Shelf Space Optimization Routine

From where do I start, given a number of paint tins of different heights and diameters I need to maximise the number of tins in a given shelf space with given length, breadth and height?

An optimization problem ...

Thanks

[Matt J]

You start from office hours with your instructor. What hints did she give you?

[Peter Vella]

No instructor. I just need to solve this for myself .. I am aware that I need to formulate a maximization algorithim but I just asked for some hints as a startign point .. Thanks

[John D'Errico]

Start by deciding what you need to optimize. What do you want to solve? This is not even close to being a MATLAB problem. Not until you understand the mathematics does anything really become a programming problem. What shape are the tins? Circular cans, so right circular cylinders with varying radii and heights? Rectangular, in some shapes? Are the shapes and sizes known in advance, or are they random from some distribution?

You might want to read about packing problems. Perhaps the knapsack problem. Perhaps circle packing might be appropriate. You could also read about the cutting stock problem. We don't know, becaue you have said nothing about the shape of the objects you will be packing. But don't bother trying to write code to do anything at all, until you know what you need to solve.

And no. We won't write your code for you, in case that is where you might be going. I will point out that all of the named problems of this form are difficult to solve.

You do need to do some reading however.

[Peter Vella]

Dear John,

Thanks for the guidance. That's all I needed - Some starter guidance ... I am aware of the areas you noted and will do the necessary reading.

I was definately not after someone trying to write the code for me.

Thanks Again & Good Day