What is Job Sequencing with Deadlines?In a job sequencing with deadlines problem, the objective is to find a sequence of jobs completed within their deadlines, giving a maximum profit. Let us consider the set of n given jobs associated with deadlines, and profit is earned if a job is completed by its deadline. These jobs need to be ordered so that the maximum profit is earned. Show
It may happen that all the given jobs can not be completed within their deadlines. Assume that the deadline of ith job Ji is di and the profit received from job Ji is pi. Hence, the optimal solution of job sequencing with deadlines algorithm is a feasible solution with maximum profit. Points to Remember for Job Sequencing with Deadlines
Job Sequencing with Deadlines AlgorithmSuppose there are jobs J(i) with the deadline D(i) and profit P(i) where 0≤i≤1. These jobs are ordered according to profit p1⩾p2⩾p3⩾...⩾pn. Job-Sequencing-With-Deadline (D, J, n, k) D(0) := J(0) := 0 k:= 1 J(1) := 1 // means first job is selected for i = 2 … n do r:= k while D(J(r)) > D(i) and D(J(r)) ≠ r do r:= r – 1 if D(J(r)) ≤ D(i) and D(i) > r then for l = k … r + 1 by -1 do J(l + 1): = J(l) J(r + 1): = i k:= k + 1 Job Sequencing with Deadlines ExampleLet us consider a given job sequencing problem, as shown in the table below. We have to find the sequence of jobs completed within their deadlines and give the maximum profit. Each job is associated with the deadline and profit as given below:
The given jobs are sorted as per their profit in descending order to solve this problem. Hence, the jobs are ordered after sorting, as shown in the following table.
From the given set of jobs, first, we select J2, as it should be completed within its deadline and contributes maximum profit.
Therefore, the sequence of jobs (J2, J4, J5) is executed within their deadline and gives the maximum profit. The total profit of the sequence is 100 + 60 + 20 = 180.
The sequencing of jobs on a single processor with deadline constraints is called as Job Sequencing with Deadlines. Here-
The problem states- “How can the total profit be maximized if only one job can be completed at a time?” Approach to Solution-
Greedy Algorithm-Greedy Algorithm is adopted to determine how the next job is selected for an optimal solution. The greedy algorithm described below always gives an optimal solution to the job sequencing problem- Step-01:
Step-02:
Step-03:
PRACTICE PROBLEM BASED ON JOB SEQUENCING WITH DEADLINES-Problem-Given the jobs, their deadlines and associated profits as shown-
Answer the following questions-
Solution-Step-01:Sort all the given jobs in decreasing order of their profit-
Step-02:Value of maximum deadline = 5. So, draw a Gantt chart with maximum time on Gantt chart = 5 units as shown- Now,
Step-03:
Step-04:
Step-05:
Step-06:
Step-07:
Now,
Now, the given questions may be answered as- Part-01:The optimal schedule is- J2 , J4 , J3 , J5 , J1 This is the required order in which the jobs must be completed in order to obtain the maximum profit. Part-02:
Part-03:Maximum earned profit = Sum of profit of all the jobs in optimal schedule = Profit of job J2 + Profit of job J4 + Profit of job J3 + Profit of job J5 + Profit of job J1 = 180 + 300 + 190 + 120 + 200 = 990 units To gain better understanding about Job Sequencing With Deadlines, Watch this Video Lecture Next Article- Huffman Coding Get more notes and other study material of Design and Analysis of Algorithms. Watch video lectures by visiting our YouTube channel LearnVidFun. Summary Article Name Job Sequencing With Deadlines | Algorithm | Example Description Job Sequencing with Deadlines- The sequencing of jobs on a single processor with deadline constraints is called as Job Sequencing with Deadlines. Greedy Algorithm is adopted to solve this problem. Job Sequencing with Deadlines Example. Author Akshay Singhal Publisher Name Gate Vidyalay Publisher Logo What is job sequencing with example?The sequencing of jobs on a single processor with deadline constraints is called as Job Sequencing with Deadlines. You are given a set of jobs. Each job has a defined deadline and some profit associated with it. The profit of a job is given only when that job is completed within its deadline.
What is job sequencing in operating system?Job scheduling is the process of allocating system resources to many different tasks by an operating system (OS). The system handles prioritized job queues that are awaiting CPU time and it should determine which job to be taken from which queue and the amount of time to be allocated for the job.
What is job scheduling and job sequencing?Sequencing is the order of tasks to be done in chain. Hence the next task is started once the previous one is completed. Scheduling, on the other hand is the process in which people are assigned to time to accomplish different tasks. It improves the delivery performance and reduces the manufacturing time and cost.
What is job sequencing in optimization techniques?The job sequencing technique is used to determine an optimal sequence. It performs a series of jobs by a number of specific orders so that it calculates the optimal cost. In this paper, we propose a novel approach to find an optimal path from source to destination by taking advantage of job sequencing technique.
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