Lecture18aa

# Lecture18aa - Lecture 02/29/08 1. LP Formulation Examples...

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Lecture 02/29/08 1. LP Formulation Examples a. Solution of Stewardess Scheduling Problem b. Capital Budgeting Problem c. Use of Solver to Solve LPs

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Definition of Variables and Implications Let x i,train = number of stewardesses that are teachers during month i, where i = 1,2 Let x i,idle = number of stewardesses that are idle during month i, where i = 1,2,3 We have 65 stewardesses available during month 1 (January). During month 2, number available = 65 +4* x 1,train During month 3, number available = 65 + 4( x 1,train + x 2,train )
Constraints January Availability – x 1,train + x 1,idle +50 =65 – => x 1,train + x 1,idle =15 (1) February Availability x 2,train + x 2,idle +75 = 65 +4* x 1,train => 4* x 1,train - x 2,train - x 2,idle = 10 (2) March Availability x 3,idle +100 = 65 + 4( x 1,train + x 2,train ) – => 4( x 1,train + x 2,train ) – x 3,idle = 35 (3) Nonnegativity Constraints: • x ,i,train ≥0 for i=1,2 ; x j,idle ≥0 for j = 1,2,3

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Simplification of Constraits • x 1,train + x 1,idle =15 (1) => x 1,idle =15- x 1,train ≥0 => x 1,train ≤15 • 4* x 1,train - x 2,train - x 2,idle = 10 (2)
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## Lecture18aa - Lecture 02/29/08 1. LP Formulation Examples...

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