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Practice Final

# Practice Final - IEOR E4007 G Iyengar August 18th 2009 IEOR...

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IEOR E4007 G. Iyengar August 18th, 2009. IEOR E4007 Final Exam Instructions : 200pts 1. You have 3 hours to do the exam. 2. The exam is closed book. You are allowed one standard sheet of paper as a cheat sheet. 3. Calculators are allowed but no computers. 4. Important : Please answer every question in the space provided. You may use the reverse sides of the pages as well. 5. If I don’t see you again, the very best of wishes for your success here at Columbia and later ! Please sign the following declaration. I declare that I did not receive nor did I give any assistance to anyone else during this exam. ———————————————————————– 1

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1. A simple problem on unconstrained optimization 50pts A retailer is planning her yearly inventory strategy for a commodity that sells at a steady demand rate D = 20. Her objective is to minimize her total costs which includes storage costs and ordering costs. The storage cost is S = 10 per unit, the fixed cost per order is C = 100, the variable cost is P = 5 per unit and there is no lead time before orders are filled. Let x denote the order size. Then, the retailers optimization problem is given by (see figure below) min { x : x> 0 } braceleftbigg D x ( C + Px ) + S 2 x bracerightbigg x D/x (a) Solve this optimization. Prove that the solution that you obtain is, in fact, the global minimum. 10pts (b) Suppose the retailer is concerned that her supplier may not be able to meet her needs and decides to diversify between two suppliers (i) Supplier 1: Fixed cost C and variable cost P/ 2 (ii) Supplier 2: Fixed cost C and variable cost 3 P/ 2 Let ( x 1 ,x 2 ) denote the order sizes for the two retailers. Formulate the new opti- mization problem faced by the retailer. 10pts
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Practice Final - IEOR E4007 G Iyengar August 18th 2009 IEOR...

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