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:

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, E(Duration) is the average expected duration given that the prospect becomes a customer, E(Acq. %) is the expected acquisition rate, or E(# Acquired)/500, Acq_Exp is the average acquisition expense across all prospects, Ret_Exp is the expected retention expense across all acquired customers, and Total expense is the total spent across prospects and customers.

For the first three scenarios we plan to simulate, we will try to maximize the three dependent variables (Profit, Duration, and Acquisition) across all prospects and customers given the following constraints. First, the amount of spending on acquisition and retention efforts needs to be positive (i.e., we cannot spend a negative amount of money on either activity). Second, the total amount spent on acquisition and retention cannot exceed the current budget of $415 000. Third, the duration of any customer relationship cannot be negative (this is conceptually straightforward, but since we are using expected duration, the prediction of duration can become negative if the acquisition and retention variables change too dramatically). In addition for the first scenario where we want to maximize acquisition rate, since acquisition rate does not impact duration directly, we will assume that the firm allocates all remaining resources not desired for acquisition efforts to retention efforts (so the sum of all expenditures is still $415 000). For the last scenario the only change to our constraints is to relax the budget constraint and allow the firm to spend an unlimited amount of money on acquisition and retention efforts. When we run the simulation we get the following results:

We get the following results for each of the scenarios:

• Maximize E(Acq. %) For the scenario where we want to maximize acquisition rate, the expected total profit is higher by $270 000, the expected duration is shorter by 198 days, the acquisition rate is higher by 9.58%, the average acquisition expense is lower by $60.85, the average retention expense is higher by $17.09, and the total marketing budget is the same. This shows that maximizing acquisition rate is better than the current scenario since the total profit is higher when we try to acquire the most customers. This happens because even though the average acquisition spending is lower, the spending on acquisition is targeted at the prospects who are more likely to join and not targeted at the prospects who are unlikely to join. This is why the expected acquisition rate is so much higher than in the current scenario. Now in this case the duration of the customers is less most likely due to the fact that the average spending on each customer had to decrease, given that so many more customers were acquired in this scenario and the budget was limited to be the same as before.
• Maximize E(duration) For the scenario where we want to maximize the average duration of the acquired customers, the expected profit is higher by $280 000, the expected duration is shorter by 98 days, the acquisition rate is higher by 1.53%, the average acquisition expense is lower by $171.60, the average retention expense is higher by $237.22, and the total marketing budget is the same when compared to the current scenario. This shows that maximizing the duration of the acquired customers is better than the current scenario or even the scenario where we maximized acquisition rate, since the total profit is higher when we try to increase the duration of each customer relationship. However, we notice that the expected duration is less than the current scenario even when we are trying to maximize customer duration. This is happening because we are maximizing the customer acquisition of the average customer who is acquired. Since we are not bringing on the ‘best’ customers we are only able to maximize the duration of the customers we were actually able to bring on. This means the firm was already acquiring better than ‘average’ customers in its current scenario.
• Maximize E(profit) For the scenario where we want to maximize the expected profit across all prospects and customers, the expected profit is higher by $300 000, the expected duration is shorter by 122 days, the acquisition rate is higher by 7.18%, the average acquisition expense is lower by $122.97, the average retention expense is higher by $116.68, and the total marketing budget is the same. This shows that maximizing the profit does lead to a much higher profit level when compared to the current scenario and also a little higher when compared to both of the previous two scenarios where we wanted to maximize customer acquisition rate and customer duration in isolation. These results also show that balance is critical to maximizing profit since the expected acquisition rate and the expected duration are between the scenarios where we maximize acquisition rate and maximize duration. Again we see that the entire budget is used, suggesting that our simulation would potentially find it more lucrative to spend even more money on acquisition and retention efforts.
• Maximize E(profit) with unlimited budget For the scenario where we want to maximize the expected profit across all prospects and customers regardless of budget level, the expected profit is higher by $1.54 million, the expected duration is shorter by 628 days, the acquisition rate is higher by 9.35%, the average acquisition expense is lower by $41.31, the average retention expense is higher by $1776.30, and the total marketing budget is higher by $685 000 when compared to the current scenario. We see that when we take away the budget constraint the desired spending level is significantly higher than the current spending level of the firm. While it may not be the case that the firm can afford to spend this much on marketing efforts for this group of prospects/customers, it does suggest that if the firm is holding back on the current budget level, there is some justification to spend more, especially on retention efforts.

The end result of this optimal resource allocation exercise is that the firm can be more profitable if it balances its acquisition and retention efforts. By focusing too much on acquisition or on retention (duration), the firm is not maximizing its profit. It only maximizes profit when it balances its spending across both activities. In addition, we see that the firm is dramatically underspending on its marketing efforts if it desires to maximize long-term profitability.

5.3.1 How Do You Implement it?

For this empirical exercise several different methods were used. First, to estimate the probit regression for the acquisition model we used PROC Logistic in SAS with the probit link function. Second, to estimate the censored regression for both the duration model and the profit model in the second and third steps we used PROC Reg in SAS. Finally, to run the optimization routine we used Solver in Excel. There are numerous other programs such as MATLAB, GAUSS, and R which could be used to estimate these models and run the optimizations.