Solver - nonlinear - optimal fee structure

cbs2015

New Member
Joined
Aug 2, 2016
Messages
3
Hi all,

I am currently trying to create an optimal fee structure for a lead generation business. Members pay a yearly fee with a variable part, a commission for transaction, and can get money if they send us a lead that converts into a transaction.

Yearly fee: flat fee + X% of transaction revenue
Variable commission: Y% of transaction
Referral commission: Z% of transaction that was referred to us

Yearly fee: X% should be higher the more revenue is created for a member
Variable commission: Y% should be higher for members with a high X% and lower for clients with a low X%
Referral commission: Z% should increase with the amount of revenue generated through a member's referral to incentivize more referrals

So a potential structure could look like this:


-- removed inline image ---


Each member pays a total at the end of the year, TOTAL FEE = [Yearly fee + Variable commission - Referral commission]

All members should be treated as equally as possible - to compare this, I am using [TOTAL fee per member/TOTAL revenue received per member] per member and I am aiming for the lowest standard deviation for this ratio across the population of all members.

Goal:
Optimzie for lowest standard deviations

Constraints:
TOTAL fees >= 5,000,000
Fee structure should be ascending throughout the brackets and [<10%;>5%]
Commission structure should be descending throughout the brackets and [<15%;>10%]
Referral structure should be ascending throughout the brackets and [<3%;>2%]
46,000 < Average yearly fee across all members < 50,000

I have last year's data and all of the formulas to adjust the numbers set up, I seem to be struggling to set the constraints in the right way, though, and to deal with the non-linearity of the problem.

Any suggestions as to how to approach this?

Thanks!
 

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