Blind Network Revenue Management

T
J (x, T |λ)
∗
:=
sup E
p(·)
p(s) · dN (s)
0
demand function is known Constraints:
T
Poisson process with intensity λ(p(s))
AdN (s) ≤ x
0
a.s., initial inventory
Capacity-Consumption matrix
5-a
Network RM: Problem Formulation
Objective: max revenues over a finite sales horizon [Gallego and van Ryzin (1997)]
T
J (x, T |λ)
∗
:=
sup E
p(·)
p(s) · dN (s)
5-c
The Blind Network RM Problem
Do not know the structure of the demand function a priori – only assume that λ ∈ L = nonparametric class of demand functions... – know value of shut-off price p∞ ...
Revenue Management
deals with complex demand management decisions... – typical decision variables: price and/or capacity allocation dates back to the airline deregulation act (∼ 1978) RM adopted by a growing number of industries... “rich” area of OR / Engineering / Statistics problems – blend of optimization, modeling, data analysis... advent of the Internet – easily implementable, costless, price changes – customized pricing, simplified price exploration
p(s) ∈ Dp 0 ≤ s ≤ T
feasible price set
p(·) is non anticipating
exists a shut-off price p∞ Bellman equation =⇒ optimal Markov policy Can rarely solve or compute optimal policy or value function...
3
Network Revenue Management
Basic ingredients finite horizon (T ) initial inventory (vector x) of primitive resources (of which there are – flights legs, links on network, raw materials, etc finished product (of which there are d types) – tickets (o-d pairs), routes, assembled/produced goods, etc see examples in Talluri and van Ryzin (2005) objective: maximize revenues by suitable pricing policy demand function [ price → mean demand rate ] types)
0
demand function is known Constraints:
T
Poisson process with intensity λ(p(s))
AdN (s) ≤ x
0
a.s., initial inventory
Capacity-Consumption matrix
p(s) ∈ Dp 0 ≤ s ≤ T
6
The Blind Network RM Problem
Do not know the structure of the demand function a priori – only assume that λ ∈ L = nonparametric class of demand functions... – know value of shut-off price p∞ ...
T
J (x, T |λ)
∗
:=
sup E
p(·)
p(s) · dN (s)
0
demand function is known
Poisson process with intensity λ(p(s))
5
Network RM: Problem Formulation
Objective: max revenues over a finite sales horizon [Gallego and van Ryzin (1997)]
• How long to experiment? • Performance guarantee?
4-c
Network RM: Problem Formulation
Objective: max revenues over a finite sales horizon [Gallego and van Ryzin (1997)]
T
J (x, T |λ)
∗
:=
sup E
p(·)
p(s) · dN (s)
0
demand function is known Constraints:
T
Poisson process with intensity λ(p(s))
AdN (s) ≤ x
0
a.s., initial inventory
Capacity-Consumption matrix
2
Network Revenue Management
Basic ingredients finite horizon (T ) initial inventory (vector x) of primitive resources (of which there are – flights legs, links on network, raw materials, etc finished product (of which there are d types) – tickets (o-d pairs), routes, assembled/produced goods, etc see examples in Talluri and van Ryzin (2005) types)
Blind Network Revenue Management
Assaf zeevi∗
Columbia University Graduate School of Business
June 2008
∗
joint work with Omar Besbes (Wharton School, UPenn)
Use past interactions to fit a parametric model – price (optimize) based on the estimated model
4-a
What’s done in Practice
Use past interactions to fit a parametric model – price (optimize) based on the estimated model With little past interaction: “price test” – pick “best” price among those tested Applicability: – “90% of large U.S. retailers conduct some type price experiments” – very ad hoc guiding principles
P = admissible learning and pricing policies π
T
AdN π (s) ≤ x
0
a.s.
[capacity constraint ] [feasible price set ]
p(s) ∈ Dp , 0 ≤ s ≤ T p(·) is non anticipating
key ingredient:
– typically (= academic studies) assumed known to decision maker...
3-a
Network Revenue Management
Basic ingredients finite horizon (T ) initial inventory (vector x) of primitive resources (of which there are – flights legs, links on network, raw materials, etc finished product (of which there are d types) – tickets (o-d pairs), routes, assembled/produced goods, etc see examples in Talluri and van Ryzin (2005) objective: maximize revenues by suitable pricing policy demand function [ price → mean demand rate ] types)