Graph Theory Unit 2

2.11 Critical Path

The Art of Multi-tasking 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

*things that MUST be done first* 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 Description Time Prerequisite A B

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

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?

*great practice for common exam questions* 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