OPIM 101 - Spring 2012 - Session 10

OPIM 101 - Spring 2012 - Session 10 - Introduction to...

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Unformatted text preview: Introduction to Operations and Information Management Session 10 1 Session 10: Integer Models m Integer Decision Variables and Integer Linear Programs m ABC Inc. Capital Budgeting Example m Extension to the HFL Example Introduction to Operations and Information Management Session 10 2 Integer Decision Variables and Integer Models m In many business settings, you cannot allow some/all decision variables to take fractional values m For example, you cannot build 2.5 aircraft m Have to either keep a service facility open or close it down m Thus, we introduce the following concepts: m Integer Variable = variable that can only take integer values m Binary Variable = variable that can only take 0 or 1 values m An integer model = LP model where some or all decision variables are integer Introduction to Operations and Information Management Session 10 3 Integer Models: Why Rounding May Not Work max 21 X + 11 Y subject to: 7 X + 4 Y <= 13 X, Y >= 0 Optimal fractional solution: X = 1.83, Y = 0. Rounded to X = 2, Y = 0 is infeasible . Rounded to X = 1, Y = 0 is not optimal . Optimal integer-programming solution: X = 0, Y = 3. 1 2 3 4 4 3 2 1 (0,3.25) (1.83, 0) X Y Optimal LP solution Optimal IP solution Introduction to Operations and Information Management Session 10 4 Example 1: Capital Budgeting at ABC Manufacturing m A manufacturing company, ABC Inc., is considering opening new plants at the following 8 locations: Philadelphia, Chicago, Boston, Phoenix, San Francisco, Seattle, Detroit, and Atlanta m ABC has a capital budget of $73 million m Net Present Values (proxy for profitability of plants) and capital requirements for plants are m Where should ABC build plants in order to maximize the total Net Present Value? Plant Location NPV ($ millions) Capital Needed ($ millions) 1 Philadelphia 33 22 2 Chicago 14 10 3 Boston 8 6 4 Phoenix 7 5 5 San Francisco 15 11 6 Seattle 10 7 7 Detroit 34 24 8 Atlanta 16 12 Introduction to Operations and Information Management Session 10 5 Algebraic Formulation 8 plant 0) ( not or 1) ( build to ... 2, plant 0) ( not or 1) ( build to 1, plant 0) ( not or 1) ( build to 8 2 1 = = = = = = = = = Y Y Y 8 3 2 1 16 ... 8 14 33 Y Y Y Y + + + + 73 12 ... 6 10 22 8 3 2 1 + + + + Y Y Y Y m Decision variables (binary) m Objective function (to be maximized) m Constraint Introduction to Operations and Information Management Session 10 6 How to tell Solver that a variable should be binary?...
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This note was uploaded on 04/04/2012 for the course OPIM 101 taught by Professor Lee during the Spring '08 term at UPenn.

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OPIM 101 - Spring 2012 - Session 10 - Introduction to...

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