Real-Life Math
You are a construction manager. You have just won a bid to renovate an office building.
Now the real work begins. There are several steps to renovating a building, from demolishing walls to installing electrical equipment.
In order to not go over budget, you need to complete the project in the least amount of time possible. In order to accomplish this, you rely on a tool called critical path management (CPM).
A critical path is a drawing outlining the order in which each phase of the project must be completed in order for the entire project to be completed in the least amount of time. Some jobs must be completed before another job can be started, while some jobs can be worked on at the same time. A critical path helps organize the project.
To create a critical path, you begin by writing down all the jobs that must be completed and the estimated time each job will take. You also assign a letter to each job.
A = Finalize blueprints = 2 weeks
B = Demolish unneeded old walls = 3 weeks
C = Finalize contracts with subcontractors = 2 weeks
D = Frame new walls = 4 weeks
E = Install heating, ventilation and air conditioning = 1 week
(This would include things like putting in heat registers and air ducts)
F = Install plumbing where needed = 3 weeks
G = Install electrical wiring in the walls, such as electrical switches and plug-ins = 5 weeks
H = Finish the walls by putting plaster over them = 2 weeks
If you waited to complete each job before starting another one, the project would take a total of 22 weeks to complete:
2 + 3 + 2 + 4 + 1 + 3 + 5 + 2 = 22
That is too long. But you can't just start ordering carpenters, electricians and laborers to begin working all at once. There are certain restrictions.
For example, the blueprints must be completed before any other work can begin. The old walls must be demolished before the new walls can be framed. Framing must be finished before you can start installing heat ducts or electrical wiring. And all the other work must be completed before you begin plastering the walls.
But, for example, E and F can be completed at the same time as G, and in a shorter time. That means you only need to account for enough time to finish G -- you don't need to add extra time for E and F.
How can you organize the order of the work in such a way that the project will be completed in as short a period of time as possible?