# Revolving Pool: Decision Function

## Decision Function

The decision function in the Tinlake contracts is using different weights to achieve the following order:

1. DROP Redeem
2. TIN Redeem
3. TIN Invest
4. DROP Invest

    uint                public weightSeniorRedeem  = 1000000;
    uint                public weightJuniorRedeem  =  100000;
    uint                public weightJuniorSupply =    10000;
    uint                public weightSeniorSupply =     1000;

Max Function:

max weightSeniorRedeem*DROP_Redeem + weightJuniorRedeem * TIN_Redeem + weightJuniorSupply*TIN_Invest + weightSeniorSupply*DROP_Invest

## Tasks
- Additional Research: Goal Programming. Does it makes sense, how we approach the problem after screening existing literature?
- Can the weights be improved? Are there any edge cases we didn't consider?
- Can our order priority list be always guranteed, can we produce counter examples?
- What should be the ideal weight difference factor? Currently it is 10x
- Should we increase it?
- Should we use preemptive goal programming or non-premetive goal programming?
- If we use non-preemptive goal programming what are the bests weights?
- Should we use a min function with penalization?

### Intro Goal Programming
Problem can be seen as a `Goal Programming` Problem.

- https://www.maths.ed.ac.uk/hall/Xpress/FICO_Docs/optimizer/HTML/section5004.html
Link is broken: See Web archive

Web archive link:
http://web.archive.org/web/20180711215700/http://www.maths.ed.ac.uk/hall/Xpress/FICO_Docs/optimizer/HTML/section5004.html

## Literature

### Book
- Practical Goal Programming Book, Springer
- https://link.springer.com/content/pdf/10.1007%2F978-1-4419-5771-9.pdf

### Relevant Papers
- A Glorious Literature on Linear Goal Programming Algorithms
- https://file.scirp.org/Html/2-1040278_44149.htm
- The double role of the weight factor in the goal programming model
- https://www.sciencedirect.com/science/article/abs/pii/S0305054803001424
- A Suggested Approach for Solving Weighted Goal Programming Problem
- http://article.sapub.org/10.5923.j.ajcam.20120202.10.html
- The setting of weights in linear goal-programming problems
- https://www.sciencedirect.com/science/article/abs/pii/0305054887900256

- An application of linear goal programming to the marketing distribution decision
www.sciencedirect.com/science/article/abs/pii/037722179190168U

- Bank Financial Statement Management using a Goal Programming
Model
https://www.sciencedirect.com/science/article/pii/S1877042815054063
- The Simplex Algorithm and Goal Programming
http://course.sdu.edu.cn/G2S/eWebEditor/uploadfile/20120921020943618.pdf

# Questions:
- Why are the different weights working if we only have 10x factor differences?
- Could it be possible that our decision function would prefer dropInvest over tinRedeem?

Example 1:

11 drop invest order
1 tin redeem order

- Assuming both are not possible because the TINratio would break

DROP_invest_weight = 1
TIN_redeem_weight = 10

- TIN_redeem should be always prefered over DROP_invest.
- TIN_redeem, DROP_invest are both reducing the ratio
- if we can't satisfy both orders, we still have 21 other combinations

(1 tin redeem, 0 drop invest)
(1 tin redeem, 1 drop invest)
(1 tin redeem, 2 drop invest)
(1 tin redeem, 3 drop invest)
(1 tin redeem, 4 drop invest)
...
(0 tin redeem, 9 drop invest)
(0 tin redeem, 10 drop invest)

- it is extremely unlikely that we can take exactly 10 drop invest or 1 tin redeem (same score increase) before the ratio breaks
- everytime we take one more DROP_invest or one TIN_redeem the ratio decreases (costs)
- we can see the negative impact on the ratio as costs
- 1 tinRedeem needs to have the same costs on the TINRatio as 10 DROPInvest which is very unlikely, therefore the TIN redeem will be always prefered because of the higher score
- if we look at the maxReserve constraint each invest (TIN or DROP) have the same costs
- both of them bring use one point closer to the maxReserve
- If TIN invest has a higher score(because of the weight) than DROP invest it will be always prefered because of the heigher score with the same costs