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Lecture3web - MBAC6080 Decision Modeling and Applications...

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1 MBAC6080 Thomas Vossen Assistant professor of Operations Management Leeds School of Business University of Colorado Boulder, CO 80309-0419 Decision Modeling and Applications

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Lecture 3, 1-30-2008 2 MBAC6080 Today’s Agenda Intro/Review Examples of LPs Solving LPs using Excel Solver LP Applications: Al-Manakh case Data Envelopment Analysis
Lecture 3, 1-30-2008 3 MBAC6080 Elements of LP Models Decision variables What we want to decide? Objective function How we will decide? Constraints What binds our decision? Quantities: How much/many to produce/buy/hire/etc . Specified as Linear Functions

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Lecture 3, 1-30-2008 4 MBAC6080 Blue Ridge Hot Tubs produces two types of hot There are 200 pumps, 1566 hours of labor, and 2880 feet of tubing available. Aqua-Spa Hydro-Lux Pumps 1 1 Labor 9 hours 6 hours Tubing 12 feet 16 feet Unit Profit \$350 \$300 Example
Lecture 3, 1-30-2008 5 MBAC6080 Linear Programming Model Maximize 350X 1 + 300X 2 Subject to 1X 1 + 1X 2 ≤ 200 (Pump Availability) 9X 1 + 6X 2 ≤ 1566 (Labor Hours Availability) 12X 1 + 16X 2 ≤ 2880 (Tubing Availability) X 1 , X 2 ≥ 0 Ingredients: Objective function Constraints Decision Variables

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Lecture 3, 1-30-2008 6 MBAC6080 Solving LPs: The Graphical Method X 2 X 1 250 200 150 100 50 0 0 50 100 150 200 250 objective function 350X 1 + 300X 2 = 35000 objective function 350X 1 + 300X 2 = 52500 optimal solution
Lecture 3, 1-30-2008 7 MBAC6080 Enumerating The Corner Points X 2 X 1 250 200 150 100 50 0 0 50 100 150 200 250 (0, 180) (174, 0) (122, 78) (80, 120) (0, 0) obj. value = \$54,000 obj. value = \$64,000 obj. value = \$66,100 obj. value = \$60,900 obj. value = \$0

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Lecture 3, 1-30-2008 8 MBAC6080 Assumptions of LP Linear objective function, constraints Proportionality Additivity Divisibility Continuous decision variables Certainty Deterministic parameters
Lecture 3, 1-30-2008 9 MBAC6080 Template Approach to formulating LPs Common Templates: Product mix problems Blending problems Covering/Packing problems (i.e. scheduling) Problems that involve Decisions over Time Cutting Stock Problems

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Lecture 3, 1-30-2008 10 MBAC6080 Financial Portfolio Selection Problem Consider a mortgage team with \$100,000,000 to finance various investments. There are five categories of loans, each with an associated return and risk (1-10, 1 best):
Lecture 3, 1-30-2008 11 MBAC6080 Financial Portfolio Selection (Ctd.) Any uninvested money goes into a savings account with no risk and 3% return. The goal for the mortgage team is to allocate the money to the categories so as to: (a) Maximize the average return per dollar (b) Have an average risk of no more than 5 (all averages and fractions taken over the invested money (not over the saving account). (c) Invest at least 20% in commercial loans

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Lecture3web - MBAC6080 Decision Modeling and Applications...

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