Many retailers run loyalty card schemes for their customers offering incentives in the form of money off coupons. The total value of the coupons depends on how much the customer has spent. This paper deals with the problem of finding the smallest set of coupons such that each possible total can be represented as the sum of a pre-defined number of coupons. A mathematical analysis of the problem leads to the development of a genetic algorithm solution. The algorithm is applied to real world data using several crossover operators and compared to well known straw-person methods. Results are promising showing that considerable time can be saved by using this method, reducing a few days worth of consultancy time to a few minutes of computation