I’m not sure if I’m wording this right but in a nutshell, my problem is:
I’m modelling potential actions a boat owner can do to their boat. Let’s say he wants to know over the 50 year lifespan of the boat, what’s the cheapest way to maintain the exterior paint.
He has three options:
Option 1: first paint at a cost of $1M/boat. Under this option, it is suggested (not a must) to redo the paint at within next 5 years of the previous paint job for the remainder life of the boat.
Option 2: If the boat has not been painted in the last 7 years, then it deteriorates to a point where it needs more significant repair at $1.4M. This will include repairs and paint at no extra cost.
Option 3: if the boat hasn’t been painted for more than 10 years straight, then some items would have to be replaced at a total cost of \$1.6M/boat. Under this option, he also must paint one year after the Option 3 repair at the same additional cost of $1M/boat.
For the sake of argument and more constraints:
- The surface area of the boat is 400 m2. (Costs should be divided by that number to get the per m2 cost)
- The boat was fully painted 2 years ago, so no paint is required on the boat until period >= 3.
- Minimum repair area = 25m2
At a max budget of \$200K/year for the first 6 years and a max budget of \$300K/yr after, how much should he do from Option 1, 2, and 3 to maximize the condition (painted area)?
Note, I’d like to run this as both a minimization of cost and maximization of condition separate models.
I’m struggling to build the constraints for this model especially the interaction variable on how to build the multiple constraints / variables and summarize them back into results.
Solution must be able to somewhat scale to
n boats and
i options, and
Initially I didn't include the deterioration Curve but there is one. I think for simplicity's sake, we can assume that deterioration occurs at a constant 3% a year and one of the constraints is to ensure that no more than 10% is in deteriorating condition.
Furthermore, at Option 1, returns the repaired section to 90% condition rate, option 2 to 95% and option 3 to 100%.