The document discusses the job sequencing with deadlines problem, aiming to maximize profits by scheduling jobs within given deadlines. It highlights the need to sort jobs by profit and outlines constraints such as a unit time for each job. The optimal solution achieves maximum profit while ensuring that jobs are completed on or before their deadlines.

1. Job Sequencing With Deadlines
By,
M. Sabiha
MCA 2nd Year

3. Problem Statement
In Job Sequencing Deadline Problem, the
objective is to find the sequence of jobs,
which is completed within their deadline
and gives maximum profit.

4. Solution
Let us consider a set of ‘n’ jobs which are
associated with deadlines.
We need to focus on three things here:
(a) The profit is earned if a job is completed.
(b) Jobs must be in an order.
(c) Maximum profit.

5. Constraints
Assume,
Then, the optimal solution of this
algorithm is a feasible solution with
maximum profit.
Deadline of ith job Ji = D(i)
Profit = Pi

6. Thus,
D(i) > 0 for 1 ≤ i ≤ n
p1 ≤ p2 ≤ p3 ≤ … ≤ pn

8. J1 J2 J3 J4 J5
2 1 3 2 1
60 100 20 40 20

9. Now, let’s sort the jobs according to their
profit …
J2 J1 J4 J3 J5
1 2 2 3 1
100 60 40 20 20
J1 J2 J3 J4 J5
2 1 3 2 1
60 100 20 40 20

10. J2 J1 J4 J3 J5
1 2 2 3 1
100 60 40 20 20
J2
J5
J1
J4
J3
Deadline
The Job Sequence:
( J2, J1, J3 )
The Maximum Profit:
100 + 60 + 20 = 180

11. Points to remember…
1. In ‘Job Sequencing With Deadline’ problem we have n jobs
J1, J2, … , Jn each has an associated deadline D1, D2, … , Dn
and profit P1, P2, ... , Pn.
2. Profit will only be awarded or earned if the job is
completed on or before the deadline.
3. We assume that each job takes unit time to complete.
4. The objective is to earn maximum profit when only one
job can be scheduled or processed at any given time.