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Cooper River Glass Works (CRGW) produces four different models of desk lamps as

ID: 392768 • Letter: C

Question

Cooper River Glass Works (CRGW) produces four different models of desk lamps as shown on the flowchart. The operations manager knows that total monthly demand exceeds the capacity available for production. Thus, she is interested in determining the product mix which will maximize profits. Each model's price, routing, processing times, and material cost is provided in the flowchart. Demand next month is estimated to be 200 units of model A, 225 units of model B, 175 units of model C, and 275 unitts of model D. CRGW operates only one 8 hours shift per day and is scheduled to work 20 days next month (no overtime). Each station requires 10% capacity cushion.

Answer the following questions:

A) Which station is a bottleneck? What is the total load of minutes for the next month?

B) Using the traditional method, which bases decisions solely on a product's contribution to profits and overhead, what is the optimal product mix and what is the overall profitability?

C) Using the bottleneck-based method, what is the optimal product mix and what is the overall profitability?

Product: Alpha Price: $65/unit Station 10 min Station min tation 15 min Station 10 min Demand: 200 units/month Raw materials Product: Bravo Price: $70/unit Demand: 225 units/month bravo tep Station 20 min tep tation 10 min Raw materials Charlie $8 tep tation 5 min tep Station 20 min Product: Charlie Price: $95/unit Demand: 175 units/month tep Station 5 min tep Station 15 min Raw materials Delta $5 tep tation 10 min tep Station 10 min Product: Delta Price: $85/unit Demand: 275 units/month tep Station 20 min tep Station 5 min Raw materials

Explanation / Answer

A)

Number of workers per workstation =1

# of workstations = 4

Capacity cushion = 10%
Available time per workstation per month considering capacity cushion

= 20 days/month x 8 hours/day x 60 minutes/hr x (1 – 0.10)

= 8640 minutes per machine per month

Summary of time required:

Processing time per unit of product

Workstation

A

B

C

D

1

10

0

5

20

2

5

20

15

5

3

15

10

5

10

4

10

0

20

10

Demand

200

225

175

275

Determining Aggregate Workload for each WS:

Workload per product = demand x time per unit

Workstation

Load from Product A

Load from Product B

Load from Product C

Load from Product D

Total Workload

Available time

1

2000

0

875

5500

8375

8640

2

1000

4500

2625

1375

9500

8640

3

3000

2250

875

2750

8875

8640

4

2000

0

3500

2750

8250

8640

As the aggregate workload of WS #2 and #3 are more than 8640 minutes, the WS #2 and #3 are bottleneck work stations.

Determine Contribution Margin per unit per product:

Product

A

B

C

D

Price

65

70

95

85

Raw Materials Cost

10

10

8

5

Contribution margin (price – Cost)

55

60

87

80

B)

Product Mix according to Traditional Method:

Select the best product mix according to the highest overall contribution margin per unit of each product.

Order of production schedule: C – D – B - A

Since minute left on WS#2 after producing B is 140, amount B that can be produced on WS#2 is calculated as follows:

Quantity = Time remaining on bottleneck WS/per unit time on Bottleneck WS = 140/5 = 28

WS #

Minutes at the start

Minutes left after making 175 C

Minutes left after making 275 D

Minutes left after making 225 B

Minutes left after making 28 A

1

8640

7765

2265

2265

1985

2

8640

6015

4640

140

0

3

8640

7765

5015

2765

2345

4

8640

5140

2390

2390

2110

Product Mix:

A – 28, B – 225, C – 175, D – 275

Overall profitability of production mix:

Product

A

B

C

D

Total

Production units

28

225

175

275

Contribution margin/unit

55

60

87

80

Total Contribution margin

$1,540

$13,500

$15,225

$14,000

$44,265

Total profitability of traditional method = $44,265

C)

Product Mix according to Bottleneck Method:

Since the major bottleneck work station is WS#2, select the best product mix according to the dollar contribution margin per minute of processing time at the bottleneck workstation 2. This method would take advantage of the principles outlined in the theory of constraints and get the most dollar benefit from the bottleneck.

Select the best product mix according to the highest overall contribution margin per minute of each product WS #2.

Product

A

B

C

D

Contribution margin

$55

$60

$87

$80

Time at bottleneck WS #2

5

20

15

5

Contribution margin per minute

$11.00

$3.00

$5.80

$16.00

Production Schedule: D – A – C - B

Since minute left on WS#2 after producing 175 units C is 3640, amount B that can be produced on WS#2 is calculated as follows:

Quantity = remaining time/time on bottleneck = 3640/20 = 182

WS#

Minutes at the start

Minutes left after making 275 D

Minutes left after making 200 A

Minutes left after making 175 C

Minutes left after making 182 B

1

8640

3140

1140

265

265

2

8640

7265

6265

3640

0

3

8640

5890

2890

2015

195

4

8640

5890

3890

390

390

Production mix: A – 200, B – 182, C – 175, D = 275

200

182

175

275

Product

A

B

C

D

Total

Units

200

182

175

275

Contribution margin/unit

55

60

87

80

Total Contribution margin

11000

10920

15225

14000

$51,145

Total profitability of bottleneck method = $51,145

Processing time per unit of product

Workstation

A

B

C

D

1

10

0

5

20

2

5

20

15

5

3

15

10

5

10

4

10

0

20

10

Demand

200

225

175

275