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Statistical Methods in Customer Relationship Management by J. Andrew Petersen, V. Kumar

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5.3 Optimal Resource Allocation

Our final task is to see what our potential profitability would be if we were to allow the resources spent on acquisition (acq_exp) and retention (ret_exp) to vary. To do this we need to take the results of the first three steps of this example and simulate different potential outcomes based on a set of constraints. To start we set up the objective function we wish to maximize. For the purpose of this example there will be have four scenarios that we will run. We will change the average amount we spend on acquisition and retention based on these desired outcomes:

1. Maximize the acquisition rate across all customers given the current marketing budget.
2. Maximize the average duration across all customers given the current marketing budget.
3. Maximize the total profit across all customers given the current marketing budget.
4. Maximize the total profit across all customers given no budget limitation.

For simplicity, in each case we will keep the average values of the other variables (outside of acquisition expense and retention expense) the same throughout the exercise. Then we want to compare the results of the optimization exercises to the current scenario to see where improvements are made and how the allocations change to get those improvements. The current level of the potential outcome variables and the acquisition and retention expenses are the following:

In this case E(Profit) is the expected total profit across all prospects and customers, ...

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