I would like to understand optimization through a simple application, and then progressing towards understanding more general concepts. My inquiry starts with its application: Optimizing duration of activities in a day.
The length of the day and duration of each activity are known. The problem I'm seeking to solve is optimizing the length of each activity. No priorities are considered, so lengths are to be adjusted proportionally.
Here's an example: Assuming the allotted time is 16 hours and the sum of the duration of activities is greater than 16 hours, time slots are squeezed proportionally like this:
(Activity, Desired length, computed optimum length)
A, 3h, 2h 50min
B, 2h, 1h 55min
C, 1h, 0h 54min
Lacking a math background, I would appreciate guidance on where to start tackling this.
- What is this sort of optimization and related concepts called?
- What are the pros and cons of possible approaches?
- Any book recommendations?