101_Session_Three_inclassnotes

101_Session_Three_inclassnotes - MGMT 101: Management...

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MGMT 101: Management Science Professor Shuya Yin Session Three § Outline for today: § Interpret answer report § Interpret sensitivity analysis § Some practice problem
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Galaxy problem § Galaxy manufactures two toy models: - Space Ray (profit of $8 per dozen) - Zapper (profit of $5 per dozen) § Resources are limited to: - 1000 pounds of special plastic - 40 hours of production time per week § Marketing requirements: - Total production cannot exceed 700 dozens - Number of dozens of Space Rays cannot exceed number of dozens of Zappers by 350 § Technological input: - Space Rays require 2 pounds of plastic and 3 minutes of labor per dozen - Zappers requires 1 pound of plastics and 4 minutes of labor per dozen § How to schedule production in order to maximize the total profit?
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Galaxy: formulation § (Step 1) Decision variables § (Step 2) Maximize the objective function value (OFV) § (Step 3) Subject to the constraints
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After problem solving using Solver Solver is ready to provide reports to analyze the optimal solution. Space Rays Zappers Dozens 320 360 Total Limit Profit 8 5 4360 Plastic 2 1 1000 <= 1000 Prod. Time 3 4 2400 <= 2400 Total 1 1 680 <= 700 Mix 1 -1 -40 <= 350 GALAXY INDUSTRIES
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How to read “Answer Report” Optimal objective function value (profit) Optimal solution (production schedule) Difference b/w RHS and LHS LHS of constraints at the optimal solution (actual consumption of that resource) 2X1 + 1X2 <= 1000 3X1 + 4X2 <= 2400 X1 + X2 <= 700 X1 - X2 <= 350
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What if? The toy models turn out to be very popular  demand goes up dramatically § What if the net profit for Space Ray changes from $8 to $10 ? § What if the net profit for Space Ray changes from $8 to $80 ? § What if the company wants to buy more special plastic ? § What if the company wants to schedule over time or hire more staff to increase the prod. time ? § What if the marketing department feels that they should allow more production than 700 ? § What if……? Max 8X1 + 5X2 (total profit) subject to 2X1 + 1X2 <= 1000 (Plastic) 3X1 + 4X2 <= 2400 (Prod. Time) X1 + X2 <= 700 (Total prod.) X1 - X2 <= 350 (Mix) Xj> = 0, j = 1,2 (Non- neg.)
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What if analysis (or sensitivity analysis) § We consider two types of changes in parameters: - The coefficient in the objective function (Type I) - The change in the right hand side of the constraints (Type II) - We change one parameter at a time and others remain the same.
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Geometric intuition behind LP sensitivity analysis § AnimaLP: A Java language web program to demonstrate LP geometry in two dimensions § http://www.cs.stedwards.edu/~wright/linprog/AnimaLP.html
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LHS of constraints at the optimal solution (actual usage of resources) RHS of constraints (maximum capacity) Optimal solution
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X1(space ray) Max 8X1 + 5X2 (total profit) subject to 2X1 + 1X2 1000 (Plastic) 3X1 + 4X2 2400 (Prod. Time)
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101_Session_Three_inclassnotes - MGMT 101: Management...

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