Modeling Sales targets by team

Question

My B2C company partners with multiple companies and sells their products on their behalf. Our specialization is distribution and sales across different US regions. Product focused companies outsource sales and distribution to us. The company receives a commission on final sales. Sales teams are regionally distributed and have a diverse portfolio of products to sell. Some are easy to sell. Others are difficult to sell. Price is not always a defining factor because of wide range of price-value propositions in our products.

My company asked me to come up with a good way to figure out how many products a sales team can sell in a week if they are focused only on one product. For example, sales team A currently sells 320 products a week (80 hair products, 200 beauty products, 30 electronic products and 10 luxury items).The company wants to understand how many products of only one type can a team sell. That is, the company wants me to tell that a team can be reliably expected to sell (xx hair products, yy beauty products, zz electronic products) if they sold products of only 1 type.

The data by team has a diverse mix of sales by week and I can't separate by more than team sales by week. The target variable of sales by team by week is not helpful because of wide range of products every week. How do I model this problem? Any help will be appreciated.

Things I tried:

1. Using days to sell as a variable. But this is sometimes very dependent on delays and lags. For example, the sales team might work for 2 days and the sale might happen 12 days later. as a result, the count of sales is not in the same week as when the effort was made to make a sale. Maybe I am not thinking about this correctly

My data has a Poisson/Negative-Binomial distribution but I don't know if modeling a Poisson model is the best approach with strong product mix in each week's sales data

Answer 1

If I understand correctly you have a time series where every row represents a week.

I am also assuming from your question that you don't have data on effort spent on every item (like hours spent selling an item per week).

I would approach the problem with a sort of latent variable model with the following assumptions:

1. We have a latent variable - effort.
2. The amount of effort per week is constant ( number of available working hours).
3. The amount of sales of a product is dependent on the effort spent on the product.
4. There is some randomness that causes random variance in the sales of the product.

We let effort be represented by variable $e$, weeks by $i$ and the product sales by $X_j$ where $j$ is the item index. so $X_{ij}$ is the sales of item $X_j$ by effort put in week $i$, $e_ij$.

So the number of sales of product $X_j$ in week $i$ is:

$X_{ij} = a_j*e_{ij} + Error$

Where $a_j$ is a learned parameter relating the amount of effort to sales. and the sum of the effort each week is 1 for simplicity ( assumption 2):

$e_i = \sum_{j=0}^ne_{ij} = 1 $

We now have a system of equations with n variables $a_j$ and $(n-1)*m$ variables $e_{ij}$ where $n$ is the number of total variables and $m$ is the number of weeks of data you have. and $n*m$ equations. We can solve the system of equations if $m \geqslant n $.

We can then easily find for each product the value if $e_j=1$, it's simply $a_j$.

The problem here is that we need to decompose the effort spent on each item which requires a lot of data.

The second problem is that we need to relate the sale to the week the work was done at. If you can't do it accurately I would start with a simple rule. a common rule used in such cases is "sales at week $i$ are from work done in week $i$" or "work done in week i results in sales in week $i+1$". This introduces errors of course. But I'd consult the sales teams to come up with a rule that covers most cases.