Operations Research (OR) and Its Applications in Industry

1. Operations Research (OR) and Its Applications in Industry Bala Vaidyanathan Operations Research Advisor FedEx Express

2. Outline • What is OR? • A Budget Problem • Network Applications • Shortest Path Problem • Traveling Salesman Problem • Applications at FedEx • Applications in Other Industries • Closing Remarks

3. 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

4. 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

5. 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}?

6. 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)

7. BP – Formulation & Solution Maximize 2 X + 3 Y + 4 Z OR 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

8. 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!!

9. 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)

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

11. 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?

12. Shortest Path Problem 2 3 4 Cost = 9 Cost = 12 1 1 2 D O 6 7 2 Cost = 15

13. Shortest Path Application

14. 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

15. 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

16. TSP – FedEx Application

17. Air Network Design NYC SEA LAX ATL MIA LAS Point-to-point Network (think SouthWest)

18. Air Network Design NYC SEA LAX ATL MEM MIA LAS Hub and Spoke Network (think Delta)

19. Air Network Design - Inputs • Origin Destination Pair Volume (cargo/passengers) • Different aircraft types • Hub capacities

20. 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

21. 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

22. 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

23. 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)

24. 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?

25. 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

26. 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