What is the role of optimization in commercial aircraft scheduling?

[lo2]

Hi there,

I need a topic for this Big Math 'Excercise' (do not know what to call it), it is a compulsive thing. I have chosen Math as the subject But I need a topic to write about. So if youn have any suggestions they will be most appreciated. My Math level is that of a High School student.

 

[murshid_islam]

what do you have to write? is it something like an essay?

 

[lo2]

what do you have to write? is it something like an essay?

Well I do not really know what you mean by Essay.

I think that it will be pretty much like a report, just there are no experiments.

 

[murshid_islam]

you can do it on RSA cryptosystem if you are interested in codes and cryptography. but you have to learn a little bit of modular arithmetic for that. or if you want something easier, you can do it on the history behind Fermat's Last Theorem. you can read the book "Fermat's Last Theorem" by Simon Singh for the history.

 

[Data]

There are obviously many branches of mathematics you could look at. What level are you at right now (ie. within high school - algebra, precalc, calculus)? What have you been most interested in with regard to mathematics so far (general subjects, though the more specific the better!)?

Also, some more details about what is expected of the report (I take it that it shouldn't be technical - maybe a review of some history of an area of mathematics?)

 

[lo2]

There are obviously many branches of mathematics you could look at. What level are you at right now (ie. within high school - algebra, precalc, calculus)? What have you been most interested in with regard to mathematics so far (general subjects, though the more specific the better!)?

Also, some more details about what is expected of the report (I take it that it shouldn't be technical - maybe a review of some history of an area of mathematics?)

I am at my last year at High School. The so called 'report' should explain the theory of the topic and then you can do some math probelsm to show that you have understood the theory.

But maybe differential equtations would be a a nice subject. But is there not also some math concerning polynomiums. And what about elipitic curves it that a bit to hardcore or could you pick that?

 

[berkeman]

If you have basic calculus (differentiation, optimization), then a fascinating topic is the optimization that is done for large scale complex scheduling problems. The commercial aircraft scheduling optimization problem is a good example. If (as a person working for one of the big airlines) you do a good job of chosing and scheduling your airline's flights, then you can save on fuel costs, personnel costs, etc., and you can become more popular as an airline because you have flights that fit the demands of your customer base well. If you chose your flights and scheduling poorly, then you waste time and fuel and maintenance costs.

It's an enoumously complex problem in real life, and you can address that level of complexity in your write-up. It also helps to motivate the subject by including some of the estimates in cost savings that have been acheived with good optimized computer scheduling algorithms. Then you can set up the math for a simpler example, say with 5 airplanes and 10-20 potential routes and schedules. Set up some basic equations that relate operating costs to route choices and scheduling, and show how to optimize that simplified example.

If I have time, I'll google a little to get you some intro articles, or you can do a little yourself to see what you find.