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solver_cee4674_excel

# solver_cee4674_excel - Airport Planning and Design Excel...

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1 of 47 Virginia Tech Airport Planning and Design Excel Solver Dr. Antonio A. Trani Associate Professor of Civil and Environmental Engineering Virginia Polytechnic Institute and State University Blacksburg, Virginia Spring 2003

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2 of 47 Virginia Tech Demand Function Example Given data representing demand at an airport (D(t)) we would like to derive the best nonlinear model to fit the data to a model of the form: Gompertz Model Logistic Model D t ( ) k a b t = D t ) ( k 1 b e at + --------------------------- =
3 of 47 Virginia Tech Data Given: data pairs for time and Demand (D(t)) Find: the best nonlinear regression equation that correlates with the data pairs (t, D(t)) Data File: airport2.xls

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4 of 47 Virginia Tech Data Set Plot 0 1000000 2000000 3000000 4000000 5000000 6000000 7000000 8000000 1970 1975 1980 1985 1990 1995 2000 2005 Series1
5 of 47 Virginia Tech Setup of Solver Procedure The idea is to minimize the Sum of Square Errors of the data and an assumed regressions equation Create a column with values of the assumed regression equation Leave parameters of the model as cells in the spreadsheet (Excel will iterate among any number of parameters) Minimize the Sum of the Square Errors (SSE) of the data You are done!

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6 of 47 Virginia Tech Setup of Solver
7 of 47 Virginia Tech Setup of Solver Cell to Minimize Cells to Iterate

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8 of 47 Virginia Tech Solution Set and Original Data 0 1000000 2000000 3000000 4000000 5000000 6000000 7000000 8000000 1970 1975 1980 1985 1990 1995 2000 2005 Series1 Series2
9 of 47 Virginia Tech Linear Programming Problems General Formulation Maximize subject to: for for c j j 1 = n x j a ij j 1 = n x j b i i 1 2 m , , , = x j 0 j 1 2 n , , , =

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10 of 47 Virginia Tech Linear Programming Objective Function (OF) Functional Constraints ( m of them) Nonnegativity Conditions ( n of these) are decision variables to be optimized (min or max) are costs associated with each decision variable c j j 1 = n x j a ij j 1 = n x j b i x j 0 x j c j
11 of 47 Virginia Tech Linear Programming are the coefficients of the functional constraints are the amounts of the resources available (RHS) a ij b i

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12 of 47 Virginia Tech LP Example (Construction) During the construction of an off-shore airport in Japan the main contractor used two types of cargo barges to transport materials from a fill collection site to the artificial island built to accommodate the airport.
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solver_cee4674_excel - Airport Planning and Design Excel...

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