# US 2019/0172082 A1 · Systems and methods for dynamic pricing

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- Number: US 2019/0172082 A1
- Document ID: US20190172082A1
- Status: Published application
- Kind: A1
- Application number: 16/202,065
- Filed: 2018-11-27
- Published: 2019-06-06
- Earliest claimed: 2017-11-27
- Assignees: Walmart Apollo, LLC
- Applicants: Walmart Apollo, LLC
- Inventors: Ravi Sastry Ganti Mahapatruni; Matyas Attila Sustik; Quoc Tan Tran; Brian Thomas Seaman
- Web page: https://patentgrep.com/patent/US20190172082A1

## CPC

- G06Q 30/0206: {Price or cost determination based on market factors}
- G06N 5/01: Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound
- G06N 5/048: Fuzzy inferencing
- G06N 7/01: Probabilistic graphical models, e.g. probabilistic networks
- G06N 20/00: Machine learning
- G06Q 10/067: Enterprise or organisation modelling
- G06Q 30/0202: Market predictions or forecasting for commercial activities
- G06Q: INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS

## Abstract

Systems and methods can include one or more processing modules and one or more non-transitory storage modules storing computing instructions configured to run on the one or more processing modules and perform acts of: estimating demand for one or more items in an electronic basket of items using one or more different demand models; estimating elasticity for the one or more items in the electronic basket of items using a multi-armed bandit model; determining a price using the demand and the elasticity; and facilitating display of the price on a video screen of a device. Other embodiments are disclosed herein.

## Claims

### Claim 1

A system comprising:
one or more processors; and
one or more non-transitory computer-readable storing computing instructions configured to run on the one or more processors and perform acts of:
estimating demand for one or more items in an electronic basket of items using one or more different demand models;
estimating elasticity for the one or more items in the electronic basket of items using a multi-armed bandit model;
determining a price using the demand and the elasticity; and
facilitating display of the price on a video screen of a device.

### Claim 2 (depends on 1)

The system of claim 1, wherein:
the one or more different demand models comprise multiple demand models;
estimating the demand for the one or more items in the electronic basket of items comprises:
calculating a weight for each demand model of the multiple demand models based on an accuracy of each demand model of the multiple demand models;
estimating the demand for the one or more items in the electronic basket of items using each demand model of the multiple demand models; and
combining the demand, as estimated by each demand model of the multiple demand models, into a combined estimated demand using the weight for each demand model of the multiple demand models.

### Claim 3 (depends on 1)

The system of claim 1, wherein the multi-armed bandit model comprises at least one of an upper confidence bound algorithm or a Thompson sampling algorithm.

### Claim 4 (depends on 1)

The system of claim 1, wherein:
the multi-armed bandit model comprises a Thompson sampling algorithm; and
estimating the elasticity for the one or more items in the electronic basket of items comprises:
placing a prior distribution over an elasticity parameter for the one or more items in the electronic basket of items;
placing a likelihood model over past revenue for the one or more items in the electronic basket of items; and
estimating the elasticity for the one or more items in the electronic basket of items using the prior distribution over the elasticity parameter and the likelihood model over the past revenue.

### Claim 5 (depends on 4)

The system of claim 4, wherein the prior distribution over the elasticity parameter for the one or more items in the electronic basket of items comprises a Gaussian prior distribution and the likelihood model over the past revenue for the one or more items in the electronic basket of items comprises a Gaussian likelihood model.

### Claim 6 (depends on 5)

The system of claim 5, wherein the Gaussian prior distribution comprises:
Π0(γ★)=N(μ0,Σ0), wherein:
γ★ comprises the elasticity parameter;
μ0 comprises a mean of the prior distribution; and
Σ0 comprises a covariance matrix of the prior distribution.

### Claim 7 (depends on 5)

The system of claim 5, wherein the Gaussian likelihood model comprises:
l(Rt;Revtγ★)=N(Rt;Revt,σ2), wherein:
Rt comprises a revenue for the electronic basket of items on a day t;
Revt comprises an average revenue of each item in the electronic basket of items;
γ★ comprises the elasticity parameter; and
σ comprises a noise variance.

### Claim 8 (depends on 4)

The system of claim 4, wherein:
estimating the elasticity for the one or more items in the electronic basket of items further comprises:
rejecting the elasticity parameter when the elasticity parameter is greater than a predetermined threshold; and
determine the price comprises:
optimizing a concave function using convex constraints.

### Claim 9 (depends on 8)

The system of claim 8, wherein the concave function comprises:
p
t
=
arg

p
max
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∑
i
∈
ℬ
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p
i
2
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f
i
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,
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γ
★
,
i
p
i
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,
t
-
1
-
p
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,
t
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γ
★
,
i
+
p
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f
i
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,
wherein:
p comprises the price;
i comprises the one or more items;
comprises the electronic basket of items;
fi,t comprises a demand forecast for the one or more items on a day t; and
γ★ comprises the elasticity parameter.

### Claim 10 (depends on 1)

The system of claim 1, wherein the one or more different demand models comprise:
d
i
,
t

(
p
i
)
=
f
i
,
t

(
p
i
p
i
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-
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γ
★
,
i
,
wherein:
di,t comprises a demand for the one or more items item i on a day t;
pi comprises a price of the one or more items;
fi,t comprises a demand forecast for the one or more items on a day t; and
γ★ comprises the elasticity parameter.

### Claim 11

A method being implemented via execution of computing instructions configured to run at one or more processors and configured to be stored at non-transitory computer-readable media, the method comprising:
estimating demand for one or more items in an electronic basket of items using one or more different demand models;
estimating elasticity for the one or more items in the electronic basket of items using a multi-armed bandit model;
determining a price using the demand and the elasticity; and
facilitating display of the price on a video screen of a device.

### Claim 12 (depends on 11)

The method of claim 11, wherein:
the one or more different demand models comprise multiple demand models;
estimating the demand for the one or more items in the electronic basket of items comprises:
calculating a weight for each demand model of the multiple demand models based on an accuracy of each demand model of the multiple demand models;
estimating the demand for the one or more items in the electronic basket of items using each demand model of the multiple demand models; and
combining the demand, as estimated by each demand model of the multiple demand models, into a combined estimated demand using the weight for each demand model of the multiple demand models.

### Claim 13 (depends on 11)

The method of claim 11, wherein the multi-armed bandit model comprises at least one of an upper confidence bound algorithm or a Thompson sampling algorithm.

### Claim 14 (depends on 11)

The method of claim 11, wherein:
the multi-armed bandit model comprises a Thompson sampling algorithm; and
estimating the elasticity for the one or more items in the electronic basket of items comprises:
placing a prior distribution over an elasticity parameter for the one or more items in the electronic basket of items;
placing a likelihood model over past revenue for the one or more items in the electronic basket of items; and
estimating the elasticity for the one or more items in the electronic basket of items using the prior distribution over the elasticity parameter and the likelihood model over the past revenue.

### Claim 15 (depends on 14)

The method of claim 14, wherein the prior distribution over the elasticity parameter for the one or more items in the electronic basket of items comprises a Gaussian prior distribution and the likelihood model over the past revenue for the one or more items in the electronic basket of items comprises a Gaussian likelihood model.

### Claim 16 (depends on 15)

The method of claim 15, wherein the Gaussian prior distribution comprises:
Π0(γ★)=N(μ0,Σ0), wherein:
γ★ comprises the elasticity parameter;
μ0 comprises a mean of the prior distribution; and
Σ0 comprises a covariance matrix of the prior distribution.

### Claim 17 (depends on 15)

The method of claim 15, wherein the Gaussian likelihood model comprises:
l(Rt;Revtγ★)=N(Rt;Revt,σ2), wherein:
Rt comprises a revenue for the electronic basket of items on a day t;
Revt comprises an average revenue of each item in the electronic basket of items;
γ★ comprises the elasticity parameter; and
σ comprises a noise variance.

### Claim 18 (depends on 14)

The method of claim 14, wherein:
estimating the elasticity for the one or more items in the electronic basket of items further comprises:
rejecting the elasticity parameter when the elasticity parameter is greater than a predetermined threshold; and
determine the price comprises:
optimizing a concave function using convex constraints.

### Claim 19 (depends on 8)

The method of claim 8, wherein the concave function comprises:
p
t
=
arg

p
max

∑
i
∈
ℬ

p
i
,
t
2

f
i

,
t

γ
★
,
i
p
i

,
t
-
1
-
p
i

f
i

,
t

γ
★
,
i
+
p
i

f
i

,
t
,
wherein:
p comprises the price;
i comprises the one or more items;
comprises the electronic basket of items;
fi,t comprises a demand forecast for the one or more items on a day t; and
γ★ comprises the elasticity parameter.

### Claim 20 (depends on 11)

The method of claim 11, wherein the one or more different demand models comprise:
d
i
,
t

(
p
i
)
=
f
i
,
t

(
p
i
p
i
,
t
-
1
)
γ
★
,
i
,
wherein:
di,t comprises a demand for the one or more items item i on a day t;
pi comprises a price of the one or more items;
fi,t comprises a demand forecast for the one or more items on a day t; and
γ★ comprises the elasticity parameter.