101_Session_Three_inclassnotes

# 101_Session_Three_inclassnotes - MGMT 101: Management...

This preview shows pages 1–11. Sign up to view the full content.

MGMT 101: Management Science Professor Shuya Yin Session Three § Outline for today: § Interpret answer report § Interpret sensitivity analysis § Some practice problem

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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?
Galaxy: formulation § (Step 1) Decision variables § (Step 2) Maximize the objective function value (OFV) § (Step 3) Subject to the constraints

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.)
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
LHS of constraints at the optimal solution (actual usage of resources) RHS of constraints (maximum capacity) Optimal solution

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
X1(space ray) Max 8X1 + 5X2 (total profit) subject to 2X1 + 1X2 1000 (Plastic) 3X1 + 4X2 2400 (Prod. Time)
This is the end of the preview. Sign up to access the rest of the document.

## 101_Session_Three_inclassnotes - MGMT 101: Management...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online