Online Resource Allocation Problems, with Applications to Revenue Management

129 Pages·2017·0.77 MB·English

Online Resource Allocation Problems, with Applications
to Revenue Management
David Simchi-Levi (MIT)
DavidSimchi-Levi (MIT) OnlineResourceAllocation 0/22
Introduction
Papers
1 Tight Weight-dependent Competitive Ratios for Online Matching
Problems
joint work with Will Ma
2 Dynamic Recommendation at Checkout under Inventory Constraint
joint work with Xi Chen, Will Ma, and Linwei Xin
DavidSimchi-Levi (MIT) OnlineResourceAllocation 3/22
OnlineResourceAllocation
Papers
1 Tight Weight-dependent Competitive Ratios for Online
Matching Problems
joint work with Will Ma
2 Dynamic Recommendation at Checkout under Inventory Constraint
joint work with Xi Chen, Will Ma, and Linwei Xin
DavidSimchi-Levi (MIT) OnlineResourceAllocation 3/22
Known at start:
number of items (resources), n
unreplenishable starting inventory of each item i, k
i
m potential prices of each item i, satisfying r(1) <...<r(mi)
i i i
For t = 1,2,...
1 Customer t Arrives:
observe p(j), the probability of customer t buying item i at price j, for
t,i
all i and j (can be based on customer features or classes)
2 Decision:
offer an item i which has not stocked out, at a price j , to customer t
t t
3 Realization:
customer makes purchase with probability p(jt)
t,it
if she purchases, then earn revenue r(jt) and decrement inventory of i
it t
Extensions:
can allow an assortment of items/prices to be offered to each customer
can allow an item to have a continuum of potential prices
can allow for fractional inventory consumption
OnlineResourceAllocation ProblemDefinition
A General Online Resource Allocation Problem
DavidSimchi-Levi (MIT) OnlineResourceAllocation 4/22
number of items (resources), n
unreplenishable starting inventory of each item i, k
i
m potential prices of each item i, satisfying r(1) <...<r(mi)
i i i
For t = 1,2,...
1 Customer t Arrives:
observe p(j), the probability of customer t buying item i at price j, for
t,i
all i and j (can be based on customer features or classes)
2 Decision:
offer an item i which has not stocked out, at a price j , to customer t
t t
3 Realization:
customer makes purchase with probability p(jt)
t,it
if she purchases, then earn revenue r(jt) and decrement inventory of i
it t
Extensions:
can allow an assortment of items/prices to be offered to each customer
can allow an item to have a continuum of potential prices
can allow for fractional inventory consumption
OnlineResourceAllocation ProblemDefinition
A General Online Resource Allocation Problem
Known at start:
DavidSimchi-Levi (MIT) OnlineResourceAllocation 4/22
unreplenishable starting inventory of each item i, k
i
m potential prices of each item i, satisfying r(1) <...<r(mi)
i i i
For t = 1,2,...
1 Customer t Arrives:
observe p(j), the probability of customer t buying item i at price j, for
t,i
all i and j (can be based on customer features or classes)
2 Decision:
offer an item i which has not stocked out, at a price j , to customer t
t t
3 Realization:
customer makes purchase with probability p(jt)
t,it
if she purchases, then earn revenue r(jt) and decrement inventory of i
it t
Extensions:
can allow an assortment of items/prices to be offered to each customer
can allow an item to have a continuum of potential prices
can allow for fractional inventory consumption
OnlineResourceAllocation ProblemDefinition
A General Online Resource Allocation Problem
Known at start:
number of items (resources), n
DavidSimchi-Levi (MIT) OnlineResourceAllocation 4/22
m potential prices of each item i, satisfying r(1) <...<r(mi)
i i i
For t = 1,2,...
1 Customer t Arrives:
observe p(j), the probability of customer t buying item i at price j, for
t,i
all i and j (can be based on customer features or classes)
2 Decision:
offer an item i which has not stocked out, at a price j , to customer t
t t
3 Realization:
customer makes purchase with probability p(jt)
t,it
if she purchases, then earn revenue r(jt) and decrement inventory of i
it t
Extensions:
can allow an assortment of items/prices to be offered to each customer
can allow an item to have a continuum of potential prices
can allow for fractional inventory consumption
OnlineResourceAllocation ProblemDefinition
A General Online Resource Allocation Problem
Known at start:
number of items (resources), n
unreplenishable starting inventory of each item i, k
i
DavidSimchi-Levi (MIT) OnlineResourceAllocation 4/22
For t = 1,2,...
1 Customer t Arrives:
observe p(j), the probability of customer t buying item i at price j, for
t,i
all i and j (can be based on customer features or classes)
2 Decision:
offer an item i which has not stocked out, at a price j , to customer t
t t
3 Realization:
customer makes purchase with probability p(jt)
t,it
if she purchases, then earn revenue r(jt) and decrement inventory of i
it t
Extensions:
can allow an assortment of items/prices to be offered to each customer
can allow an item to have a continuum of potential prices
can allow for fractional inventory consumption
OnlineResourceAllocation ProblemDefinition
A General Online Resource Allocation Problem
Known at start:
number of items (resources), n
unreplenishable starting inventory of each item i, k
i
m potential prices of each item i, satisfying r(1) <...<r(mi)
i i i
DavidSimchi-Levi (MIT) OnlineResourceAllocation 4/22
1 Customer t Arrives:
observe p(j), the probability of customer t buying item i at price j, for
t,i
all i and j (can be based on customer features or classes)
2 Decision:
offer an item i which has not stocked out, at a price j , to customer t
t t
3 Realization:
customer makes purchase with probability p(jt)
t,it
if she purchases, then earn revenue r(jt) and decrement inventory of i
it t
Extensions:
can allow an assortment of items/prices to be offered to each customer
can allow an item to have a continuum of potential prices
can allow for fractional inventory consumption
OnlineResourceAllocation ProblemDefinition
A General Online Resource Allocation Problem
Known at start:
number of items (resources), n
unreplenishable starting inventory of each item i, k
i
m potential prices of each item i, satisfying r(1) <...<r(mi)
i i i
For t = 1,2,...
DavidSimchi-Levi (MIT) OnlineResourceAllocation 4/22
2 Decision:
offer an item i which has not stocked out, at a price j , to customer t
t t
3 Realization:
customer makes purchase with probability p(jt)
t,it
if she purchases, then earn revenue r(jt) and decrement inventory of i
it t
Extensions:
can allow an assortment of items/prices to be offered to each customer
can allow an item to have a continuum of potential prices
can allow for fractional inventory consumption
OnlineResourceAllocation ProblemDefinition
A General Online Resource Allocation Problem
Known at start:
number of items (resources), n
unreplenishable starting inventory of each item i, k
i
m potential prices of each item i, satisfying r(1) <...<r(mi)
i i i
For t = 1,2,...
1 Customer t Arrives:
observe p(j), the probability of customer t buying item i at price j, for
t,i
all i and j (can be based on customer features or classes)
DavidSimchi-Levi (MIT) OnlineResourceAllocation 4/22