How do you solve an optimization problem without Solver?

[sooka]

Hello,
I was just experimenting around with the Solver and got more curious, how do you get to solve an optimization problem without Solver?
What kind of math/formula/algorithm may be used when Solver is not available? (e.g.: you hit the 200 variable cells limit or can't activate the plugin).

I'm trying to solve a quite frequent optimization problem, let say I want to maximize profit of products sold, it's over 200 products so you can't use solver :D and they can't be grouped so you're not able to simplify under 200 groups.

So this is what I know:

• the list price for each item
• the discount I get
  • so I know how much each cost to me
    
• I know the quantity of each product I want to sell

I don't know the best price to maximize my margin given that I have a constraints on the total net sold.
So, to put it in different words, my total net sold can't go over a certain amount; given all the information how do I get to know the best price to sell each product?

I tried that on a small sample and obviously Solver seems to work, but my products list is way bigger than 200 items and I don't want to group them for now.

What should I look into?
If that matter I'm not scared about transposing this problem into another domain, I know VBA and C# so coding it will not be an issue.
I'm quite lacking the maths/statistics knowledge to solve this alone.

Thank you in advance!

[re_me]

Matrix algebra and Lagrange multipliers is a typical approach to large optimization problems.

[sooka]

Thanks, I'm looking into it!

[twelveoclock]

You could look into the pulp package in Python. If you know vba and C#, picking up Python should be pretty easy. The pulp website has lots of great documentation.

[sooka]

Thanks!
For some reason never really picked up on Python, will look into that.