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Operations Research (OR) and Its Applications in Industry

Bala VaidyanathanOperations Research Advisor

FedEx Express

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Outline• What is OR?• A Budget Problem• Network Applications– Shortest Path Problem– Traveling Salesman Problem

• Applications at FedEx• Applications in Other Industries• Closing Remarks

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What is OR?O.R. is a practice, not just software

O.R. is real world, not just theory

O.R. is not about the ideal, but about sound

judgment and conclusions

O.R. provides alternatives and options

“ THE DISCIPLINE OF APPLYING ADVANCED MATHEMATICAL METHODS

TO HELP MAKE BETTER DECISIONS ”

Lies at the interface of mathematics, computer science, and business

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History of OR• Originated during World War II• 1935 – 1937: Research on Radar• 1938 – “Operations Research” group set up at

Bawdsey, England• 1942 – Anti-submarine Warfare Operations

Research Group (ASWORG) set up• Post war – Success of OR in war effort spurred

further interest in using it for decision making

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Budget Problem• You have $50 to spend and 5 hours of time• Options– Movies • $10/movie, 2 hours/movie, Fun factor: 2

– Concert• $20/concert, 3 hours/movie, Fun factor: 3

– Mall• $40/visit, 4 hours/visit, Fun factor: 4

• What should I do to Maximize {Total Fun}?

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Budget Problem – Key Aspects• Objective: Maximize {Total Fun}• Constraints– Total time spent <= 5 hours– Total money spent <= $50

• Decision Variables– Number of movies to watch (X)– Number of concerts to attend (Y)– Number of mall visits (Z)

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BP – Formulation & SolutionOptions Cost($) Time (Hr) Fun Variable

Movie 10 2 2 X

Concert 20 3 3 Y

Mall 40 4 4 Z

Constraints

Total money $50

Total time 5 Hr

Maximize 2 X + 3 Y + 4 Z OR FormulationConstraints:10 X + 20 Y + 40 Z <= 50 (Money)2 X + 3 Y + 4 Z <= 5 (Time)X >= 0, Y >=0, Z >= 0, integer

Opt. Fun Value 5

X 1

Y 1

Z 0

Money Spent Time Spent

$10 2 hr

$20 3 hr

$0 0 hr

Unused money

Unused Time

$20 0 hr

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BP - Conclusions• Formally (mathematically) define the problem using OR

• Solve the OR problem to determine the “optimal” choices

• Gather additional insights. For e.g.– Money is not a bottleneck – We could have $100 or even $1000;

nothing changes– Time is a bottleneck

• Used OR analysis to make policy decisions - Bargain for time!!

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Learning so far

• Every practical OR problem has:– An objective – Maximize or Minimize something– Decision variables – Constraints

• Operations Research used to:– Define a decision problem using math– Solve the math problem– Enable better decision making (Decision Support)

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Network or Graph Applications

• Network – Collection of nodes and arcs• Nodes – Entities (cities, people, computers)• Arcs – Connections between entities

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Shortest Path Problem

4

6

2

2

2

1 1

3

7

O D

• Objective – Determine the shortest path from O to D• Constraints – Have to travel “on” the network• Decision variable – Which path to take?

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Shortest Path Problem

4

6

2

2

2

1 1

3

7

O D

Cost = 15

Cost = 12

Cost = 9

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Shortest Path Application

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Traveling Salesman Problem (TSP)

C

H A

B

2

5

434

1

Cost = 12

Cost = 10

• Tour – A sequence of nodes such that each node in the network is visited once

• Objective – Find the minimum cost tour

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TSP – Problem Size• Problem size: How many candidate tours are

there? A network with:– 2 nodes: 1 tour– 3 nodes: 2 tours– 5 nodes: 24 tours– 10 nodes: 362 thousand tours– 20 nodes: 87 billion tours– N nodes: (N-1)! tours

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TSP – FedEx Application

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Air Network Design

SEA

LAX

LAS

NYC

ATL

MIA

Point-to-point Network (think SouthWest)

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Air Network Design

SEA

LAX

LAS

NYC

ATL

MIA

MEM

Hub and Spoke Network (think Delta)

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Air Network Design - Inputs

• Origin Destination Pair Volume (cargo/passengers)

• Different aircraft types

• Hub capacities

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Air Network Design• Objective – Determine the minimum cost way to transport

volume/passengers using existing aircraft fleet

• Decisions– Every O-D pair is connected to which hub?– For each O-D pair what is the exact delivery path (with aircraft types)

?

• Constraints– Aircraft capacities– Hub capacities– Operational considerations

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Decision Options

A

B

H1

C

H2

D

E

F

A->DA->EA->F

B->DB->EC->DC->EC->F

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Other Applications• HP

– O.R. used to reduce complexity of HP’s product portfolio – Impacted sales, marketing, and supply chain– OR bridges the organizational divide between marketing and supply chain– $500 million/ongoing $180 million per year

• Intel– Start with improving factory operations– Factory design, factory construction, factory to factory supply chain– Impacts every aspect of the Intel business– Over $4 billion over the last decade

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Other Applications

• NBC– Develop detailed sales plans for the inventory of advertising slots – Fast plan creation, decreased rework, improved quality, better pricing – Increased revenues by at least $50 million a year

• American Airlines– First large corp. to benefit from adopting OR– Revenue management generated $1.4 billion in incremental revenue – OR used to support all airline operations– Spun off OR group into Sabre (travelocity)

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Should you consider a career in OR?• Operations researchers help make critical

decisions in many different areas– How many elevators should be installed to reduce

wait time?– What is the most efficient way to route a call?– How often should check-ups be scheduled for

members of a health plan?– How should a dress/furniture manufacturer lay

out patterns to minimize wastage?

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How can one contribute?

• Academia– Develop new mathematical theories to

formulate/define OR problems– Develop newer and faster algorithms to solve the

associated math problems

• Industry– Apply OR techniques/develop new techniques to

improve profits

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Further Information

• Institute for Operations Research and the Management Science– www.informs.org

• High School Operations Research– http://www.hsor.org/

• The Cosmic Distance Ladder (Terry Tao)– http://youtu.be/7ne0GArfeMs– http://www.math.ucla.edu/itunes