Graph Theory Unit 2 2 11 Critical Path

Graph Theory Unit 2

2. 11 Critical Path

Cooking Dinner • Let’s make a steak and potato dinner • We want: – Salad – Baked Potatoes – BBQ Steak • How do we get it all done? The Art of Multi-tasking

Multi-tasking • Certain jobs will take your full concentration, but then you get it to a point and “there’s no need to watch the kettle boil” • If you do, your jobs will take you a lot longer to complete. • This leads us to planning your process

Planning Process • You can make a list of all of the tasks that much be completed and the amount of time each task takes. • On this list you would also include any ‘prerequisite tasks’* *things that MUST be done first* Task A B Description Time Prerequisite

Example: Starting a Company Step A B C D E F G H Description Preparing a business plan Conducting market research Looking for partners Looking for a location Analyzing the market research Evaluating the product-distribution systems Arranging for financing Launching the company Execution Time (days) Prior Steps 30 10 25 20 5 15 35 None A A A B C and D E and F G

Turning Chart into a Graph • You are reading the chart one row at a time from right to left • There will always be at least one vertex with NO Prerequisite Steps – Start with this vertex • Next, identify the vertices that name that vertex as their prerequisite steps. – Draw these to the right of the first vertex, connect with a directed edge and weight the edges with the time it takes to complete the prerequisite step. • Continue with this process until all steps are accounted for

The Final Graph • Vertices represent Tasks • Parallel paths represent series of tasks that can be carried out simultaneously (multi-tasking)

Questions • Which is the first task that must be completed? • Which is the last task that will be completed? • What are all of the possible paths from start to finish?

Critical Path • The Critical Path is the LONGEST path from the start of the project to the finish. • You do not have to go to/through every vertex – This is because you are multitasking • The Critical Path represents the MINIMUM AMOUNT OF TIME it would take to complete the entire project.

Questions • Which of the following paths is the critical path? ABEGH = 80 ACFGH = 105 ADFGH = 100 • What is the minimum amount of time it would take to Start this Company?

2. 11 Practice • Visions Book 2 • Page 52 #3, 5, 17, 19, 21* *great practice for common exam questions*

2. 11 Practice 2 • Carousel • Page 120 #1 -5