Job Scheduling Problem

AI Summary

An AI-generated summary of this video lecture.

The video lecture introduces the Job Scheduling Problem, a classic optimization problem in computer science. The instructor begins by defining the problem parameters on a slide: a single CPU, non-primitive scheduling, and n-jobs where each job has an arrival time of 0, a burst time of 1, a deadline Di, and a profit Pi. The objective is to select a subset of jobs that can be completed within their deadlines to maximize total profit. A visual chart titled '10X10 Job Shop Scheduling Problem' is displayed to illustrate an unconstrained schedule. The lecture then transitions to a specific numerical example from a GATE 2005 exam question involving 9 tasks (T1 to T9). The instructor demonstrates a greedy algorithm approach, drawing a timeline and filling slots with tasks based on their profits and deadlines to determine the optimal schedule and identify which tasks must be left out.

Chapters

1. 0:00 – 2:00 00:00-02:00

   The instructor presents the problem definition on a slide titled 'Job scheduling problem'. He highlights key constraints: 'single CPU with Non-Primitive Scheduling and n-jobs'. He specifies that 'arrival time is 0, burst time of each job requirement is 1'. The goal is to 'Select a Subset of 'n' jobs, such that, the jobs in the subset can be completed with in the deadline and generate Max profit.' A chart labeled '10X10 Job Shop Scheduling Problem' shows colored bars representing an 'Unconstrained Schedule'. The instructor underlines 'Non-Primitive Scheduling' and circles 'deadline Di'. He writes 'J1 -> S' on the screen, indicating the mapping of a job to a time slot. The slide also mentions 'Knowledge Gate Educator' and 'Sanchit Jain Sir' in the bottom left corner.

2. 2:00 – 5:00 02:00-05:00

   The slide changes to a specific problem statement: 'Q. We are given 9 tasks T1, T2... T9.' A table lists tasks, profits, and deadlines. For example, T3 has profit 30 and deadline 5. T1 has profit 15 and deadline 7. The question asks, 'Are all tasks completed in the schedule that gives maximum profit? (Gate-2005) (2 Marks)'. Four options are provided: (A) All tasks are completed, (B) T1 and T6 are left out, (C) T1 and T8 are left out, (D) T4 and T6 are left out. The instructor draws a timeline with 9 boxes labeled 1 through 9. He begins solving by writing 'T3' into slot 3, as it has the highest profit (30) and a deadline of 5. He then writes 'T7' into slot 2 (profit 23, deadline 2).

3. 5:00 – 6:50 05:00-06:50

   The instructor continues filling the timeline to construct the optimal schedule. He writes 'T9' (profit 25, deadline 3) into slot 1. He places 'T2' (profit 20, deadline 2) into slot 2, but then adjusts. Looking at the final board state, the slots are filled as: Slot 1 with T2, Slot 2 with T7, Slot 3 with T9, Slot 4 with T5, Slot 5 with T3, Slot 6 with T1, and Slot 7 with T8. This arrangement satisfies all deadlines. The tasks T4 and T6 are not placed in any slot. The instructor concludes that T4 and T6 are the tasks left out, corresponding to option (D). The board shows the final schedule clearly.

The lecture effectively bridges theoretical problem definition with practical application. It starts by establishing the constraints of the Job Scheduling Problem, emphasizing the trade-off between deadlines and profits. The instructor then applies a greedy strategy to a concrete example, visually demonstrating how to map tasks to time slots. By sorting tasks by profit and placing them in the latest possible slot before their deadline, he derives the optimal subset of jobs. The final board state clearly shows which tasks are feasible and which are excluded, reinforcing the algorithmic approach to solving scheduling problems.