Leading retailers and marketplaces like Amazon and Groupon implemented very sophisticated, and highly automated price management solutions over the recent years. These solutions are able to dynamically change prices every several minutes, intelligently personalize discounts, and respond to competitor moves in order to optimize profits and inventory. It creates pressure on other retailers and manufacturers, and challenges traditional price management techniques, making it increasingly more complex to stay competitive and profitable. In this talk, we will discuss how predictive modeling and reinforcement learning can be used to build advanced price management systems that unlock the potential of dynamic and personalized pricing. We will present price optimization methods for a number of use cases including introductory pricing, promotion calendars, replenishable and seasonal products, targeted offers, and flash sales. We will also review case studies that demonstrate how these methods were applied in practice and how algorithmic price management components were fitted into pricing strategies.

1. Building an Algorithmic
Price Management
System
Privileged and Confidential, February 2019

2. Drivers of Algorithmic Pricing
2
● Algorithmic pricing has a proven disruptive
potential - airlines, hotels, etc.
● Algorithmic pricing methods are increasingly
adopted by companies like Amazon, Walmart, and
Groupon.
● The frequency of price changes in retails
constantly increases.
● Digital channels provide a great environment for
algorithmic pricing.
Monthly duration of regular and posted price changes, 2008-2017
Monthly duration of regular price changes by retail sector, 2008-2017

3. Why Algorithmic Pricing is Challenging?
3
Supply Price Management Demand
Product
properties
Willingness
to pay
Product life
cycle
Costs
Margins
Price
perception
Competitor
pricing
Weather

4. Privileged and Confidential
Example — Algorithmic Pricing in the Context of Pricing Strategy
4
Introductory
price estimator
Profit optimizer
Competitor response optimizer
Sales event optimizer
KVI scorer
Introductory
strategy
Exit strategyKVI
strategy
Non-KVI
strategy
Promotion optimizer
Time
Product
price

5. Problem Types
Revenue Modeling Dynamic Pricing Personalized Pricing
years
months to
days
Price
Demand
Time
PricePrice
TimeTime
Use cases:
● Price optimization for replenishable items.
● Price optimization for seasonal items.
● Promotion calendars optimization.
● Introductory product price optimization.
Use cases:
● Short-time offers optimization (flash
sales).
● Inventory-constrained price optimization.
Use cases:
● Price segmentation.
● Personalized offers and promotions.

6. Revenue Modeling

7. 7
Profit Modeling and Optimization — Approach
Pricing model
Cross elasticity for
competitor pricing
Own item price
elasticity of
demand
Halo and
affinity effects
Cross item
price
elasticity
KVI and price
perception
effects
Pull
forward
effects
The real-life model accounts for a much larger number of factors:
The basic price optimization model:
Price
Demand

8. 8
Profit Modeling and Optimization — Approach
Time
Current date Forecast
date
Demand/profit
7
days
30
days
365 days
GBDTree, Neural Network
Season/time
Sales data
Marketing activity
Product properties
Region
Channel
Weather
Public events
Markups
Markdowns
profit =
Internal
signals
Externals
signals
Variables to
be optimized
Segment
qualifiersDesign Goals
Forecast profits for new (previously
unobserved) products
● Introductory price
● Long-tail items
A product can be sold at different prices
(e.g. BOGO offers)
● Demand can be a function of price
distribution, not a single price
The model should support different levels
of aggregation
● By store groups, regions, climate zones
● By merchant hierarchy

9. Privileged and Confidential 9
Profit Modeling and Optimization — Case Study, Promotion Calendar
Situation
● A tier-one retailer has multiple types of offers and promotions: store level sales
events, category level promotions, and product level offers.
● Some combinations of promotions harm profits but there are no appropriate tools
to detect such combinations in advance or automatically optimize the promotion
calendar.
Goals
● Detect harmful offers – find offers with
negative contribution to profits
● Find opportunities – find promotion
opportunities missed by a merchant
● Maximize profits – find the optimal
combination of offers
Active offers
Offer
Engine
Shopping cart
$149 $429 2 x $99
Total:
$677 → $474 (30% off)
Filter Condition Action
Brand=Nike Buy 2+ $20 off
All Total $100+ 30% off
Type=shoes Buy 1+ Get 1 free
… … …

10. Privileged and Confidential 10
Profit Modeling and Optimization — Case Study, Promotion Calendar
Initial Calendar
5% off 7% off
3% off 30% off
20% off 15% off
Optimized Calendar
5% off 7% off
3% off 30% off
30% off 15% off
Time
Product properties
Weather
Public events
Markups
Markdowns
profit =
~90% of
losses
prevented

11. Privileged and Confidential 11
Other Considerations — Pricing Policies and Product Types
Replenishable Seasonal
Elasticity, cross
elasticity, etc.
KVI
Priority
Filler
Tail
Importance to consumer
Importancetobusiness
Digital
Brick & MortarStore type
Climate zone

12. Dynamic Pricing

13. Privileged and Confidential 13
Why Do We Need Dynamic Pricing
● Demand constantly changes
● Competitor prices change frequently
● Demand curve is unknown or cannot be accurately estimated
● Digital channels provide the ability to change prices rapidly
● Some business models are inherently dynamic - seasonal products, flash sales, etc.
● The number of products in ecommerce can be very large - need better automation

14. Privileged and Confidential 14
Design Goals for Dynamic Pricing
● Exploration-exploitation trade-off
● Compliance with the pricing policy
○ Valid and invalid price points (e.g. $39.99)
○ Valid and invalid price combinations
○ Limited number of price changes
● Optimization under inventory constraints
● Optimization at a large scale (many products, price levels, time intervals)

15. Privileged and Confidential 15
Approach 1 — Passive Learning
Time
Stock level
Price
Model re-
evaluation
Algorithm
1.Collect historical data about the demand at
different price points
2.Fit price-demand model
3.Calculate optimal prices for price-demand curve
4.Apply optimal price and observe the demand
The price-demand dependency is passively observed, no
effort is made to explore it.

16. Theoretical Result 2
● Lost profit (regret) decreases very rapidly as a function of the number of
allowed price changes
Privileged and Confidential 16
Approach 2 — Learning with Limited Price Experimentation (Groupon)
0 1 2 3 ...
Number of price
changes
Lost
profit
L
log L
log log L
log log log L
Theoretical Result 1
● Given stationary demand, selling time T, and m allowed
price changes, the optimal exploitation-exploitation
schedule is as follows:
Time
0 Tlog(m)(T) log(m-1)(T)
log(m)(T) = log(log(...log(T)))

17. Privileged and Confidential 17
Approach 2 — Learning with Limited Price Experimentation
Algorithm
1. h(p) = generate a set of demand curves
2. p = initial price
3. for i = [1, m] # rounds
4. apply p for log(m-i)(T)
time intervals
5. observe average demand
di for round i
6. find h*(p) with
minimal |h(p) - di|
7. p = optimal price for
h*(p)

18. 18
Approach 2 — Learning with Limited Price Experimentation
Algorithm
1. h(p) = generate a set of demand curves
2. p = initial price
3. for i = [1, m] # rounds
4. apply p for log(m-i)(T)
time intervals
5. observe average demand
di for round i
6. find h*(p) with
minimal |h(p) - di|
7. p = optimal price for
h*(p)

19. Idea
Demand model:
Prior distribution:
For t = [1, T]
1. Sample demand parameters from posterior:
2. Find optimal price for given sampled parameters:
3. Apply price p* and observe demand
4. Update the posterior with the observed price-demand pair
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Approach 3 — Thompson Sampling (Walmart)
Demand function
Demand distribution

20. Privileged and Confidential 20
Reminder — Poisson-Gamma Bayesian Update

21. Privileged and Confidential 21
Approach 3 — Thompson Sampling
Realization
Demand model (average demand for each price level):
For t = [1, T]
1. Sample demands from posterior:
2. Find optimal price for given sampled parameters:
3. Apply price p* and observe demand
4. Update history with the observed price-demand pair
w(𝛼) n (𝛽
)
d(𝜇)
p1 1 1 1
p2 1 1 1
p3 1 1 1
w(𝛼) n (𝛽
)
d(𝜇)
p1 1 1 1
p2 5 2 2.5
p3 1 1 1
The
total
demand
The
number
of times
the price
was
offered
Initial state
First trial

22. 22
Approach 3 — Thompson Sampling
Realization
Demand model (average demand for each price level):
For t = [1, T]
1. Sample demands from posterior:
2. Find optimal price for given sampled parameters:
3. Apply price p* and observe demand
4. Update history with the observed price-demand pair

23. Price Segmentation and
Personalization

24. Privileged and Confidential 24
Why Do We Need Price Segmentation
Price
Demand
Price
Demand
● Product level (luxury, mainstream, budget)
● Personalized discounts
● Geo location
● Sales channel
● Seasonal discounts
● ...
Volkswagen AG
Lost
revenue
Lost
revenue

25. Privileged and Confidential 25
Personalized Pricing through Promotion Targeting
● Goal - differentiate pricing based on
customer’s price sensitivity.
● ML models can identify customers
with highest potential uplift and/or
impact on lifetime-value.
● The models are build for different
objectives (acquisition, maximization,
retention)

26. Privileged and Confidential
Promotion Targeting — Look-Alike Modeling
Look-alike modeling:
time
positive
observation window buffer ?
Model training
Model scoring
negative
positive
observation window buffer outcome
Customer profiles for training
Customer profile to be scored

27. Privileged and Confidential 27
Acquisition ⇒ Current non-buyers with high propensity to buy new
Maximization ⇒ Current buyers with high propensity to buy more
Retention ⇒ Current buyers with high propensity to buy less
strict condition + propensity score
Promotion Targeting — Relationship with Business Objectives

28. Objective Selection Plan and Forecast
Review
User Experience
Execution and
Measurement
Privileged and Confidential 28
Promotion Targeting — Case Study

29. Summary
Models
Data
Solvers
External signals
● Competitor prices
● Public events
● Weather
Internal data
● Sales
● Promotions
● Inventory
● Marketing activity
● Product attributes
● Store data
Textual and visual
● Product descriptions
● Product images
Customer data
● Customer profiles
● Customer segment
Offline profit
models
Online profit
models
(reinforcement
learning)
Product
similarity scoring
Econometric
models
Propensity
scoring
Product
scoring
Profit
maximization
Inventory-constraint
revenue
maximization
Introductory
pricing
Offer targeting
Pricing
policy

30. Thank you!
www.griddynamics.com

31. Problem
● Demand is not always smooth: slow moving products, store-level models, etc.
● Standard ML models do not work well on such sparse data.
Privileged and Confidential 31
Other Considerations — Sporadic Demand
Solution
● Create specialized models e.g. to
predict zero demand intervals
● Use outputs of the specialized
models to make final demand
prediction