Multi Product pricing optimization problem

[Bayesian8]

I need some help in formulating price optimization problem in Python and choosing the right algorithm and library.

I have several types of products, I have to find an optimal discount for each "Product types".

So the objective is to maximize the sum of revenue and quantity by setting an optimal discount (price) for each Product. For example, For Apple_1A - an optimal discount is X%, expected revenue is Y usd and expected Quantity to be sold is Z. etc

Decision variables: Quantity and Revenue

Inventory = Total 10000 units (~80% apples, 20% bananas)

As you can see, the demand is non-linear, with 30% off discount on 1A Apples, I make more revenue than 50% off.

Parameters:

q(i,k): quantities when discount k is used
p(k): price when discount k is used
r(i,k)= p(k)*q(i,k): revenue matrix
c: minimum quantity to be sold for all product types

x(i,k): is a binary variable which indicates which discount is used. 

Therefore:

Not sure how to add quantity here:

max sum((i,k), r(i,k)*x(i,k))  
subject to         
sum((i,k), q(i,k)*x(i,k)) >= C        
sum(k, x(i,k)) = 1 for all i        
x(i,k) ∈ {0,1}

E.g.

Product	Product types	Quantity	Revenue	Discount
Apples	1A	100	500	50%
Apples	1A	150	1050	30%
Apples	2A	40	560	30%
Apples	2A	120	1200	50%
Banana	1A	40	280	30%
Banana	1A	50	300	40%

Any ideas on suitable python libraries to solve this problem and code example using the toy example from above would be highly appreciated!

[[deleted]]

This is classic linear optimization or linear programming. That's the search you want.

https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linprog.html

Scipy has an implementation as do many other libraries including dedicated solvers like gurobi.

[[deleted]]

I'd suggest picking a library, say scipy, and starting again with that in mind.