Two-dimensional Automated Planograms
Ruibin Bai1, Tom van Woensel2,
Graham Kendall1, Edmund K. Burke1
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 13-16th 2007 Dagstuhl
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
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Shelf space allocation: Introduction
Traffic Flow Design
C
Category and brand
location
E
Planograms
Promotions and
special display
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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
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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.
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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 eyelevel.
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Objectives
•
Minimise cost (Economic Order
Quantity (EOQ) model)
•
Minimise number of
replenishment
•
Maximise total sales
•
Maximise total profit
EOQ model
EOQ model
Sales
facing
SSA model
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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
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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
• xij: length facing of shelf j allocated
to SKU I
• πij: Stacking coefficient
• xi: total facing and
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Notation
• yij
Sales
A 2D SSA Model – Problem Definition (2)
otherwise
• Fi: demand function:
facing
Location factor
• A
• D
• c
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A 2D SSA Model
st.
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1D vs 2D Model
A numerical example: m=4, n=4 (drawn from (Hwang et al. 2004)).
Sales:
2492.55
2616.29
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.
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Optimisation Methodologies
 Gradient approach
 Meta-heuristic

Multiple neighbourhood search approach
hybridised with a simulated annealing hyperheuristic learning mechanism.

Neighbourhoods: swap, shift, Interchange, add
facing, delete facing.
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Simulated Annealing Hyper-heuristic
Simulated Annealing Hyper-heuristic
Apply the selected
heuristic
SA
SA
Criterion
Stochastic Heuristic
Selection Mechanism
Feedback
Collecting domain-independent information
Domain Barrier
Heuristic Repository
H1
Hn
H2
…
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Problem representation
Evaluation Function
Initial Solution
Others…
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…
Two-dimensional Automated Planograms
Problem Domain
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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
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Computational results (1)
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Computational results (2)
Computational results for Pn29
Gradient
MultiNeighbourhood
Objective
97134.70
Best: 110640.14
Avg: 109556.84
Time (s)
< 0.5
43.4
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Sensitivity Analysis
Shelf Space
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Sensitivity Analysis
Sensitivity of parameter estimation error
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Conclusions
•
Shelf space allocation and its relationship with multiknapsack 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
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Optimising Retail Shelf Space Allocation
Thank you!!!
Comments / Questions?
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