Two-dimensional Automated Planograms

1. Two-dimensional Automated Planograms Ruibin Bai1, Tom van Woensel2, Graham Kendall1, Edmund K. Burke1 • ASAP Research Group, School of Computer Science & IT, University of Nottingham, Nottingham NG8 1BB, UK • Technische Universiteit Eindhoven, Den Dolech 2, Pav. F05, Eindhoven NL 5600 MB, The Netherlands. March 13-16th 2007 Dagstuhl

2. 1998 2005 % UK food retail market Share Motivation Why Shelf Space Allocation? • Retail industry is extremely competitive • Very large product assortment (30,000+). • Shelves are expensive and limited resources. • Research shows that attractive product layout can increase sales. However, designing it can be tedious and time consuming. • Shelf space is related to inventory control and replenishment operations Two-dimensional Automated Planograms

3. Shelf space allocation: Introduction Traffic Flow Design C E Category and brand location Planograms Promotions and special display Two-dimensional Automated Planograms

4. State-of-the-art planograms software • Current software: • Retek SpaceMan GalaXXi • Can check physical violations • Drag and drop procedure (needs human interaction) • Very few automation tools are available • Experience based, no optimisation A snap shot of GalaXXi 10.0 from Space IT Two-dimensional Automated Planograms

5. Basic Concepts SKU (stock-keeping unit) unique identity of a specific product or goods. SKU is the smallest management unit in a retail store. Inventory refers to the quantity of each SKU that is currently held by a retailer = displayed stock + back room stock. Planogram A retail map or blue-print, defining the amount of the shelf space allocated to each SKU and its location. Two-dimensional Automated Planograms

6. Basic Concepts Facing The quantity of an SKU that can be directly seen on the shelves or fixtures by the customers. Space elasticity Measure the responsiveness of the sales with regards to the change of allocated space (Curhan, 1972). Location More attractive locations: Entrance, End of aisles, Shelves at similar eye-level. Two-dimensional Automated Planograms

7. Objectives • Minimise cost (Economic Order Quantity (EOQ) model) • Minimise number of replenishment • Maximise total sales • Maximise total profit EOQ model EOQ model SSA model Two-dimensional Automated Planograms

8. Constraints • Physical constraints • 1D, 2D or even 3D • Integrality constraints • Constraints 1 and 2 are similar to constraints in multi-knapsack problem – NP-Hard Problem • Display requirements • Lower and upper bounds, • providers request, etc. • Cluster Constraints • Adjacency • Weight constraints Two-dimensional Automated Planograms

9. A 2D SSA Model – Problem Definition (1) Given nSKUs (or items) and m shelves, with each shelf and SKU having non-changeable sizes both in height and in length, the problem is to allocate appropriate facings to each SKU in order to maximise the total sales. • Notation • xij: length facing of shelf j allocated to SKU I • πij: Stacking coefficient • xi: total facing and Two-dimensional Automated Planograms

10. A 2D SSA Model – Problem Definition (2) • Notation • yij • Fi: demand function: • A • D • c otherwise Location factor Two-dimensional Automated Planograms

11. A 2D SSA Model st. Two-dimensional Automated Planograms

12. 2492.55 2616.29 1D vs 2D Model A numerical example: m=4, n=4 (drawn from (Hwang et al. 2004)). Sales: H. Hwang, B. Choi, M.-J. Lee, A model for shelf space allocation and inventory control considering location and inventory level effects on demand, International Journal of Production Economics 97 (2) (2005) 185-195. Two-dimensional Automated Planograms

13. Optimisation Methodologies • Gradient approach • Meta-heuristic • Multipleneighbourhood search approach hybridised with a simulated annealinghyper-heuristic learning mechanism. • Neighbourhoods: swap, shift, Interchange, add facing, delete facing. Two-dimensional Automated Planograms

14. H1 H2 Hn … Simulated Annealing Hyper-heuristic Simulated Annealing Hyper-heuristic Apply the selected heuristic SA Criterion • For example: • No. of heuristics • The changes in evaluation function • A new solution or not • The distance between two solutions • Whether it gets stuck or not • Others… SA Criterion Stochastic Heuristic Selection Mechanism Feedback Collecting domain-independent information Domain Barrier • Problem representation • Evaluation Function • Initial Solution • Others… Heuristic Repository Two-dimensional Automated Planograms Problem Domain

15. Empirical input data • Collected from a European supermarket chain, experiment data contained SKUs from 44 stores • Data are separated into two groups based on the store sizes: large/ small. • Parameters estimation (α,β ) • ---Linear regression • Two problem instances were created • Pn6: m=3, n=6 • Pn29: m=5, n=29 Two-dimensional Automated Planograms

16. Computational results (1) Two-dimensional Automated Planograms

17. Computational results (2) Computational results for Pn29 Two-dimensional Automated Planograms

18. Sensitivity Analysis Shelf Space Two-dimensional Automated Planograms

19. Sensitivity Analysis Sensitivity of parameter estimation error Two-dimensional Automated Planograms

20. Conclusions • Shelf space allocation and its relationship with multi- knapsack problem • A practical model that be used to automate and optimise the design of planograms and product layout. • Heuristic/meta-heuristic approaches for optimising retail shelf space allocation • Future work: uncertainty of market and demand • --stochastic programming models? • --integrated with inventory control models • --integrate with RFID systems Two-dimensional Automated Planograms

21. Optimising Retail Shelf Space Allocation Thank you!!! Comments / Questions? Two-dimensional Automated Planograms