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# Linear Programming Operations Management PowerPoint Presentation, PPT - DocSlides

liane-varnes | 2018-11-24 | General

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linear-programming-operations-management-1587476
112 time
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112
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Dr. Ron . Lembke. Motivating Example. Suppose you are an entrepreneur making plans to make a killing over the summer by traveling across the country selling products you design and manufacture yourself. To be more straightforward, you plan to follow the Dead all summer, selling . ID: 733402

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Slide1

Slide4

Linear Programming

Operations Management

Dr. Ron

Lembke

Slide2Motivating Example

Suppose you are an entrepreneur making plans to make a killing over the summer by traveling across the country selling products you design and manufacture yourself. To be more straightforward, you plan to follow the Dead all summer, selling

tie-dyed t-shirts and

screenprinted

sweatshirts.

Slide3Slide4

Example

You are really good with tie-dye, so you earn a profit of $25 for each t-shirt.

The sweatshirt screen-printed sweatshirt makes a profit of $20.

You have 4 days before you leave, and you want to figure out how many of each to make before you head out for the summer.

You plan to work 14 hours a day on this. It takes you 30 minutes per tie dye, and 15 minutes to make a sweatshirt.

Slide5Example

You have a limited amount of space in the van. Being an engineer at heart, you figure:

If you cram everything in the van, you have 40

cubic

feet of space in the van.

A tightly packed t-shirt takes 0.2 ft

3

A tightly packed sweatshirt takes 0.5 ft

3.

How many of each should you make?

Slide6Summary

14 hrs / day

Van: 40.0 ft

3

4 days

Tshirt: 0.2 ft

3

30 min / tshirt

Sshirt: 0.5 ft

3

15 min / Sshirt

How many should we make of each?

Slide7Trial and Error

Use up all of the space?

Sweatshirts: 40/0.5 = 80. 80*20 = $1,600

T-shirts: 40/0.2 = 200! 200*25 = $5,000 cool!

Use all of your time?

Ss: 56/0.25 = 224. 224 * $20 = $4,480

Ts: 56/0.5 = 112. $25*112 = $2,800

Fill it with

Tshirts

? Only time to make 112

Spend all your time making Ss? Only space for 80

Slide8Trial and Error

S T Space Time Profits Comments

8 0 0 40 20 $1,600 << 56hr

0 200 40

100

$5,000 > 56 hrs

224 0

112

56 $4,480 > 40 cu ft

0 112 22.4 56 $2,800 << 40 cu ft

Slide9Improving the Solution

(0,112) all time is used, van not full $2,800

Look for a compromise solution

What if make one less T?

Frees up 0.5 hrs, revenue goes down $25

In 0.5hrs, could make 2 S, brings in $40 more

Same amt of time, $15 more!

1 T less frees up 0.2 ft

3

2 S add 1.0 ft

3

Increase 0.8 ft

3

van wasn’t full, so no problem

Trade 1 T for 2 S, gain $15! $2,815

Slide10Improving Solution

Keep making trade. How many times?

Use up 0.8 more space

At (0,112) using 22.4, so 40 – 22.4 = 17.6 avail

17.6/0.8 = 22 Make trade 22 times

(0,112) + 44S – 22T = (44,90)

Space 44*0.5 + 90*0.2 = 22+18 = 40 cu ft

Time 44*0.25 + 90*0.5 = 11 + 45 = 56 hrs

Van is full, all the time is used

Profits 44*20 + 90*25 = 880 + 2250=$3,130

Slide11Write down the problem

We could express the problem like this:

Max

20 S

+

25 T

s.t

.

0.5 S +

0.2 T

<=

40

0.25 S

+

0.5 T

<=

56

S

>= 0

T >= 0

Space

Time

Slide12Linear Programming

What we have just done is called “Linear Programming.”

Has nothing to do with computer programming

Invented in WWII to optimize military “programs.”

“Linear” because no x

3, cosines, x*y, etc.

Slide13Standard Form

Linear programs are written the following way:

Max 3x + 4y

s.t. x + y <= 10

x + 2y <= 12

x >= 0

y >= 0

Slide14Standard Form

Linear programs are written the following way:

Max 3x + 4y

s.t. x + y <= 10

x + 2y <= 12

x >= 0

y >= 0

Objective

Function

Constraints

LHS (left hand side)

RHS (right hand side)

inequalities

Non-negativity

Constraints

Objective Coefficients

Slide15Summary

Solved a linear program

Wrote the problem mathematically, in “standard form”

Solved the problem using trial and error

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