Turn on suggestions

Auto-suggest helps you quickly narrow down your search results by suggesting possible matches as you type.

Showing results for

Options

- RSS Feed
- Mark Topic as New
- Mark Topic as Read
- Float this Topic for Current User
- Bookmark
- Subscribe
- Mute
- Printer Friendly Page

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

Posted 07-10-2014 06:39 PM
(726 views)

I used a logistic regression to build a model to score the value of each customer. Now suppose we have scored 10K customers and plan to run a marketing campaign on them. Two pilot programs had been conducted and the outcomes are summarized below.

Program 1:

Spent $.40 on each customer of first 1K customers. Got 10 purchases and $.45/customer profit.

Spent $.30 on each customer of next 3K customers. Got 20 purchases and $.28/customer profit.

Spent $.20 on each customer of next 5K customers. Got 40 purchases and $.22/customer profit.

Spent $.10 on each customer of next 2K customers. Got 10 purchases and $.12/customer profit.

Program 2:

Spent $.40 on each customer of first 1K customers. Got 10 purchases and $.45/customer profit.

Spent $.30 on each customer of next 2K customers. Got 10 purchases and $.32/customer profit.

Spent $.20 on each customer of next 7K customers. Got 50 purchases and $.20/customer profit.

Spent $.10 on each customer of next 1K customers. Got 5 purchases and $.09/customer profit.

Based on these 2 pilot program outcomes, I would like to see the optimal allocation of marketing spend to maximize the purchases and profit. That each, how many customers need to allocate to spend $.4 group, how many to spend $.3 group. I don't know which math/statistics methods I should use to solve this problem.

1 REPLY 1

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

Looks like you have 11K customers and a budget of $2500. Suppose you knew the expected return r[i,j] if customer i is assigned to group j. Then your expected profit for that assignment would be r[i,j] - c

var Assign {CUSTOMERS, GROUPS} binary;

max TotalExpectedProfit = sum {i in CUSTOMERS, j in GROUPS} (r[i,j] - c

con AssignOnce {i in CUSTOMERS}:

sum {j in GROUPS} Assign[i,j] = 1;

con Budget:

sum {i in CUSTOMERS, j in GROUPS} c

If you are allowed not to assign a customer to any group, you can change the = 1 to <= 1 in the AssignOnce constraint. Alternatively, you can define a dummy group j = 5, with cost c[5] = 0, if there is some nonzero expected return r[i,5] for customer i not being assigned to a group.

It remains to use the results of your two pilot programs to estimate r[i,j] for each customer-group pair. I'll leave that for a statistician to discuss, but maybe you can do some kind of Bayesian update of your initial scoring model.

Registration is open! SAS is returning to Vegas for an AI and analytics experience like no other! Whether you're an executive, manager, end user or SAS partner, SAS Innovate is designed for everyone on your team. Register for just $495 by 12/31/2023.

**If you are interested in speaking, there is still time to submit a session idea. More details are posted on the website. **

Multiple Linear Regression in SAS

Learn how to run multiple linear regression models with and without interactions, presented by SAS user Alex Chaplin.

Find more tutorials on the SAS Users YouTube channel.