Developing a "Score" for the pricing of a used car

remembering spock

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Greetings Mathematicians!

I am so rusty on my math, I don't even know if this is an algebra II question! I am trying to develop a way to score prices on used cars based on 3 variables; price, age, and mileage. All of these variable need to be somehow expressed on a sliding scale, for example a 2012 vehicle with 70000 miles being sold for 15K should not score as "high" as the same car being sold for 12K. I would think this will look like some kind of simple equation with slopes accompanying the main variables, but I am just conjecturing. The main problem is that when looking at used cars, they are always a little different. How do you "score" a 2012 vehicle with 50000 miles going for 13K against the same type of vehicle only its a 2015 with 33000 miles and going for 22K? This question assumes that cosmetic eliminators such as color, condition etc. are not necessary to factor in (automatic disqualifies). Can someone help me set this up?

Thanks!
 
Help with a Decision Matrix

Greetings everyone!
I am trying to make a decision matrix that will produce an overall "score" based on three mathematical criteria. All of the examples of decision matrices that I am finding require that you assign a value or ranking for each criteria based on a relative comparison to other options. That is not what I am trying to do; I would like a decision matrix that produces an overall value or score based on three criteria that are variable in scale, with the ability to apply weight or increased importance to the criteria as my wife (boss) and I see fit. We might only be evaluating one thing at a time, the goal of this is to see clearly based on our criteria's upper and lower limits. We are trying to evaluate the overall deal in used cars (which are not ever exactly equal to each other when comparing options) taking into account the following criteria:
Cost, on a scale of 0-$20,000 (lower is better)
age, on a scale of 0-8 years old (younger is better)
and mileage on a scale of 0-100000 miles (lower is better)

Again, we need the ability to weight the different criteria, but aren't certain exactly how to assign just yet. If I had to pick now, I would assign the cost at a weight of 3, mileage as a 2, and age as a 1 (provided all were on the scales listed above). Meaning, we think cost is the most important variable, mileage next, and age up to 8 years old is the least most important.

Ideally, plugging in one make of used car considering the year, cost and mileage would yield an overall "score" that could be compared to another make of used car, understanding that the cars will likely be different in every category.

One final thought, cosmetic issues such as color, interior condition, etc. aren't necessary for this. Those will be automatic eliminators. We are only evaluating the overall "deal" when looking at those three criteria while perusing the many options between dealers and independent sellers.

I hope this is clear! At one point, the Army showed me how to do this, but I can't seem to find the correct example on line.

Many thanks!
 
I would try the following approach:
1. Find a reasonable range of values for each attribute. E.g. age: 0-10, mileage: 0-50,000, etc.
2. Figure out the formula to calculate % based on the range and given value, with 100% corresponding to the best option. E.g. new car, 0 years - 100%, 8 years - 20%.
3. Decide on "relative weights of importance" for each attribute, set up a table in excel (see https://en.wikipedia.org/wiki/Weighted_sum_model)

For other methods see https://en.wikipedia.org/wiki/Multiple-criteria_decision_analysis.

Good luck!
 
Thanks Lev888

That is great advice, and very in line with what I was thinking. I ended up coming up with something that is working pretty well. I determined the limits of each criteria; no more than 25K in price, 115K in mileage, and 10 years old. Then I take the specifics of each vehicle that I am considering on Craigslist (I should mention that we are only in the market for a Toyota Tundra crewmax) and divide them by the max in that category, then inverse to get a score. The cost, which is the most important metric, is weighted double (or multiplied by 2). All three scores are then added to yield an overall score for that offer. So if the truck was being offered for 21.5K, the formula is 2(1/(215000/25000)), and if it had 85K miles the formula is 1/(85000/115000); you get the idea. BTW, most vehicles that we are tracking, from either dealer or private seller, are naturally scoring in the 5.1-5.4 range. If the vehicle scores 6 or over, it jumps out and we start negotiating, the lower we can get the price the higher the score ends up being. This just gives us a tool to evaluate if we are getting a good "deal" compared to all the other offers out there.

Thanks again for taking a minute to look at this.
 
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