This document contains summaries of three projects related to pricing optimization: 1) Optimal discount strategy for products in close-out phase to balance margin loss and inventory costs. The solution involved sales forecasting, price elasticity modeling, and discount optimization. 2) Online pricing optimization using contextual multi-armed bandit algorithms to maximize ticket revenues. The solution used algorithms like UCB1 and ORAT. 3) Renewal price optimization for subscription products by developing elasticity curves and using simplex optimization to determine optimal prices given business objectives and constraints.

1. PRICING OPTIMIZATION
IN DATA REPLY
Ilaria Gianoli | Data Scientist
Giovanni Corradini | Data Scientist
Riccardo Lorenzon | Senior Data Scientist

2. OPTIMAL DISCOUNT
STRATEGY FOR PRODUCTS
IN CLOSE-OUT PHASE
Ilaria Gianoli | Data Scientist

3.  Customer:
Retail/GDO Leader
 Description:
Identify the optimal discount
strategy for products in their
close-out phase, as a trade-off
between margin loss and
inventory cost
THE PROBLEM

4. PROJECT BACKGROUNDInfo
• The purchasing department
establishes when a product goes
out of range
• In the close-out phase, the stores
have limited time to get rid of the
leftover stock, otherwise the have
to pay a penalty
• Each store chooses autonomously
the discount to apply
Alert
• The product prices do not change
often, except during the
marketing campaign
• The wide product range requires
the elasticity model to be product-
specific

5. SOLUTION OVERVIEW
DATA
TECH
• Elasticity model: linear regression
• Clustering model: DBscan
• Time series forecast: arima + FFNN + seasonal rescaling
ALGOS
Sales
Prices
Product info
Stock
Promotions

6. SOLUTION DETAIL
STEP 1:
SALES
FORECASTING
STEP 2:
PRICE
ELASTICITY
STEP 3:
DISCOUNT
OPTIMIZATION
• Use all the information about sellout, stock, prices,
calendar, marketing and discount campaigns to
create a clean time series;
• Create a forecast model on a weekly basis according
to the nature of the product (new, young, historical).
The forecast is at a product-store level;

7. SOLUTION DETAIL
• Use specific department weights to remove
seasonality from the time series;
• Create an elasticity model at product level;
• Clusterize the products according to their sales
potential and price range;
• Create a hierarchical elasticity model
STEP 1:
SALES
FORECASTING
STEP 2:
PRICE
ELASTICITY
STEP 3:
DISCOUNT
OPTIMIZATION

8. SOLUTION DETAIL
• Use the forecast model to estimate T*, i.e. the time
in which the stock is exhausted;
• Use the price elasticity coefficent to compute the
Δp for the desired Δq;
• Choose the optimal discount as
ത𝑇 = 𝑎𝑟𝑔 max
𝑡 ∈[𝑇,𝑇∗]
(𝑚𝑎𝑟𝑔𝑖𝑛 𝑝 𝑡 − 𝑓𝑒𝑒 𝑡 ) with stock(t) = 0
STEP 1:
SALES
FORECASTING
STEP 2:
PRICE
ELASTICITY
STEP 3:
DISCOUNT
OPTIMIZATION

9. BUSINESS BENEFITS
Quantitative
• Revenue improvement
• Reduction in penalties
• Reduction in inventory costs
Qualitative
• More visibility to new products
• Better space allocation in stores
• Homogeneity among stores

10. ONLINE PRICING: FROM
THEORY TO APPLICATION
Giovanni Corradini| Data Scientist

11. THE PROBLEM
 Customer:
Ticket selling company
 Problem:
Choose the price that maximize the total
revenue through application of Contextual
Multi-Armed Bandit algorithm

12. THE TRADE-OFF
 Exploration
 Find the best price by proposing different prices
 Many mistakes
 Exploitation
 Propose current best price to make money
 Maybe not the optimal one

13. A/B TESTING VS
MULTI-ARMED BANDIT
 A/B Testing
 Multi-Armed Bandit

14. THEORETICAL BACKGROUND
History of
contracts
 Bandit setting:
 Consider n rounds
 At every round we receive a request and propose a price (arm)
 We receive a reward from the environment (the customers)
 The price proposed if the customer bought the ticket
 0 otherwise
 Goal: maximize the sum of the rewards (minimize the “regret”)

15. BASIC ALGORITHMS
History of
contracts
 ε-greedy
 UCB

16. BASIC ALGORITHMS
 ε-greedy
 UCB
Round t
Random arm Current best arm
ε 1 − ε

17. BASIC ALGORITHMS
History of
contracts
 𝜺-greedy
 UCB
Compute UCB
for the mean of
each arm
Round t
Play arm with
highest UCB
UCB1, for arm j
ො𝑥 𝑗 +
2log 𝑡
𝑡𝑗

18. HYPOTHESIS AND LIMITATIONS
 Stationarity
 People can change behaviour
over time
 No context
 Additional information can be
used to take a better decision
Sliding windows
Contextual MAB

19. PROJECT BACKGROUND
 A part of the revenue of the provider comes from Metasearch engines
 Providers have access only to the context x and not to the user directly
User MS Provider
R(x) x
p(x)p(x)

20. SOLUTION OVERVIEW
DATA
TECH
• UCB1
• ORAT (Online Risk Averse Tree)ALGOS
Simulated requests from users

21. ALGORITHM DETAIL
 Contextual Multi-Armed Bandit
 Decision tree to partition the space of contexts
 Splits are made with confidence level
 A different policy in each partition based on UCB1
 Non-stationary environment
 Sliding window for UCB1
 Batch phase to change the partition of the decision tree
RM-LON
LON-PAR
3
21
! RM-LON
! LON-PAR

22. BUSINESS BENEFITS
Quantitative
• Increase of revenues
• Decrease of cost of maintenance
Qualitative
• Increase in customer satisfaction
• Increase in analytic know-how of
the process
• Improvement in testing process

23. RENEWAL PRICE
OPTIMIZATION FOR
SUBSCRIPTION PRODUCTS
Riccardo Lorenzon | Senior Data Scientist

24. THE PROJECT
 Customer:
Publishing Leader
 Description:
Let an algorithm decide the optimal
prices for renewal to subscription
products, given some boundaries and
objectives input by the customer

25. SUBSCRIPTION ECONOMY
In the Subscription Economy, every company must better
manage a direct, complex, responsive, multi-channel relationship
with its customers. Customers are absolutely key in this
relationship and rather than putting the focus of the business on
the “product” or the “transaction,” subscription economy
companies live and die by their ability to focus on the
customer. Now, the formula for growth is focused on monetizing
long-term relationships rather than shipping products.
Tien Tzuo – CEO, Zuora

26. SOLUTION OVERVIEW
DATA
TECH
• Elastic Net Regression
• Simplex Optimization Method + Euristics
ALGOS
History of
subscriptions
Refused price
proposals
Promotions
Customer Service
contacts

27. SOLUTION OVERVIEW
STEP 1:
DATA MODEL
PREPARATION
STEP 2:
ELASTICITY
CURVES
STEP 3:
PRICE
OPTIMIZATION

28. DATA PREPARATION
History of
subscriptions
Refused price
proposals
Promotions
Customer Service
contacts
Renewal Price Features
1 50 ...
0 58 ...
... ... ...

29. ELASTICITY CURVES
𝑙𝑜𝑔𝑖𝑡(𝑝) = 𝑓 𝑋 + 𝑔(𝑌)
𝑙𝑜𝑔𝑖𝑡(ෝ𝑝𝑖) = 𝛼𝑖 ∗ 𝑥 + 𝛽𝑖
ෝ𝑝𝑖 =
1
1 + 𝑒−(𝛼 𝑖∗𝑥+𝛽𝑖)
X: actionable variables
Y: non-actionable variables
p: renewal probability
x: price

30. ELASTICITY CURVES
We need to estimate a whole probability distribution
What is a good metric?

31. ELASTICITY CURVES
renewal probability vs. price
expected margin vs. price

32. PRICE OPTIMIZATION
Let the user input:
• Target KPIs
• Business specific onstraints
Get a global proposal of optimal
price for each contract

33. BUSINESS BENEFITS
Quantitative
• Increase of Revenues
• Increase of Margins
• Increase of Sales Volume
• Increase of Renewal Rate
• Increase of Campaigns success
rate
• Process Costs reductions
Qualitative • Increase Marketing analytic
know-how of customers

34. THANK YOU
i.gianoli@reply.it
g.corradini@reply.it
r.lorenzon@reply.it