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BUAD 311 Week 6 Notes

by: Emily Laurienti

BUAD 311 Week 6 Notes BUAD 311

Emily Laurienti

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About this Document

These notes cover Thursday's introduction to linear optimization with written out steps for the Excel solver. If you have any questions, feel free to email me at
Operations Management
Prof. Hamid Nazer-Zadeh
Class Notes
Management, business, operations, optimization
25 ?




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This 2 page Class Notes was uploaded by Emily Laurienti on Friday September 30, 2016. The Class Notes belongs to BUAD 311 at University of Southern California taught by Prof. Hamid Nazer-Zadeh in Fall 2016. Since its upload, it has received 20 views. For similar materials see Operations Management in Business Administration at University of Southern California.

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Date Created: 09/30/16
9.29.16 Linear Optimization  Optimization—mathematical techniques to identify the best decision given the tradeoffs and the constraints Optimal Product Mix Example  Two products  Low Speed vs. High Speed Computer Assembly Testing Packaging Profit Margin High Speed 30 min/part 10 min/part 20 min/part $100 Low Speed 10 min/part 20 min/part 20 min/part $75  How many of each product should we produce?  Each machine operates 600 minutes a day  Step 1—identify the decision variables  What do you want to know?  We want to know the number of high speed (y) and the number of low speed (x) to produce  Step 2—identify objective function  What do you want to achieve?  We want to maximize our profit margin  Find this equation by adding each profit margin multiplied by its corresponding variable  100y + 75x  Step 3—write each constraint in terms of the decision variables  You may realize you need extra decision variables  Don’t forget implicit constraints (like non-negativity)  We are constrained by each machine having only 600 minutes available per day  Find this equation by multiplying each variable by the amount of time the machine takes for that variable and adding the total time up  Have to write a separate equation for each machine  Have to include all equations, not just the bottleneck. This is because the bottleneck changes with different product mixes  Assembly constraint—30y + 10x ≤ 600  Testing constraint—10y + 20x ≤ 600  Packaging constraint—20y + 20x ≤ 600  Non-negativity constraint—x ≥ 0, y ≥ 0  Solver Steps  Enter objective function into a cell, Set as target cell  Enter your variable cells (x, y), select as you “by changing cells”  Enter your constraint functions with variables in one cell, symbol in next cell, and constraint in the third cell. Add constraint, select cell reference with your variable equations, then select your constraint cells  Check “assume non-negative”  Assume linear model  Solve  Answer: 15 of each High Speed and Low Speed computers Portfolio Management Example  Three options:  Treasury Note, stock fund, gold fund  Three economic scenarios:  Good, Normal, Bad  Want at least a 3% return in all scenarios  What are the decision variables?  Percentages of the capital allocation  % invested in Treasure—x  % invested in Stock—y  % invested in Gold—z  What is the objective?  Maximize the expected return  Express this as the average return (each % multiplied by its variable)  3%x + 6%y + 3%z  What are the constraints?  Under all scenarios, must earn at least 3%  Express this as an equation by taking each economic scenario and multiplying the % return by each variable  Good: 3%x + 21%y + 1%z ≥ 3%  Normal: 3%x + 7%y + 2%z ≥ 3%  Bad: 3%x + (-10%)y + 6%z ≥ 3%  Non negative  Solution—purchase only treasury notes, it is the only way to guarantee a return of 3%


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