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Operations Research (OR) and Its Applications in Industry. Bala Vaidyanathan Operations Research Advisor FedEx Express. Outline. What is OR? A Budget Problem Network Applications Shortest Path Problem Traveling Salesman Problem Applications at FedEx Applications in Other Industries

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Operations Research (OR) and Its Applications in Industry

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Operations Research (OR) and Its Applications in Industry

Bala Vaidyanathan

Operations Research Advisor

FedEx Express


Outline

  • What is OR?

  • A Budget Problem

  • Network Applications

    • Shortest Path Problem

    • Traveling Salesman Problem

  • Applications at FedEx

  • Applications in Other Industries

  • Closing Remarks


What is OR?

O.R. is real world, not just theory

O.R. is a practice, not just software

“ THE DISCIPLINE OF APPLYINGADVANCED

MATHEMATICAL METHODS

TO HELP MAKE BETTER DECISIONS”

O.R. is not about the ideal, but about sound judgment and conclusions

O.R. provides alternatives and options

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


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


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}?


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)


BP – Formulation & Solution

Maximize 2 X + 3 Y + 4 ZOR Formulation

Constraints:

10 X + 20 Y + 40 Z <= 50 (Money)

2 X + 3 Y + 4 Z <= 5 (Time)

X >= 0, Y >=0, Z >= 0, integer


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!!


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)


Network or Graph Applications

  • Network – Collection of nodes and arcs

  • Nodes – Entities (cities, people, computers)

  • Arcs – Connections between entities


Shortest Path Problem

2

3

4

D

1

1

O

2

6

7

2

  • Objective – Determine the shortest path from O to D

  • Constraints – Have to travel “on” the network

  • Decision variable – Which path to take?


Shortest Path Problem

2

3

4

Cost = 9

Cost = 12

1

1

2

D

O

6

7

2

Cost = 15


Shortest Path Application


Traveling Salesman Problem (TSP)

2

H

A

5

Cost = 12

4

3

4

C

B

1

Cost = 10

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

  • Objective – Find the minimum cost tour


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


TSP – FedEx Application


Air Network Design

NYC

SEA

LAX

ATL

MIA

LAS

Point-to-point Network (think SouthWest)


Air Network Design

NYC

SEA

LAX

ATL

MEM

MIA

LAS

Hub and Spoke Network (think Delta)


Air Network Design - Inputs

  • Origin Destination Pair Volume (cargo/passengers)

  • Different aircraft types

  • Hub capacities


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


Decision Options

A->D

A->E

A->F

B->D

B->E

C->D

C->E

C->F

D

A

H1

B

E

H2

F

C


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


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)


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?


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


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


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