Operations Research Instructor Xiaoxi Li 李晓蹊 Wuhan University

Operations Research Instructor: Xiaoxi Li (李晓蹊) Wuhan University， Fall 2017 1

• Textbook: Introduction to Operations Research, F. Hillier & G. Lieberman, 10 th edition • • Grade: 25% exercises + 25% mid-term exam + 50% final exam (待定) Email: xli_whu@163. com Course website: http: //xiaoxili. weebly. com/teaching TA: 杨昊郑晓瑜常雅男 • Office: 亮胜楼 c 151 • Office hour: to be specified (by appointment) 2

• Course materials: Textbook + PPT/Board + Lecture notes + Case papers • Course goals: 1. analyze the real-application problem and design for it a OR model; 2. able to solve some small-scale OR problems by hand (algorithm); 3. use some software (ex. Excel, Matlab) to solve some OR models. • Evaluation details (HW and Exam, written in English): 1. Sets of exercises to be distributed. You are required to solve them independently and hand them in. Corrections will be given. 2. [Sets of reading papers (case study) to be distributed. You are required to read them selectively and hand in 2 -3 reports (typed by computer). ] (deleted) --> possibly a team project 3. Mid-term exam: mainly focus on LP. 4. Final exam. 3

Course plan (preliminary) 1. Introduction; 2. Linear Programming 2. 1 LP: modeling and graphical solution; 2. 2 LP: simplex method; 2. 3 LP: duality, sensitive analysis and other algorithms; 2. 4 Transportation and assignment problems; 3. Networking optimization model; 4. Integer programming; 5. Queueing theory 4

Lecture 1: OR: an introduction week one • Course Scope: 1. OR: concept, origin and development. 2. The classification of OR models. 3. The steps of an OR study: an overview. 4. OR applications: real-world cases. 5

Introduction • Operations Research is an Art and Science • OR has its early roots in World War II and is flourishing in business and industry with the aid of computer • Application areas of OR include military, industry, business, public sector, healthcare… 6

1. 1 OR: concept, origin and development Operations (作业/运作/操作) The activities carried out in an organization. 例如: 手术，反恐，安检，招聘 … Research （研究） The process of observation and testing characterized by the scientific method. “Operations Research is a discipline that deals with the application of advanced analytical methods (optimization, statistics, algorithm) to help make better decisions. ” OR: the science of better. ----- INFORMS 7

OR: Terminology The British refer to “Operational Research", the Americans to “Operations Research" - but both are often shortened to just "OR". “Operational” was named, as opposed to the word “technical”, for the Radar Control System in the World War II. Another term used for this field is “Management Science" ("MS"). In U. S. OR and MS are combined together to form "OR/MS" or "ORMS". Yet other terms sometimes used are “Industrial Engineering" ("IE") or “Decision Science" ("DS") with a possibly different focus. 8

OR: Academic Journals Theory: 1. Operations Research 2. Management Science 3. European Journal of Operational Research 4. Journal of the Operational Research Society 5. Mathematical Programming 6. Networks 7. Naval Research Logistics … Application / Case study: Interfaces 9

OR: Societies and Institutes International: The International Federation of OR Societies UK: The OR Society US: Operations Research Society of America (ORSA) The Institute of Management Sciences (TIMS) The Institute for OR and MS (INFORMS) 1. The largest and most influential institute in OR 2. Publisher of 14 academic journals including OR, MS, Interfaces. . 3. Organizer of influential conferences for academics + professionals 4. Various resources on OR education 5. Interfaces: many real-word cases with successful application of OR; some of them selected as reading materials for our course 6. The Franz Edelman Prize: recognizes outstanding examples of 10 innovative use of OR/MS in practice.

Hillier-Lieberman Textbook: Interfaces Articles Chapter 1 1. Absolutely, Positively Operations Research: The Federal Express Story Chapter 2 1. Supply Chain-Wide Optimization at TNT Express 2. Product Line Design and Scheduling at Intel 3. Planning the Netherlands' Water Resources 4. A Scheduling and Capable-to-Promise Application for Swift & Company 5. Bombardier Flexjet Significantly Improves Its Fractional Aircraft Ownership Operations 6. General Motors Increases Its Production Throughput 7. Philips Electronics Synchronizes Its Supply Chain to End the Bullwhip Effect 8. Pricing Analysis for Merrill Lynch Integrated Choice 9. SLIM: Short Cycle Time and Low Inventory in 11 Manufacturing at Samsung Electronics • … …

List of Edelman Prize Winners (articles + videos) • • • UPS for “ its proprietary routing software ORION (On-Road Integrated Optimization and Navigation)” 2016 Syngenta for “Advanced Analytics for Agricultural Product Development“ 2015 The U. S. Centers for Disease Control and Prevention (CDC), with Kid Risk, Inc. for “Polio Eradicators Use Integrated Analytical Models to Make Better Decisions” 2014 Delta Commissioner of Holland for “Economically Efficient Flood Standards to Protect the Netherlands against Flooding” 2013 TNT Express for “Supply Chain–Wide Optimization at TNT Express” 2012 Midwest Independent Transmission System Operator (ISO) for “ISO Unlocks Billions in Savings Through the Application of Operations Research for Energy and Ancillary Services Markets” 2011 Indeval for “INDEVAL Develops a New Operating and Settlement System Using Operations Research” 2010(central securities depository: 中央证券登记结算机构) HP for "HP Transforms Product Portfolio Management with Operations Research” 2009 Netherlands Railways for “The New Dutch Timetable: The OR Revolution” 2008 …. since 1972 12

History of OR • OR is a relatively new discipline. • 70 years ago it would have been possible to study mathematics, physics or engineering at university it would not have been possible to study OR. • It was really only in the late 1930's that operationas research began in a systematic way. 13

Origins of OR in World War II Radar control system: effective deployment and operation of the new invention 1. Radar invented by British scientist Robert Watson-Watt; 2. Originally a detection range only 16 km, difficult for effective use in air defense; 3. Using quantitative analysis of various data, the British military OR team directed by experimental physicist Patrick Blackett (Nobel Prize in Physics, 1948) designed the effective implementation of the man-machine radar control system.

Anti-U-boat (undersea-boat/submarine): 1. U-boats are efficient ship weapons during WW I and WW II, whose main targets are troop transport ships; 2. Bombers (carrying radar) were used to attack the U-boats, with a low sinking rate; 3. The depth charge was set 100 -150 ft, calculated as the maximal depth the U-boat can submerge itself from the time it saw the bomber; 4. The OR team (again directly by F. Blackett) suggested to shorten this depth to 25 ft by arguing that: if the U-boat has sufficient time to submerge, it could have escaped already to other directions; it is targeted only when at the time it saw the bomber it was very near the surface, so it will not submerge too deep. Leads to big success.

Bomber armor-adding problem: 1. Aircrafts back from bombing task, with shot-hole statistics as follow; 2. Experiences told that armors should be added to areas with more shot-holes; 3. The OR team with statistics discipline pointed out that there is a problem of “bias sampling” -- the returned aircrafts are ONLY those survived from the battle -- meaning that those areas with heavy shot-holes are insignificant for survival, so they suggested to put more armor to areas with no or less holes; 4. This again leads to higher survival rate. 16

Post-war development of OR In UK: most of war time OR experts (physicists, engineers) returned to their original lab, while some (such as Charles Goodeve, Pat Rivett) remained in particular industries (coal, steel) who continue to advocate/promote the potential industrial applications of OR. In US: OR spread to the universities/research institutes so that systematic training in OR for future workers began, such as G. Kimball (Columbia), P. Morse (MIT), H. Kuhn, A. Tucker, J. Nash (Princeton), R. Gomory (Princeton, IBM), R. Bellman (RAND), J. Little* (MIT), N. Karmarkar (BELL)… *The first PH. D of OR in U. S. was rewarded to J. Little at MIT 1968, advised by P. Morse. Later, as IT advances, OR spread to commercial use. 17

1890 Frederick Taylor Scientific Management [Industrial Engineering] 1900 • Henry Gannt [Project Scheduling] • Andrey A. Markov [Markov Processes] • Assignment [Networks] 1960 • John D. C. Little [Queuing Theory] • Simscript - GPSS [Simulation] 1950 • H. Kuhn - A. Tucker [Non-Linear Prog. ] • Ralph Gomory [Integer Prog. ] • PERT/CPM • Richard Bellman [Dynamic Prog. ] ORSA and TIMS 1970 • Microcomputer 1980 • N. Karmarkar [Linear Prog. ] • Personal computer • OR/MS Softwares 1910 • F. W. Harris [Inventory Theory] • E. K. Erlang [Queuing Theory] 1920 • William Shewart [Control Charts] • H. Dodge – H. Roming [Quality Theory] 1940 • World War II • George Dantzig [Linear Programming] • First Computer • John Von Neuman – Oscar Morgenstern [Game Theory] 1990 • Spreadsheet Packages • INFORMS ( ORSA+TIMS) 2000+ • You are here 18

1. 2 Operations Research Models Deterministic Models Stochastic Models • Linear Programming • Discrete-Time Markov Chains • Network Optimization • Continuous-Time Markov Chains • Integer Programming • Queuing Theory (waiting lines) • Nonlinear Programming • Decision Analysis • Dynamic Programming • Inventory Models Game Theory Inventory Models Simulation 19

Mathematical Programming Basically an optimization problem: x=(xj) are the decision variables; f(·) is the objective function; “g(·) ≤ b”, “xj ≥ 0” are the constraints. • • • LP: both f(·) and g(·) are linear in x; Non-LP: either f(·) or g(·) is nonlinear; Integer Prog. : to add in the LP the constraint “xj are integers”; Mixed Integer Prog. : only some xj are required to be integers; Dynamic Prog. : multi-stage decision problem. 20

1. 3 An OR study: the general steps Operations Research is a quantitative approach to decision making based on the scientific method of real-world problem solving. An OR study usually contains the following steps: 1. Identify the problem; 2. Formulate the problem as a math model; 3. Validate the model (by historical or new data); 4. Develop effective algorithms or computer packages to solve the model; 5. Obtain numerical solution for the model; 6. Implementation

COMMENTS. An OR study consists of: – The art of mathematical modeling of complex situations (建模) By observing the problem in reality and analyzing the data on hand, we choose the corresponding math model, then fix the function forms and in particular the parameters; – The science of the development of solution techniques to solve these models (求解) 1. construct algorithms and/or computer packages for possibly large-scale problems; 2. usually, we obtain a family of solutions with respect to the variation of the model parameters. – The ability to effectively communicate the results to decision maker (说明) results are reported in an easy-to-understand way, with explanations on 1. the correspondences of functions/parameters to reality; 2. the conditions for the model’s applicability; 3. the different optimal solutions according to variations of parameters.

1. 4 Examples of OR Applications • Case 1. Continental Airlines (now merged with United Airlines). • Case 2. Merrill Lynch. • More Successful stories … please see the references 23

Case 1: Continental Airlines Survives 9/11 • Reference: “ A New Era for Crew Recovery at Continental Airlines”, G. Yu (于刚) etc. Interfaces, 33(1): 5 -22, 2003. (Edelman Prize Winner 2003) • Problem: Long before September 11, 2001, Continental asked what crises plan it could use to reach recovery from potential disasters such as limited and massive weather delays. 24

Continental Airlines (con’t) • Strategic Objectives and Requirements are to accommodate: – 1, 400 daily flights – 5, 000 pilots – 9, 000 flight attendants – FAA regulations – Union contracts 25

Continental Airlines (con’t) • Model Structure: Working with CALEB Technologies, Continental used an optimization model to generate optimal assignments of pilots & crews. The solution offers a system-wide view of the disrupted flight schedule and all available crew information. 26

Continental Airlines (con’t) • Project Value: Millions of dollars and thousands of hours saved for the airline and its passengers. After 9/11, Continental was the first airline to resume normal operations. 27

Continental Airlines (con’t): An appetizer of the OR modeling behind Terminology: • Cities (source/destination): A, B, …, E • Flights (connecting two cities): A B, D E, etc. • Pairing (a sequence of connections of two cities): A B|B D|D E, etc (not A B|D E, not connected). Notation: • F: the set of flights to be covered; • P: the set of feasible pairings; • i: index for a flight; • p: index for a pairing; • cp: the running cost of the paring p; • yp: the indicator function for the pairing p, i. e. yp =1 if p is carried out, yp =0 otherwise; • i∈p: the flight i is included (covered) by the pairing p. 28

Case 2: Merrill Lynch Integrated Choice • Problem/Background: 1. In the late 1990 s, Merrill Lynch, one of the largest full-service financial services firms was threatened by the electronic brokerage firms (IT advance) which offered extremely low trading costs. full-service broker: providing various services as research and advice, retirement planning tax tips, and much more, all which come at a high price (commission) discount broker: less/no financial advise service, and the price is set by the amount of trade. 2. How should Merrill Lynch deal with online investment firms without alienating financial advisors, undervaluing its services, or incurring substantial revenue risk? 29

Merrill Lynch (con’t) • Objectives and Requirements: Evaluate new products and pricing options, and options of online vs. traditional advisor-based services. 30

Merrill Lynch (con’t) • Model Structure: Merrill Lynch’s Management Science Group simulated client-choice behavior (how would clients, in probability, respond to potential different products), allowing it to: – Evaluate the total revenue at risk – Assess the impact of various pricing schedules – Analyze the bottom-line impact of introducing different online and offline investment choices • Rationale behind the model: Even with the advance of IT, there are still clients with less time or interest to analyze the very complicated financial market. The study on historical data helped to differentiate them from those DIY-er, at least probabilistically. 31

Merrill Lynch (con’t) • Project Value: – Introduced two new products which garnered $83 billion ($22 billion in new assets) and produced $80 million in incremental revenue – Helped management identify and mitigate revenue risk of as much as $1 billion – Reassured financial advisors 32

A Short List of Successful Stories (1) • Air New Zealand – Air New Zealand Masters the Art of Crew Scheduling • AT&T Network • – Delivering Rapid Restoration Capacity for the AT&T Network Bank Hapoalim – Bank Hapoalim Offers Investment Decision Support for Individual Customers • British Telecommunications • – Dynamic Workforce Scheduling for British Telecommunications Canadian Pacific Railway – Perfecting the Scheduled Railroad at Canadian Pacific Railway • Continental Airlines – Faster Crew Recovery at Continental Airlines • FAA – Collaborative Decision Making Improves the FAA Ground-Delay Program 33

A Short List of Successful Stories (2) • Ford Motor Company – Optimizing Prototype Vehicle Testing at Ford Motor Company • General Motors – Creating a New Business Model for On. Star at General Motors • IBM Microelectronics – Matching Assets to Supply Chain Demand at IBM Microelectronics • IBM Personal Systems Group – Extending Enterprise Supply Chain Management at IBM Personal Systems Group • Jan de Wit Company – Optimizing Production Planning and Trade at Jan de Wit Company • Jeppesen Sanderson – Improving Performance and Flexibility at Jeppesen Sanderson 34

A Short List of Successful Stories (3) • Mars – Online Procurement Auctions Benefit Mars and Its Suppliers • Menlo Worldwide Forwarding – Turning Network Routing into Advantage for Menlo Forwarding • Merrill Lynch – Seizing Marketplace Initiative with Merrill Lynch Integrated Choice • NBC – Increasing Advertising Revenues and Productivity at NBC • PSA Peugeot Citroen – Speeding Car Body Production at PSA Peugeot Citroen • Rhenania – Rhenania Optimizes Its Mail-Order Business with Dynamic Multilevel Modeling • Samsung – Samsung Cuts Manufacturing Cycle Time and Inventory to Compete 35

A Short List of Successful Stories (4) • Spicer – Spicer Improves Its Lead-Time and Scheduling Performance • Syngenta – Managing the Seed-Corn Supply Chain at Syngenta • Towers Perrin – Towers Perrin Improves Investment Decision Making • U. S. Army – Reinventing U. S. Army Recruiting • U. S. Department of Energy – Handling Nuclear Weapons for the U. S. Department of Energy • UPS – More Efficient Planning and Delivery at UPS • Visteon – Decision Support Wins Visteon More Production for Less 36

Finale Please Go to http: //www. scienceofbetter. org or https: //www. informs. org For details on these successful stories 37