Applied Management Science Introduction Tran, Van Hoai Faculty of Computer Science & Engineering HCMC University of Technology Tran Van Hoai

Jam jam jam Tran Van Hoai2

…and still jam jam jam Tran Van Hoai3

Ideas ? General solutions – to remove network of roads – to …destroy all vehicles – to open more roads to extend existing roads – To reduce vehicles (or people) To extend existing vehicles’ size Tran Van Hoai4 Beginning of human-beings HCMC, Hanoi LONG TERM

Ideas Operational solutions – to modify intersection geometry – to control traffic light(s) static, dynamic (adaptive) – to assign lanes for each vehicle type routes assigned for each lane – to enforce law/regulations on drivers Tran Van Hoai5 Road(s) Control(s) Vehicle(s) SHORT TERM

Challenge in proposed solutions Ideas to solve traffic jam are quite obvious But how to solve is not easy Tran Van Hoai6 SCIENTIFIC APPROACH Modeling Optimizing Analyzing Simulating QUANTITATIVE RESULT

Definitions Management science is the discipline that adapts the scientific approach for problem solving to executive decision making in order to accomplish the goal of “doing the best you can with what you’ve got” (Laurence & Pasternack) Operations research is an interdisciplinary branch of applied mathematics and formal science using mathematical modeling, statistical analysis, and mathematical optimization, … to arrive at optimal or near-optimal solutions to complex decision-making problems (wiki) Tran Van Hoai7

More (historical) definitions Scientific methods of providing executive departments with a quantitative basis for decisions regarding operations under their control (Morse & Kimball – 1951) The use of techniques such as statistical inference and decision theory, mathematical programming, probabilistic models, network and computer science [to solve complex operational and strategic issues] (US Army Pamphlet 600-3) Tran Van Hoai8

Who need MS/OR ? (1) Profit company – To make money for stockholders – To subject to responsibilities/restrictions Delivering in reasonable time Fair wage/working conditions for workers Good products/services … Tran Van Hoai9 Doing the best with what you’ve got

Who need MS/OR ? (2) Nonprofit organization – To provide minimum cost – To subject to responsibilities/restrictions Being responsible to oversees (donors, subscribers,…) Good service … Tran Van Hoai10 Doing the best with what you’ve got

Who need MS/OR ? (3) Government agencies – To expect citizens,company to obey laws – To subject to responsibilities/restrictions Limitation of resources (capital, personnel, technology,…) … Tran Van Hoai11 Doing the best with what you’ve got

Who need MS/OR ? (4) My wife: to choose among n foods, each provides some of each of m nutrients – To find least expensive diet – To subject to responsibilities/restrictions Guaranteeing nutrients totally provided … Tran Van Hoai12 Doing the best with what you’ve got

Some applications (not in Vietnam) Producing Hamburgers at Burger King – Linear programming Scheduling Crews at American Airlines – Integer linear programming Planning the Sony Advanced Traveler Information System – Shortest path network Planning Environmental Policy in Finland – Decision analysis Cooking at Mrs. Fields – Inventory modeling Designing Attractions at Disneyland – Queuing models Transporting Trash in New York City – Simulation model Tran Van Hoai13

What is crew scheduling ? SGN 0730 HAN 0940 HAN 1340 DAD 1455 DAD 1655 SGN 1810 SGN 1510 DAD 1625 HAN 1010 SGN 1215 Aircraft 1 Aircraft 2 DAD 1650 HAN To assign pilots to flight legs -To manage pilot database, including  Personal information  Timetable for training, vacation, day-off, … -To monitor/report daily operations -To assign pilots to flight legs -To manage pilot database, including  Personal information  Timetable for training, vacation, day-off, … -To monitor/report daily operations

Trivial schedule SGN 0730 HAN 0940 HAN 1340 DAD 1455 DAD 1655 SGN 1810 SGN 1510 DAD 1625 HAN 1010 SGN 1215 Aircraft 1 Aircraft 2 DAD 1650 HAN 1800 AAA BBB - Easy to make manually, but  Having critical drawbacks … - Easy to make manually, but  Having critical drawbacks … Better schedule (pilot A) 4h + 2h + (pilot B) 2h55' + 25' = 9h20' idle for duty/ground out-base (pilot A) 4h + 2h + (pilot B) 2h55' + 25' = 9h20' idle for duty/ground out-base

PrimeSolution schedule SGN 0730 HAN 0940 HAN 1340 DAD 1455 DAD 1655 SGN 1810 SGN 1510 DAD 1625 HAN 1010 SGN 1215 Aircraft 1 Aircraft 2 DAD 1650 HAN 1800 ABA AAB - Much less duty/ground out-base time  Less payment for idle time  Backup pilots for disruptions - Much less duty/ground out-base time  Less payment for idle time  Backup pilots for disruptions and MS/OR has more (pilot A) 30' + 30' + (pilot B) 1h55' = 2h55' idle for duty/ground out-base (pilot A) 30' + 30' + (pilot B) 1h55' = 2h55' idle for duty/ground out-base

PrimeSolution fulfillment of rules SGN 0730 HAN 0940 HAN 1340 DAD 1455 DAD 1655 SGN 1810 SGN 1510 DAD 1625 HAN 1010 SGN 1215 Aircraft 1 Aircraft 2 DAD 1650 HAN 1800 AAA BBB Do not allow connection with rest time less than 30' violates SGN 0730 HAN 0940 HAN 1340 DAD 1455 DAD 1655 SGN 1810 SGN 1510 DAD 1625 HAN 1010 SGN 1215 Aircraft 1 Aircraft 2 DAD 1650 HAN 1800 ABA AAB

Key challenges – rules  Must comply with sets of rules – Issued by the government (Cục hàng không dân dụng) – Union/Contractual agreements – Operational rules - Number of flying time per day - Number of duty time per week - Minimum resting time between consecutive flights - Minimum resting time for a week, month, year - … - Number of flying time per day - Number of duty time per week - Minimum resting time between consecutive flights - Minimum resting time for a week, month, year - … - Maximum number of consecutive flights out-base - Maximum days for consecutive flights out-base - Bases for night resting - … - Maximum number of consecutive flights out-base - Maximum days for consecutive flights out-base - Bases for night resting - … - Cannot check manually - Often changed - Cannot check manually - Often changed COMPLEX

Key challenges – cost structures  Crew cost only less than fuel cost – Payment for crew flying time – Payment for duty/ground out-base time – Operational objectives - Hotel costs - Per diem expenses - Dead-heading cost - … - Hotel costs - Per diem expenses - Dead-heading cost - … - Maximize number of patterns (tour-of-duty) - Minimize number of patterns - Minimize number of out-base night rests - … - Maximize number of patterns (tour-of-duty) - Minimize number of patterns - Minimize number of out-base night rests - … - Non-expert cannot model - Often changed - Non-expert cannot model - Often changed SPECIFIC TRADEOFF

Key challenges – number of solutions  Business view point – Find low cost/high profit solution, but do not violate any rules  Operational view point – Find robust (for disruption) solution, but do not violate rules - Good solution but violating rules - Valid solution but high cost - … - Good solution but violating rules - Valid solution but high cost - … - Manual schedule is impossible - Only information technology and mathematics can help - Manual schedule is impossible - Only information technology and mathematics can help HARD HUGE # - Robust solution but violating rules - Valid solution but weak - … - Robust solution but violating rules - Valid solution but weak - …

Current schedule Possible rule violation MS/OR provides better schedule 61 duty/ground out-base nights

A better schedule 35 duty/ground out-base nights No rule violation

History Reading materials (given later) Similar words: – Operation research – Management science – Decision sciences – Quantitative methods Take (often) a quantitative view of decision making – Industrial engineering Tran Van Hoai23

MS/OR process Tran Van Hoai24 Problem Definition Mathematical Modeling Solution of the Model Communication/Imple- mentation of Results