1. 1 ICARUS: Intelligent Coupon Allocation for Retailers Using Search Stephen Swift 1, Amy Shi 2, Jason Crampton 3, Allan Tucker 1 1 SISCM, Brunel University, UK 2 Loyalty Logic Limited, Fleet, Hampshire, UK 3 Information Security Group, Royal Holloway, UK

2. 2 Introduction (1) Many retailers run loyalty card schemes They offer incentives in the form of money off coupons The total value of the coupons depends on how much the customer has spent

3. 3 Introduction (2) 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 these coupons

4. 4 Introduction (3) For example, if the reward totals ranged between £2 and £6 The smallest set that can span all solutions is considered the best, i.e. {1, 2, 3}

5. 5 Introduction (4) A mathematical analysis of the problem is presented Leading to a Genetic Algorithm solution The algorithm is applied to real world data using several crossover operators Compared to straw-person methods Considerable time can be saved

6. 6 Business Description (1) Coupons mailed out every 4-6 months The reward value is a percentage of the customer’s expenditure The expiry date and value is encoded as a barcode on each coupon The number of coupons is fixed (very important!)

7. 7 Business Description (2) As small a number of denominations of coupons is needed – –The barcode space (hence range of values) is small – –A large number of coupon values will mean that the scheme will have to be redesigned too quickly

8. 8 Business Description (3) Retailer Ltd. Dear Dr Swift, £ Coupon 1£ Coupon 2 £ Coupon 3£ Coupon 4 Some other money saving offers, such as fixed amounts off certain targeted products …………

9. 9 The Allocation Problem (1) The monetary value of each coupon should be evenly distributed “Good looking” numbers are preferred by customers, e.g. divisible by five Coupon values should not exceed the typical basket value, which is between £25 and £35

10. 10 The Allocation Problem (2) An example of well-allocated coupons: : An example of badly allocated coupons: Number of vouchers = 4 Customer with total reward value of £20.00 balanced good looking numbers values fit a typical basket X not balanced X odd looking numbers X values are low/high for a typical basket £2£5 £10 £1 £17

11. 11 A Short Note The problem would be trivial if: – –The number of coupons required was not specified, e.g. 1, 2, 5, 10, 20, 50, 100, … – –The number of overall coupon denominations did not have to be as small as possible

12. 12 Mathematical Representation We extensively use the fact that an instance of the problem can be split into several smaller instances A recursive algorithm can be developed to see if a particular instance of the problem can be solved

13. 13 ICARUS ICARUS: Intelligent Coupon Allocation for Retailers Using Search We solve the coupon allocation problem using a binary Genetic Algorithm (GA) Find the smallest coupon set (A) that spans a given reward set V in m coupons

14. 14 ICARUS - Representation A Binary string where the length is application dependant (see paper) A candidate coupon solution set is constructed from the corresponding chromosome, if gene i is 1 then the set A contains i For 5 genes, 10101 : coupons {1, 3, 5}

15. 15 ICARUS – Fitness Function Fitness = G(A) x H(V, m, A) (low is better) Measures how “Good Looking” the values are G(A) : Measures how well A spans V (uses the recursive function) H(V, m, A) :

16. 16 ICARUS – Operators Crossover: Uniform, One Point & AND/OR Mutation: Binary Survival: Ranked

17. 17 ICARUS – Post Processing The recursive function can be used to generate all possible solutions for all reward totals The “best” solution for each reward total can be selected either by the user or by using some criteria

18. 18 Evaluation Three Crossover operators Simulated Annealing Hill Climbing The current manual results

19. 19 Test Problem A real world reward, run last year 85 reward totals between £0 to £116 m = 4 (number of coupons) Additional post processing required

20. 20 Results (1)

21. 21 Results (2)

22. 22 Results (3)

23. 23 Results (4)

24. 24 Concluding Remarks We have presented a method for solving the reward scheme coupon allocation problem This is achieved through the use of a binary Genetic Algorithm The results show that ICARUS using one point crossover performs best The ICARUS method runs in a few minutes

25. 25 Future Work The ICARUS algorithm is really a prototype/proof of concept The use of a Multi-Objective GA could be exploredThe use of a Multi-Objective GA could be explored It is intended that ICARUS be used to determine the next run for the retailerIt is intended that ICARUS be used to determine the next run for the retailer

26. 26 Acknowledgements The authors would like to thank the unnamed retailer who provided the dataset used within this paper, Janet McFall for her helpful comments and the reviewers for their constructive advice