Practice: A Production System Manufacturing Two Products, P and Q
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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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Purchased part

  • 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

$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.


Purchased part

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


2 exploit the constraint find the throughput world s best solution

2. Exploit the Constraint : Find the Throughput World’s Best Solution

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


2 exploit the constraint find the world s best solution to throughput

2. Exploit the Constraint : Find the World’s Best Solution to Throughput

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.


2 exploit the constraint find the world s best solution to throughput1

2. Exploit the Constraint : Find the World’s Best Solution to Throughput

  • 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.


Purchased part

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


Purchased part

Practice: Optimal Solution

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


A practice on sensitivity analysis

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 analysis1

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


Step 4 elevate the constraint s do we try to sell in japan

Step 4 : Elevate the Constraint(s). Do We Try To Sell In Japan?

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

$/Constraint

Minute

4.5

1.57

2.7

1


2 exploit the constraint find the world s best solution to throughput2

2. Exploit the Constraint : Find the World’s Best Solution to Throughput

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.


Purchased part

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

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

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

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


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