Ch 01_03v2

# Ch 01_03v2 - Ch01 (OR WorldWarII19411945 RapidGrowthDueTo 1.GoodTheory 2.ComputerRevolution 3.GreatSoftware 1 OR=ManagementScience ObjectiveofOR

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Ch 01 History of Operations Research (OR) World War II – 1941-1945 Rapid Growth Due To 1. Good Theory 2. Computer Revolution 3. Great Software 1

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OR = Management Science BS in Management Science MS in Operations Research PhD in Operations Research Objective of OR Find the “best” solution = “optimal” solution 2
Societies the Institute for Operations Research and the Management Sciences INFORMS – student membership is about \$30/year World Series of OR  Continental Airlines Story (better, cheeper, faster) 3

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Ch 02 – How To Do An OR Study My Experience With Carreker-CheckFree-FiServ 1. Define the problem 2. Formulate a math model - – 2000 lines of code (OPL) 3. Develop Software – integrate with database Implemented and Successful! 4
Saving Money For Their Clients 5

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Ch 03 – Linear Programming Linear – all functions are linear f(x) = a 1 x 1  + a 2 x 2  + . .. + a n x n     Programming – not computer programming    but a military plan 6
Wyndor Glass Company Production Time/Batch (Hours) Possible Solution: x1 = 1 and x2 = 1 Profit: \$3000 + \$5000 = \$8000       Can you do better? 7 Plant Products Plant Capacity 1 2 1 1 HR 0 HR 4 HRS 2 0 HRS 2 HRS 12 HRS 3 3 HRS 2 HRS 18 HRS Profit/Batch \$3000 \$5000 - Variables x1 x2 -

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The Model maximize  3000x1 + 5000x2 subject to x1 <  4 2x2 <  12 3x1  +  2x2 <  18 x1 >  0  x2 >  0 2 variables and 5 constraints Solve Graphically 8
x1 <  4 2 points for x1 = 4 are (4,0), (4,4)    9

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2x2 <  12 2 points for 2x2 = 12 are (0,6), (6,6)    10
3x1 + 2x2 <  18  3x1 + 2x2 = 18 points (6,0), (0,9)    11

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x1 >  0  non-negativity    12
Obj Function  3000x1 + 5000x2 = 18000  (6,0) (0,3.6) 13

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Move Obj Function to Last Point  (6,0) (0,3.6) 14 Optimum
To Determine Optimum Point Solve 2 equations in 2 unknowns x2 = 6 and 3x1 + 2x2 = 18 therefore, 3x1 + 2(6) = 18 => 3x1 = 6 => x1 =  2 optimum is x1 = 2, x2 = 6 15

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The Optimal Objective Value is 3000(2)+5000(6) = 36000   16 Optimum at (2,6)
Optimal Solution x1 = 2 and x2 = 6 Plant 1: Use  2 Hours  (4 available) Plant 2: Use 12 Hours (12 available) Plant 3: Use 18 Hours (18 available) Profit: (3000)(2) + (5000)(6) = 36,000 Can anyone in the universe beat this? 17

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AMPL Model # WyndorGlass; reset; option solver cplex; var x1 >= 0;  var x2 >= 0; maximize Profit: 3000*x1+5000*x2; subject to C1: x1 <= 4; subject to C2: 2*x2 <= 12; subject to C3: 3*x1+2*x2 <= 18; solve; expand; display x1,x2; 18
Solution sw: ampl ampl: model a:wyndor.txt; CPLEX 10.1.0: optimal solution; objective 36000 0 dual simplex iterations (0 in phase I) maximize Profit: 3000*x1 + 5000*x2; subject to C1: x1 <= 4; subject to C2: 2*x2 <= 12; subject to C3: 3*x1 + 2*x2 <= 18; x1 = 2 x2 = 6 ampl:  19

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Terminology for Solutions p. 34
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## This note was uploaded on 08/11/2009 for the course EMIS 3360 taught by Professor Dr.kennington during the Fall '08 term at SMU.

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Ch 01_03v2 - Ch01 (OR WorldWarII19411945 RapidGrowthDueTo 1.GoodTheory 2.ComputerRevolution 3.GreatSoftware 1 OR=ManagementScience ObjectiveofOR

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