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# Purchased Part - PowerPoint PPT Presentation

Practice: A Production System Manufacturing Two Products, P and Q. \$90 / unit. \$100 / unit. Q:. P:. 60 units / week. 110 units / week. D. D. Purchased Part. 10 min. 5 min. \$5 / unit. C. B. C. 10 min. 5 min. 25 min. B. A. A. 15 min. 10 min. 10 min. RM1. RM2. RM3. \$20 per.

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## PowerPoint Slideshow about ' Purchased Part' - sunee

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\$90 / unit

\$100 / unit

Q:

P:

60 units / week

110 units / week

D

D

Purchased Part

10 min.

5 min.

\$5 / unit

C

B

C

10 min.

5 min.

25 min.

B

A

A

15 min.

10 min.

10 min.

RM1

RM2

RM3

\$20 per

\$20 per

\$25 per

unit

unit

unit

Time available at each work center: 2,400 minutes per week.

Operating expenses per week: \$6,000. All the resources cost the same.

1. Identify The Constraint(s)

Contribution Margin: P(\$45), Q(\$55)

Market Demand: P(110), Q(60)

Can we satisfy the demand?

Resource requirements for 110 P’s and 60 Q’s:

• Resource A: 110 (15) + 60 (10) = 2250 minutes
• Resource B: 110(10) + 60(35) = 3200 minutes
• Resource C: 110(15) + 60(5) = 1950minutes
• Resource D: 110(10) + 60(5) = 1400 minutes

Resource B is Constrained - Bottleneck

Product P Q

Profit \$ 45 55

Resource B needed (min) 10 35

Profit per min of Bottleneck 45/10 =4.555/35 =1.6

Per unit of bottleneck Product P creates more profit than Product Q

Produce as much as P, then Q

For 110 units of P, need 110 (10) = 1100 min. on B, leaving 1300 min. on B, for product Q.

Each unit of Q requires 35 minutes on B. So, we can produce 1300/35 = 37.14 units of Q.

We get 110(45) +37.14(55) = 6993 per week.

After factoring in operating expense (\$6,000), we make \$993 profit.

• How much additional profit can we make if market for P increases from 110 to 111; by 1 unit.
• We need 1(10) = 10 more minutes of resource B.
• We need to subtract 10 min of the time allocated to Q and allocate it to P.
• For each unit of Q we need 35 min of resource B.
• Our Q production is reduced by 10/35 = 0.29 unit.
• One unit increase in P generates \$45. But \$55 is lost for each unit reduction in Q. Therefore if market for P is 111 our profit will increase by 45(1)-55(0.29) = \$29.

Practice: LP Formulation

Decision Variables

x1 : Volume of Product P

x2 : Volume of Product Q

Resource A

15 x1 + 10 x2  2400

Resource B

10 x1 + 35 x2  2400

Resource C

15 x1 + 5 x2  2400

Resource D

10 x1 + 5 x2  2400

Market for P

x1 110

Market for Q

x2 60

Objective Function

Maximize Z = 45 x1 +55 x2 -6000

Nonnegativity

x1  0, x2 0

Practice: Optimal Solution

Continue solving the problem, by assuming the same assumptions of 20% discount for the Japanese market.

A Practice on Sensitivity Analysis
• What is the value of the objective function? Z= 45(?) + 55(37.14)-6000!
• 2400(0)+ 2400(1.571)+2400(0) +2400(0)+110(29.286)+ 60(0) =6993
• Is the objective function Z = 6993?
• 6993-6000 = 993
A Practice on Sensitivity Analysis
• How many units of product P?
• What is the value of the objective function?
• Z= 45(???) + 55(37.14)-6000 = 993.
• 45X1= 4950
• X1 = 110

Even without increasing capacity of B, we can increase our profit.

\$/Constraint

Minute

4.5

1.57

2.7

1

For 110 units of P, need 110 (10) = 1100 min. on B, leaving 1300 min. on B, for product P in Japan.

Each unit of PJ requires 10 minutes on B. So, we can produce 1300/10 = 130 units of PJ.

We get 110(45) +130(27) = \$8460 - \$6000 = \$2460 profit.

Check if there is another constraint that would not allow us to collect that much profit. Let’s see.

1. Identify The Constraint(s)

Contribution Margin: P(\$45), PJ(\$27)

Market Demand: P(110), PJ(infinity)

Can we satisfy the demand?

Resource requirements for 110 P’s and 130 PJ’s:

• Resource A: 110 (15) + 130 (15) =3600 minutes
• Resource B: 110(10) + 130(10) = 2400 minutes
• Resource C: 110(15) + 130(15) = 3600minutes
• Resource D: 110(10) + 130(10) = 2400 minutes
• We need to use LP to find the optimal Solution.
Step 4 : Exploit the Constraint(s).

Not \$2460 profit, but \$1345. The \$6000 is included.

Let’s buy another machine B at investment cost of \$100,000, and operating cost of \$400 per week. Weekly operating expense \$6400. How soon do we recover investment?

Step 4 : Elevate the Constraint(s). New Constraint

Original Profit: \$993

No Machine but going to Japan: \$1345 profit.

Buy a machine B: \$2829 profit. The \$6400 is included.

Going to Japan has no additional cost. Buying additional machine has initial investment and weekly operating costs.

\$2829-\$1345 = \$1484  \$100,000/\$1484 = 67.4 weeks

Buying a machine A at the same cost

Also add one machine A. Initial investment 100,000. Operating cost \$400/week.

From \$2829 to \$3533 = \$3533 - \$2829 = \$704. The \$6800 included..

\$100,000/\$704 = 142 weeks

Now B & C are a bottleneck