Real World Problem From a Large Retail Company

[zebing]

Hi all, I am working at a very large retailer in the USA and have come across an interesting math question in my work. We have noticed that several categories of our items are no longer selling well, and my boss has asked me to figure out why. On top of that, he has asked me to quantify the dollar impact of several changes that we have seen in our sales.

Here is how to calculate sales.

Baskets=B
Units per basket=UPB
Average Unit Revenue=AUR
Last Year=LY
This Year=TY
S=Sales
and
Sales dollars(S)=AUR*UPB*B
Change in sales=TYS-LYS

Here is how far I have come:

TYS-LYS=LYS(Growth%)
Change=LYS(TYS/LYS-1)
Change=LYS(((AUR*UPB*B)/(LYAUR*LYUPB*B))-1)
Change=LYS((AUR/LYAUR)*(UPB/LYUPB)*(B/LYB))-1)

I did algebra to write it this way because I actually know all of these numbers

Change=3,465
LYS=88,922
AUR/LYAUR=.975
UPB/LYUPB=1.007
B/LYB=.978

And now for the big question. How can I write the formula that tells me what impact each percentage has on the total change? I know that a one means no impact, but let's take the example of AUR. How can I write a formula that tells me how many dollars of the $3,465 change is due to the 2.5% decrease in AUR since last year (1-.975)? And yes, I need to write a formula so that I can do this for other areas of the business.

I appreciate the help!

 

[Deleted member 4993]

Hi all, I am working at a very large retailer in the USA and have come across an interesting math question in my work. We have noticed that several categories of our items are no longer selling well, and my boss has asked me to figure out why. On top of that, he has asked me to quantify the dollar impact of several changes that we have seen in our sales.

Here is how to calculate sales.

Baskets=B
Units per basket=UPB
Average Unit Revenue=AUR
Last Year=LY
This Year=TY
S=Sales
and
Sales dollars(S)=AUR*UPB*B
Change in sales=TYS-LYS

Here is how far I have come:

TYS-LYS=LYS(Growth%)
Change=LYS(TYS/LYS-1)
Change=LYS(((AUR*UPB*B)/(LYAUR*LYUPB*B))-1)
Change=LYS((AUR/LYAUR)*(UPB/LYUPB)*(B/LYB))-1)

I did algebra to write it this way because I actually know all of these numbers

Change=3,465
LYS=88,922
AUR/LYAUR=.975
UPB/LYUPB=1.007
B/LYB=.978

And now for the big question. How can I write the formula that tells me what impact each percentage has on the total change? I know that a one means no impact, but let's take the example of AUR. How can I write a formula that tells me how many dollars of the $3,465 change is due to the 2.5% decrease in AUR since last year (1-.975)? And yes, I need to write a formula so that I can do this for other areas of the business.

I appreciate the help!

Since you work for a large retailing company, and your request is pertaining to your work, you should go to your local community college or university and hire a "graduate" student who would be very glad to derive the equation for you in exchange of a small remuneration.

 

[zebing]

@Subhotosh

First off, let me respond to your comment by saying that we already have a solution that closely approximates the reality that we are quite satisfied with. I thought it an interesting enough question to post on a forum to get other people's thoughts and see if there was a more elegant solution.

But secondly, I remember being in high school math class and hearing many of my classmates complain that math was stupid because they would never use it in real life. It's disappointing to see that when someone comes along with a real-world problem, the response is essentially "get lost". I think such responses are part of the reason young people are so disinterested in math - they see it as largely academic and of no real benefit to their lives. It's a shame to get that kind of response on a math forum.