AEM412 Computational Methods for Management and Economics Carla P. Gomes Module 1 Introduction

Overview of this Lecture Course Administration Course Themes, Goals, and Syllabus Background on Mathematical Programming The Impact of Information Technology on Business Practice

Course Administration

Lectures: Tuesday and Thursday - 11: :55 Location: WN 245 Lecturer: Prof. Gomes Office: 448 Warren Hall Phone: or or TA: Vivian Eliza Hoffmann Administrative Assistant: Dawn Vail ( ) 147 Warren Hall, Web Site: AEM412 - Introduction to Mathematical Programming

Office Hours Prof. Gomes TA – Vivian Hoffmann Monday and Wednesday: 3:00p.m – 4:00 p.m. Tuesday (WN360) and Wednesday (WN201): 1:30 p.m – 2:30 p.m.

Grades Midterm (15%) Homework (35%) Participation (5%) Final (45%) Note: The lowest homework grade will be dropped before the final grade is computed.

Required Textbook Introduction to Operations Research by Frederick S. Hillier and Gerald. J. Lieberman, 7 th Edition

Overview of this Lecture Course Administration Course Themes, Goals, and Syllabus Background on Mathematical Programming The Impact of Information Technology on Business Practice

Course Themes, Goals, and Syllabus

What’s Mathematical Programming (MP)? Main focus: Optimization Optimization is pervasive in business and economics and almost all aspects of human endeavor, including science and engineering. Optimization is everywhere: part of our language and the way we think! –Firms want to maximize value to shareholders –People want to make the best choices –We want the highest quality at the lowest price –In games, we want the best strategy –We want to optimize the use of our time, –etc

Optimization Financial planning Marketing E-business Telecommunications Manufacturing Operations Management Production Planning Transportation Planning System Design Health Care

Some of the themes of 412 Optimization!!! Models, Models, Models (insights not numbers) Applications in business and economics Algorithms, Algorithms, Algorithms Efficient Algorithms --- whenever possible Importance of factoring in computational issues in business and economic applications: computational limits and intractability

What’s Mathematical Programming? –Linear Programming –Advanced Linear Programming Models –Network Models –Integer Programming –Dynamic Programming –Heuristic techniques Simulated Annealing Genetic Algorithms Tabu Search Neural Networks –Non-linear Programming –Decision Making under Uncertainty –Decision Making with Multiple Objectives –Game Theory –etc Very broad discipline covering a variety of Optimization topics such as:

Syllabus 412 Linear Programming –Introduction –Simplex/Revised Simplex –Duality and Sensitivity Analysis –Other LP Algorithms

Network Models –Transportation Problems –Assignment Problems –Network Optimization Models Special Topics(*) –Integer Programming –Dynamic Programming –Heuristic techniques Simulated Annealing Genetic Algorithms Tabu Search Neural Networks –Computational complexity(*) (*)time permitting

Goals in 412 –Present a variety of models, algorithms, and tools for optimization –Illustrate applications in business and economics, and other fields. –Prepare students to recognize opportunities for mathematical optimization as they arise –Prepare students to be aware of computational complexity issues: importance of using efficient algorithms whenever possible and the limits of computation that can affect the validity of business and economic models.

Background on Mathematical Programming

Origins of Operations Research (OR) The roots of OR can be traced back many decades and even centuries (Newton, Euler, Bernoulli, Bayes, Lagrange, etc). Beginning of the activity called Operations Research --- attributed to the military services early in the World War II (1937). – Need to allocate scarce resources to the various military operations in an effective manner. –The British first and then the U.S military management called upon a large number of scientists to apply a scientific approach to dealing with several military problems

End of war – scientists understood that OR could be applied outside the military as well. The industrial boom following the war led to an increasing complexity and specialization of organizations  scientific management techniques became more and more crucial. By the early 1950s, OR techniques were being applied to a variety of organizations in business, industry, and government.

Impact of Operations Research

Key Factors for Rapid Growth of OR Substantial progress was made early in improving the techniques in OR –Simplex, Dynamic Programming, Integer Programming, Inventory Theory, Queing Theory, etc Computer revolution s the PC further boosted this trend.

Timeline

Operations Research Over the Years 1947 –Project Scoop (Scientific Computation of Optimum Programs) with George Dantzig and others. Developed the simplex method for linear programs. 1950's –Lots of excitement, mathematical developments, queuing theory, mathematical programming. cf. A.I. in the 1960's 1960's –More excitement, more development and grand plans. cf. A.I. in the 1980's. Source: J. Orlin (MIT) 2003

Operations Research Over the Years 1970's –Disappointment, and a settling down. NP- completeness. More realistic expectations. 1980's –Widespread availability of personal computers. Increasingly easy access to data. Widespread willingness of managers to use models. 1990's –Improved use of O.R. systems. Further inroads of O.R. technology, e.g., optimization and simulation add-ins to spreadsheets, modeling languages, large scale optimization. More intermixing of A.I. and O.R.

Operations Research in the 00’s LOTS of opportunities for OR as a field Data, data, data –E-business data (click stream, purchases, other transactional data, and more) –The human genome project and its outgrowth Need for more automated decision making Need for increased coordination for efficient use of resources (Supply chain management)

The Impact of Information Technology on Business Practice

Advances in information technology are increasingly impacting on business and business practices. Exciting new opportunities (and some risks). Examples of applications

Driving Force Exponential Growth a) Compute power b) Data storage c) Networking Combined with algorithmic advances (software)

Compute power: Doubling every 18 months 4,000 transistors per processor 100,000,000 transistors per processor

How much can be stored in one Terabyte? video1 Gigabyte/hour 1000 hours scanned color images 1 Megabyte each 1 million images text pages3300 bytes/page 300 million pages (Library of Congress) Wal-Mart customer data: 200 terabyte --- daily data mining for customer trends Microsoft already working on a PC where nothing is ever deleted. You will have a personal Google on your PC. Storage for $200 Yr ’06, 1 Terabyte for $200.

computers , M M M The Network: The Internet This new level of connectivity allows for much faster, and more substantive interactions between companies/suppliers/customers (e.g. electronic markets)

Examples of business impact 1)Supply-chain-management 2)Electronic markets 3)Beyond traditional scheduling application

Michael Dell founds Dell 1996 – Dell starts selling computers via Internet at – "E-Support Direct from Dell" online technical support 2001 – Company sales via Internet exceed $40 M per day Dell ranks No 1 in global market share 2003 – Revenue – $32.1 Billion Dell premier example of integration of information technology into the business model. Direct business-to-consumer model

Legacy Systems Supply Logistics Center Collaboration Factory Planner Reporting Solution Supply Chain Planning Supplier Collaboration Suppliers Supply Hubs Internet Real-time Access and Transactions Report Users Supply Chain Planning Users Factory Planner Users Supply Chain Strategy and Processes Efficient supply chain: Innovative product design, An Internet order-taking process, An innovative assembly system, Close cooperation with suppliers. Power of Virtual Integration DELL manages relationships with over 80% of suppliers through the Internet. Over half of Dell customers use Web- enabled support (over 40,000 Premier Pages-10,000 in Europe). Direct business-to-consumer model Product configuration tools Online design of made-to-order system. Constraint-based reasoning tools (knowledge about allowable system configurations) Customer-to-Knowledge Customers search Dell databases Knowledge content for typical responses Personalization tools Optimization is everywhere

Electronic Markets Combinatorial Auctions

Why Combinatorial Auctions? More expressive power to bidders In combinatorial auctions bidders have preferences not just for particular items but for sets or bundles of Items due because of complementarities or substitution effects. Example Bids: Airport time slots [ (take-off right in time slot X ) AND (landing right in time slot y)] for $9, Delivery routes ( “ lanes ” ) [(NYC - Miami ) AND [((Miami – Philadelphia) AND (Philadelphia – NYC)) OR ((Miami – Washington) AND (Washington – NYC))]] for $700.00

Managing over 100,000 trucks a day (June 2002), >$8 billion worth of transportation services. OPTIBID - software for combinatorial auctions Procurement Transportation Services on the web. FCC auctions spectrum licenses ( geographic regions and various frequency bands). Raised billions of dollars Currently licenses are sold in separate auctions USA Congress mandated that the next spectrum auction be made combinatorial.

FCC Auction # MHz Winner Determination Problem Choose among a set of bids such that: Revenue to the FCC is maximized Each license is awarded no more than once Bid Bid amt. 2 $12e6 3 $30e6$22e6 1 4 $16e6 5 $8e6 Package B ABCABDADC 6 $11e6 BC 7 $10e6 A 8 $7e6 D (source: Hoffman) Hard Computational Problem x 3 + x 5 + x 6 + x 3 x1x1 + x 4 + x 7 x1x1 + x 4 + x 8 B C A D <= x 2 + x 3 x1x1 + x 6 Example: 4 licenses, 8 bids $30e6 $22e6 + $8e6 = $36e6 $12e6 + $16e6 +$8e6 = 

Combinatorial Auctions cont. There exists a combinatorial auction mechanism (“Generalized Vickrey Auction”), which guarantees that the best each bidder can do is bid its true valuation for each bundle of items. (“Truth revealing”). However, finding the optimal allocation to the bids is a hard computational problem. No guarantees that an optimal solution can be found in reasonable time. What about a near-optimal solution? Does this matter? Yes! Problem: if the auctioneer cannot compute the optimal allocation, no guarantee for truthful bidding. So, computational issues have direct consequences for the feasibility and design of new electronic market mechanisms. A very active area in discrete optimization. (Bejar, Gomes 01)

Beyond Traditional Scheduling Applications Enforcing Safety Constraints

Nuclear Power Plant Outage Management Given: activities for refueling and maintenance resources technological constraints Find a schedule that minimizes the duration of the outage while safely performing all the activities ( up to 45,000 activities). Cost of shutdown - $1M per day. ACTIVITY Activity Name EST LST Duration Predecessors Name: D21-1 Affects: ACPLOSS DIV1 Predecessors EST: 65 LST: 65 DURATION: 15 START: 65 FINISH: 80 PECO ROME LABORATORY OUTAGE MANAGER (ROMAN) Parameters Load Run Gantt Charts Utilities Exit D23-3 RHRB-1 D23-2 D21BUS-1 DIV4DC-1 RHR A-1 D21-1 Parameters Load Run Gantt Charts Utilities Exit Name: D21-1 Affects: ACPLOSS DIV1 Predecessors EST: 65 LST: 65 DURATION: 15 START: 65 FINISH: 80 PECO ROME LABORATORY OUTAGE MANAGER (ROMAN) Parameters Load Run Gantt Charts Utilities Exit D23-3 RHRB-1 D23-2 D21BUS-1 DIV4DC-1 RHRA-1 D : ACPOWER? 0 NUM-UNAV-RESS 1 UNAV-RES-MAP (DIV2 D24BUS-3 D24-2 D24-1) (ACPLOSS D24BUS-3 D24-2 D24-1) LIST-AV-RESS (DIV1 DIV3 DIV4 SU10 SU20) ROME LABORATORY OUTAGE MANAGER (ROMAN) Parameters Load Run Gantt Charts Utilities Exit AC-POWER Status AC Power DIV1 DIV2 DIV3 DIV4 SU10 SU impacts STATE-Of-PLANT SCHEDULE Limitations of Traditional Approaches Rely heavily on manual procedures; Current procedures – PERT/CPM Outage Risk Assessment Methodology, simulation performed to assess the risks inherent to a schedule. [ Gomes et al, 1996, 1997, 1998 ] Main risk The residual heat produced by the nuclear materials can melt the fuel and breach the reactor nvessel Examples of Monitored Safety Systems ac power control system primary containment system shutdown cooling system

Nuclear Power Plant Outage Management Activity with AC Power loss Potential? Example of decision tree for a safety function for AC-Power Offsite sources available Operable emergency Safeguard bus > no yes 2 Operable emergency Safeguard bus 1>3 2 1 (…) Name: D21-1 Affects: ACPLOSS DIV1 Predecessors EST: 65 LST: 65 DURATION: 15 START: 65 FINISH: 80 PECO ROME LABORATORY OUTAGE MANAGER (ROMAN) Parameters Load Run Gantt Charts Utilities Exit D23-3 RHRB-1 D23-2 D21BUS-1 DIV4DC-1 RHRA-1 D : ACPOWER? 0 NUM-UNAV-RESS 1 UNAV-RES-MAP (DIV2 D24BUS-3 D24-2 D24-1) (ACPLOSS D24BUS-3 D24-2 D24-1) LIST-AV-RESS (DIV1 DIV3 DIV4 SU10 SU20) ROME LABORATORY OUTAGE MANAGER (ROMAN) Parameters Load Run Gantt Charts Utilities Exit AC-POWER Status AC Power DIV1 DIV2 DIV3 DIV4 SU10 SU Roman extends the functionality of traditional project management tools It incorporates the technological constraints, automatically enforcing safety constraints Robust schedules guaranteeing feasibility over time-windows Fast schedules Solutions better than manual solutions Safety threshold Time

Syllabus 412 Linear Programming –Introduction –Simplex/Revised Simplex –Duality and Sensitivity Analysis –Other LP Algorithms

Network Models –Transportation Problems –Assignment Problems –Network Optimization Models Special Topics(*) –Integer Programming –Dynamic Programming –Heuristic techniques Simulated Annealing Genetic Algorithms Tabu Search Neural Networks –Computational complexity(*) (*)time permitting

Goals in 412 –Present a variety of models, algorithms, and tools for optimization –Illustrate applications in business and economics, and other fields. –Prepare students to recognize opportunities for mathematical optimization as they arise –Prepare students to be aware of computational complexity issues: importance of using efficient algorithms whenever possible and the limits of computation that can affect the validity of business and economic models.