Question

The Cardiff Carbon Fiber factory consists of four sequential steps that process many types of carbon fiber tubing for customers. All products must go through each of the four stations in order. Setups are required when a station is changed over from one batch of tubes to another. Production planners decide on the number of units in a batch. The setup for an item at a station cannot be carried out until a batch of that item is ready for processing at that station. After the setup, each unit in the batch is processed in the time indicated in the table below. So, for example, if the batch size is 9 units, the time to complete a batch at Station B would be 45 minutes for the setup, plus 36 minutes for processing (4 minutes per unit times 9 units) – for a total of 81 minutes. Units in a batch are carried together from one station to the next. You may assume that the transit time from one station to the next is essentially zero. Times in the table below are in minutes. There is one worker per station. The demand rate is 8 units per hour. You can ignore any startup or shutdown times. In other words, use long run averages.

	Station A	Station B	Station C	Station D
Setup time [min]	110	45	80	0
Processing time per unit [min]	1	4	3	4.5

Assume the factory uses batch sizes of 20 units.

1. What is the capacity of each station, measured in batches per hour? In other words, how many batches per hour could each station make?

2. What is the capacity of each station, measured in units per hour?

3. Which station is the bottleneck?

4. What is the capacity of the facility in units per hour?

5. What is the flow rate of the facility in units per hour, and what are the utilizations of each station?

6. If the factory decided to use batch sizes of 10 units, what would be the capacity of each station, measured in units per hour?

7. Which station would be the bottleneck?

8. What would be the flow rate of the facility in units per hour, and what would be the utilizations of each station?

Answer 1

Batch Size has been given as 20 units.

Station A Setup Time = 110 min. Processing Time = 1 min per unit. => 20 units will take 20 minutes. Hence Batch turnaround time = 110 + 20 minutes = 130 minutes. Hence batches per hour = (1/130)*60 = 0.46. Units per hour = (20/130)*60 = 9.23 Units per hour.

Applying the same formula to the other three stations we get the following answers

Station B Setup time = 45 minutes. Processing time = 4 min per unit => 20 units wil take 20*4 = 80 minutes. Batch turnaround time = 45 +80 = 125 minutes. Batches per hour = (1/125)*60 = 0.48. Units per hour = (20/125)*60 = 9.6 Units per hour

Section C Setup Time = 80 mins. Processing Time = 3 min per unit => 20 units will take 20*3 = 60 minutes. Batch turnaround time = 80+60 = 140 minutes. Batches per hour = (1/140)*60 = 0.428. Units per hour =(20/140)*60 = 8.57 Units per hour

Section D Setup time = 0. Processing Time = 4.5 minutes per unit => 20 units will take 20*4.5 = 90 minutes. Batch turnaround time =0 + 90 = 90 minutes. Batches per hour = (1/90)*60 = 0.66. Units per hour = (20/90)*60 = 13.2 Units per hour.

[The above answers both the fiirst two capacity questions for each station].

The station with the greatest turnaround will be the bottleneck and that will be the capacity of the overall facility as well. In this case it is Station C at 140 minutes. Hence capacity of the facility will be capacity of Station C calculated above = 8.57 Units per hour.