### Author Topic: Quantifying Reasonableness  (Read 798 times)

#### dandarc

• Magnum Stache
• Posts: 3113
• Age: 35
##### Quantifying Reasonableness
« on: August 29, 2017, 09:04:42 AM »
Background:

The project I work on is tasked with controlling costs.  The basic method is this:

1.  Calculate mean price paid for each item we buy - we'll call this A (example 1.00)
2.  Set maximum payable price to A + A * X% = MPP (example 1 + 1 * 20% = 1.20)
3.  Go through each transaction over the reporting period, and "knock down" any prices that are above MPP (example - transaction was for 1.30, we collect .10)
4.  Total all the amounts in 3 and collect - basically we just don't pay a vendor in the next month until the amount is covered.

We've been doing this since 2013, and have settled on a value of X that seems fair and practical, however we're being asked to demonstrate the chosen value for X is "reasonable".

So far, we've only been able to provide qualitative arguments - "Well, at X we are collecting a non-trivial amount, and our vendors are not complaining.  When X was lower, they complained much more.  If X gets much higher, we won't be collecting as much."

I guess I'm wondering if anyone knows of a statistical method we could apply that would demonstrate that X is reasonable?  It will make our lives a lot easier if we had a report that established a range of "reasonable" values for X and show that our value of X is within the range.  Just too far removed from doing anything like this to think of a good way to do this.

#### ncornilsen

• Pencil Stache
• Posts: 800
##### Re: Quantifying Reasonableness
« Reply #1 on: August 29, 2017, 12:51:59 PM »
how do you establish "A?"   It sounds like by averaging your costs for similar items.... Why do you spread your purchases around like that?

how do your vendors agree to continue working with you if you abritrarly give thier invoices a X% haircut every period?  I'd guess because you give them a x% haircut, and they're charging you x%+5% over what it could cost.

I install industrial equipment, and given our purchasing power, we lock in an hourly rate, and a mark up on the hardware. I can audit any job I want. might be a way to do it.

Maybe you can should competively bid for contracts for your key materials... lock in your prices for a certain timeframe. then you can quit wasting time with these excercises that probably just piss your vendors off or cause them to find other ways to game you.
« Last Edit: August 29, 2017, 12:53:51 PM by ncornilsen »

#### MDM

• Walrus Stache
• Posts: 8074
##### Re: Quantifying Reasonableness
« Reply #2 on: August 29, 2017, 12:54:08 PM »
I guess I'm wondering if anyone knows of a statistical method we could apply that would demonstrate that X is reasonable?  It will make our lives a lot easier if we had a report that established a range of "reasonable" values for X and show that our value of X is within the range.  Just too far removed from doing anything like this to think of a good way to do this.
If you have enough transactions, you could fit the prices to some distribution (normal; Poisson; whatever; etc.) and then show that your X is within some cumulative distribution limits.

Don't know, however, how you get around the underlying issue of how much "you" get vs. how much "they" get....

#### Freedom2016

• Pencil Stache
• Posts: 529
##### Re: Quantifying Reasonableness
« Reply #3 on: August 29, 2017, 01:29:37 PM »
Are you buying commodities in which there is no value differential between what vendor A and B and C are selling you? What else does your company care about besides cost containment? (e.g. speed, service, quality) And what is the priority order of those interests?

Is it worth saving 10% if what you get is 30% worse in delivered value?

Without more information, the percentage seems arbitrary and hard to defend. I spend a lot of time with clients coaching them on how to address positional bargaining tactics like this. :)

#### dandarc

• Magnum Stache
• Posts: 3113
• Age: 35
##### Re: Quantifying Reasonableness
« Reply #4 on: August 29, 2017, 01:30:40 PM »
Trying not to be evasive, so I'll just say this is a government welfare program - the specifics of why are not relevant, but we are required to control our costs in an environment where we are not directly negotiating each purchase with each vendor.  All that is to say, the method described above is not what is at question - this is what is happening and it isn't going to change.  It is an approved method by our over-sight, and is used in many other states.

A in the process above is a simple average Total Dollars Paid / Total items purchased - sure we do some categorization, and there are complexities to it, but once everything is categorized appropriately nobody is questioning how we compute A.

What we are being asked to review and justify as "reasonable" is our choice for the value of X - the percentage applied to determine a maximum allowed price.  As mentioned, we can explain in words how we arrived at this particular value for X, but we're now being asked to demonstrate that X is appropriate.  To date, we've provided the qualitative analysis, but it would help us to establish an objective criteria.

Basically if we can come up with another method to look at our data which will say "cost containment haircut should be between Y and Z.  X results in a reasonably sized haircut based on being in this range", it would simplify our lives a lot.  I just don't know of a valid technique for coming up with that "valid range", because we're not being told anything other than "X must be reasonable".

#### dandarc

• Magnum Stache
• Posts: 3113
• Age: 35
##### Re: Quantifying Reasonableness
« Reply #5 on: August 29, 2017, 01:45:26 PM »
I guess I'm wondering if anyone knows of a statistical method we could apply that would demonstrate that X is reasonable?  It will make our lives a lot easier if we had a report that established a range of "reasonable" values for X and show that our value of X is within the range.  Just too far removed from doing anything like this to think of a good way to do this.
If you have enough transactions, you could fit the prices to some distribution (normal; Poisson; whatever; etc.) and then show that your X is within some cumulative distribution limits.

Don't know, however, how you get around the underlying issue of how much "you" get vs. how much "they" get....
Yeah - we were thinking of trying something like " within 2 standard deviations = acceptable " or something like that, but then you get into how to compute standard deviation, not to mention why
2 SDs and not 1 or 3 or 7, is the data normally distributed?

One thing we do have is a lot of transactions.  Over 4.5 million last month.  While we have many transactions, much harder to say how many independent samplings we have.  If you and I buy the same widget at the same store on the same day, is that really 2 independent measurements of the price of that widget?  On the other hand, what other number do we really have that makes any sense at all for N?

We have another report that is clearly defined in terms of statistical technique.  Federal auditors just told us how to do it.  That one was easy to implement, but it still gives me some misgivings because it assumes normal distributions, when that is anything but clear, and due to a large, possibly inappropriate N, it makes the pricing range look much narrower than it actually is.  But ultimately, we have to provide this report to demonstrate a certain aspect of our program, so we just do it.  We've structured the program in such a way that even without any fancy statistical analysis, it is impossible to not pass this particular test, but still they want the data in this format so we just do it that way.