, d3 = 3, d4 = 1) and profits earned as (p1 = 100, p2 = 20, p3 = 50, p4 = 40).
[Job sequencing using deadlines]
Let us suppose that there are n jobs (J1, J2, … Jn) each of which takes a unit of
time to be processed by a machine and there is just one single machine to process
the jobs. Let us suppose that (d1, d2, d3, …dn) are the deadlines in units of times to complete the jobs and (p1, p2, p3, …pn) are the profits earned if the jobs are processed within the deadline. The objective is obviously to select those jobs and complete them within their deadlines so that maximum profit is earned.
Design a greedy method to obtain the optimal sequence of jobs that will earn
maximum profits. Demonstrate it on the case where there are four jobs, with n = 4,
deadlines given by (d1 = 2, d2 = 1, d3 = 3, d4 = 1) and profits earned as (p1 = 100,
p2 = 20, p3 = 50, p4 = 40).
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