Industrial Engineering and Optimization

Barrett Summer Scholars 2011Sustainable Engineering:

Learning to Engineer Truly Green Products

Learning Objectives

• What is an Industrial Engineer• Discuss various forms of optimization

– Linear Programming– Constraint Management– Lean– Optimization via Simulation

• http://www.youtube.com/watch?v=RvXUlFnC2XQ&feature=player_embedded

Industrial Engineers• Combine the use of physics, mathematics, and social

sciences• Design efficient manufacturing/service systems by

optimizing resources• People• Time• Equipment• Information

• As technology increases, so does the need for industrial engineers

Optimization

• Optimization is:– A routine practice during the engineering design

process to improve designs– A necessity for a variety of business problems

dealing with complex decision making and resource allocation

– Mathematical algorithms to locate optimal solutions quickly

Linear Programming• Linear Programming finds optimal solutions to

business problems.• Assumes a linear objective function to

maximize or minimize

• Subject to constraints

A0X 1+ A1X2+A2X3+ … + AnXn

B0X 1+ B1X2 + … + BnXn <= CnXn

X 1, X2 … Xn >= 0

Linear Programming Example• A company produces two calculators, X and Y.

Projections indicate 100 of X and 80 of Y are in demand each day. However no more than 200 and 170 calculators of X and Y, respectively can be produced. 200 calculators a day must be shipped. The company losses $2 dollars on each X calculator and makes $5 dollars on every Y calculator.

Linear ProgrammingP= –2x + 5y, subject to: x>=100x<= 200y>= 80y <=170x + y > 200 

Test all the corners: Maximum at (100, 170) P = $650

Staple, Elizabeth. “Linear Programming: Word Problems”. Purple Math.http://www.purplemath.com/modules/linprog3.htm

Linear Programming Example• Izzy arrives to class late because he overslept from

playing 42 hours of soccer last weekend, and therefore, has only 35 minutes to complete a BSS Engineering exam. The exam has 6 open-ended questions and 20 multiple-choice questions. Each correct open-ended question is worth 10 points, and each multiple-choice question is worth 2 points. He knows that it usually takes him 4 minutes to answer an open-ended question and one minute to answer a multiple-choice question.

Linear Programming Example• Assume that for each question Izzy answers,

he receives full credit. How many of each type of question should he answer to receive the maximum possible points? What is the maximum possible points that Izzy can receive?

Linear Programming Example• Max or Min?

– Maximize points, p

• Maximize p = 10X + 2Y subject to• X <=6• Y <=20• 4X + 1 Y <=35

Optimal Solution: p = 82; x = 6, y = 11

Constraint Management

• For systems, to optimize flows, one can apply constraint management.

• You slowest operation step is your bottleneck

STEP 1

120units/hr

STEP 2

70units/hr

STEP 3

90units/hr

Machine A

Machine B

Machine C

Joe Sally John

MATERIALRELEASE

PRODUCTOUTPUT

Lean

• Philosophy from Japanese companies to focus on continuous improvement and the eliminate of waste.

• Applicable to all disciplines designing and improving systems– 5-S– Value Streaming

5-S• Philosophy from

Japanese companies to focus on continuous improvement and eliminate waste.

Source: http://www.lean.state.mn.us/images/5S_circle.gif

Value Streaming

https://www.greensuppliers.gov/gsn/html/users/gsn/docs/VSM.pdf

Value Streaming

Simulation

• Excellent for performing what-if scenarios that help us figure out how to optimize a system.

Questions?

17