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

2. March 14-16 th 2007Two-dimensional Automated Planograms2 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 Motivation % UK food retail market Share 1998 2005 Why Shelf Space Allocation?

3. March 14-16 th 2007Two-dimensional Automated Planograms3 Shelf space allocation: Introduction Traffic Flow Design Category and brand location Planograms Promotions and special display E C

4. March 14-16 th 2007Two-dimensional Automated Planograms4 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

5. March 14-16 th 2007Two-dimensional Automated Planograms5 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.

6. March 14-16 th 2007Two-dimensional Automated Planograms6 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.

7. March 14-16 th 2007Two-dimensional Automated Planograms7 Objectives Minimise cost (Economic Order Quantity (EOQ) model) Minimise number of replenishment Maximise total sales Maximise total profit EOQ model SSA model EOQ model

8. March 14-16 th 2007Two-dimensional Automated Planograms8 Constraints 1.Physical constraints 1D, 2D or even 3D 2.Integrality constraints Constraints 1 and 2 are similar to constraints in multi-knapsack problem – NP-Hard Problem 2.Display requirements Lower and upper bounds, providers request, etc. 3.Cluster Constraints 4.Adjacency 5.Weight constraints

9. March 14-16 th 2007Two-dimensional Automated Planograms9 A 2D SSA Model – Problem Definition (1) Given n SKUs (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 x ij : length facing of shelf j allocated to SKU I π ij : Stacking coefficient x i : total facing and

10. March 14-16 th 2007Two-dimensional Automated Planograms10 A 2D SSA Model – Problem Definition (2) Notation y ij F i : demand function: A D c Location factor otherwise

11. March 14-16 th 2007Two-dimensional Automated Planograms11 A 2D SSA Model st.

12. March 14-16 th 2007Two-dimensional Automated Planograms12 1D vs 2D Model Sales: A numerical example: m=4, n=4 (drawn from (Hwang et al. 2004)). 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. 2616.29 2492.55

13. March 14-16 th 2007Two-dimensional Automated Planograms13 Optimisation Methodologies Gradient approach Meta-heuristic Multiple neighbourhood search approach hybridised with a simulated annealing hyper- heuristic learning mechanism. Neighbourhoods: swap, shift, Interchange, add facing, delete facing.

14. March 14-16 th 2007Two-dimensional Automated Planograms14 Simulated Annealing Hyper-heuristic SA Criterion Domain Barrier Stochastic Heuristic Selection Mechanism Simulated Annealing Hyper-heuristic Feedback 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… Heuristic Repository Problem Domain H1H1 H2H2 HnHn …  Problem representation  Evaluation Function  Initial Solution  Others… SA Criterion Collecting domain-independent information Apply the selected heuristic

15. March 14-16 th 2007Two-dimensional Automated Planograms15 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 Empirical input data

16. March 14-16 th 2007Two-dimensional Automated Planograms16 Computational results (1)

17. March 14-16 th 2007Two-dimensional Automated Planograms17 Computational results (2) Computational results for Pn29 Gradient Multi- Neighbourhood Objective97134.70 Best: 110640.14 Avg: 109556.84 Time (s)< 0.543.4

18. March 14-16 th 2007Two-dimensional Automated Planograms18 Sensitivity Analysis Shelf Space

19. March 14-16 th 2007Two-dimensional Automated Planograms19 Sensitivity Analysis Sensitivity of parameter estimation error

20. March 14-16 th 2007Two-dimensional Automated Planograms20 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

21. March 14-16 th 2007Two-dimensional Automated Planograms21 Optimising Retail Shelf Space Allocation Thank you!!! Comments / Questions?