Editor’s note: Michael Lieberman is founder and president of Princeton, N.J., research firm Multivariate Solutions.

Do loyalty programs work? Some do. Some don’t. Still, nearly 75 percent of U.S. shoppers now belong to at least one loyalty program. A marketing program for loyalty has three known goals: 1) acquire new customers; 2) keep existing customers; 3) grow these customers to into larger, and more lucrative, customer categories.

As loyalty programs and their related tactics have matured, increased attention has been placed on maximizing the bang for the buck. Industry knowledge, guesswork or instinct are no longer suitable substitutes for strategic risk analysis. When marketing managers are asked how they are optimizing their budgets, specific promotions are often questioned. Marketers today are under increasing pressure from their bosses to show a greater return on investment (ROI). What gets measured gets done, as the saying goes. Budgets are limited, so how does the manager know he is doing his best?

This article is an abbreviated rundown of how a segmentation/ROI study functions. First, there is the market research/data mining component of segmentation, followed by uses of Monte Carlo forecasting and optimization of a company’s promotion.

We will use a fictional example - Colossal Supermarkets and its flagship store, Food City - to show how to design a specific loyalty promotion and to maximize its return within the company’s promotional budget.

Colossal has a loyalty program that it wants to deploy for the U.S. holiday season. Food City is a regional chain, with stores concentrated in the Pacific Northwest. It wants a bigger share of the turkey and pie the locals are rushing to supermarkets to fill up on. So Colossal Supermarkets initiates a program in which all Food City preferred customers are enrolled in a new and enhanced loyalty program called Food City’s Holiday Gift Bag. In all, nearly a million Food City customers are enrolled. They receive color-coded cards in the mail. Each color represents the amount of money spent on a monthly basis at Food City by each customer unit (a unit can be an individual, couple, family, household, etc.).

Food City’s Holiday Gift Bag actually operates on a per-month baseline. The smaller spenders receive an invitation to join at the Preferred membership level. Those who spend more at Food City receive a Gold Gift Bag card. There is a Platinum Gift Bag card, then the highest level, the Food City Mayor’s Club.

Each tier is tied to a level of benefits. The higher the tier, the more extras Food City will dish out. To make the program more attractive, Colossal Supermarkets has tied its benefits to other loyalty programs, such as car rental discounts, frequent flier points on partner airlines or even discounts on menswear. Basically, the more you spend, the more you get “free.”

Two stages

There are two stages to the analysis. First, determine the confines of customer segmentation. That is, where would be the best place to draw lines among the different colors of the Gift Bag cards in order to divide up return? These customer boundaries are commonly referred to as the “efficient frontier.” This stage utilizes a mixture of cluster analysis (multivariate segmentation) and Monte Carlo simulation.

The next step: How much should each point be worth, assuming each point with the program had a cost? (For example, if one point returned a 1 percent discount, the “cost” of a point might be 1 cent) We want to set the “optimal” ratio of points to spending, so that the return on each point is maximized.

Market segmentation is a behaviorally-based statistical approach to putting respondents into baskets. Each basket is mutually exclusive, and the final basket is tied to the amount of money each unit spends at Food City each month. Food City has been asking customers to fill out a small survey card, which captures demographics information about their food purchase behavior, which is then tied to their customer identification number. This information provides invaluable information about marketplace complexities facing Food City consumers.

The final groups are formed by combining the results of the cluster analysis, which is tied to spending amounts. These are shown in Figure 1.

Monte Carlo simulation is a method for iteratively evaluating a deterministic model using sets of statistical distributions as inputs. This method is often used when the model is complex or involves more than just a couple of uncertain parameters. A simulation can typically involve over 10,000 evaluations of the model.

In a Monte Carlo simulation, a model in spreadsheet format is set up and the cells - whose values come from the survey results, customer databases, financial reports, etc. - are identified. For each of these cells, a distribution of possible values using the appropriate means and errors is specified. In other words, the shape (referred to in statistics as a distribution) of spending per month for Food City customers could be different from, say, the number of trips to Food City a given customer makes per month. Monte Carlo allows for these different distributions.

A series of trials is then generated, each one of which represents a possible outcome of the process. Instead of a simple spreadsheet that yields one answer, Monte Carlo allows the spreadsheet to run 10,000 times, each different parameter moving within its shape, given 10,000 different outcomes. When these are shown in a cumulative chart, the chances of a given outcome can be determined. For example, what is the chance that Food City customers will spend more than $500 a month?

In our case, parameters of spending and input are set up using their customer survey and a customer database. In order to determine the output of the optimization, these spreadsheets are run, say, 10,000 times. This is called the forecast.

Input value

The goal of any optimization is to determine the input value (decision variables) that make the output (forecast) as large - or as small - as possible. Figure 2 summarizes the process.

There are many applications for optimization:

  • utilization of employees for workforce planning;
  • configuration of machines for production scheduling;
  • location of facilities for distribution;
  • tolerances in manufacturing design;
  • management of portfolios; and
  • calculation of optimal price/promotional points.

In our case, as is often the case in ROI projects, the decision variable is the value of the points that will be rewarded for each tier in the Food City program. The forecast will be the incremental increase in spending for each value of the points.

Once all the variables are entered and the spreadsheet complete, the final step is to let the optimization software run and run. It is common for the forecast (which runs, say, 10,000 outputs), to run 10,000 times to find the optimal level.

These are the constraints that are built into the optimization process: maximize ROI; stay within the promotional budget; try to stimulate growth of all Food City shoppers.

Given the nature of customer behavior, it is natural to expect those customers in the Platinum or Mayor’s Club categories to have a higher increase in spending due to the promotion. That is all well and good. However, in the market reality, the percentage of Preferred shoppers is far greater. Food City wants them to spend more as well. In addition, it is commonly understood that not everyone will redeem every point he receives. The “expected redemption” is another variable that is built into the model.

Now that the optimization is run, there are two outputs that need to be analyzed. The first is called the spending hurdle. That is, at what point do members move from one category to the next. These are not necessarily the same as the spending segments shown above, for the simple reason that spending is not static, but moves up and down depending on holidays, family, and life’s events (e.g., birth of a child, moving, promotion at work).

The second output we will look at will be the value of each point when redeemed. Remember: The name of the game is return on investment; if Food City gives away too much, that return drops.

After the optimization is complete, the top results are analyzed. A few scenarios are rerun to validate the results. Some things needed to be tweaked so that they made market sense. For example, if the optimization suggested that the spending hurdle was $563.35, it makes more sense to set it at $575. If the suggested point value was $0.0986, it makes more marketing sense to set it at $0.10. Each of these things is tested.

Once they are analyzed, final decisions about where to set the spending hurdles and the value of a point are set. Figure 3 summarizes the findings of the Food City study.

The data show that the most efficient segmentation of Food City customers occurs at the monthly spending ratings. That is, as monthly spending for each customer passes another hurdle, the customer’s behavior changes. For example, if monthly spending of a given “unit” is $550, they are likely to be in the Platinum group (see Figure 1); perhaps a large family or a professional, two-income household. If unit spending is, say, $850 a month, they are likely in the Food City Mayor’s Club, where they are more likely to purchase premium items, have a professional mom, and perhaps send their kids to private school.

Finally, the point value of 15 cents maximizes Food City’s return on investment, keeping in mind how much more each level of spending will increase with the awards, and the incremental cost of giving away 15 cents a point. A good way to understand this figure is that if Food City made each point worth 10 cents, customer spending would not rise as much. If it made each point worth 20 cents, customer spending would rise, but the cost to the company would be greater. Food City makes the most money if it prices each point at 15 cents.

Cost-efficient results

As computing power increases and as marketers become more savvy (e.g., Amazon knows your favorites), it becomes easier to facilitate an optimization project like Food City’s. Experience has shown that implementing the new technique, and other risk-analysis measures, can have a high learning curve but ultimately yield effective, cost-efficient results.

The marriage of survey research, data mining techniques, the Monte Carlo method and optimization can take more and more of the risk out of developing these promotional programs and can improve ROI for marketing managers in almost any industry.