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 materialsExplanation / 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