Question

C&A makes two types of products using four machines from 9 a.m. to 5 p.m. each day. Product A visits machines 1, 2, and 4. Product B only visits machines 1 and 3. The capacity is 0.4 unit per minute at machine 1, 0.12 unit per minute at machine 2, 0.2 unit per minute at machine 3, and 0.3 unit per minute at machine 4. The demand per day is 40 units for Product A and 160 units for Product B. Which is the implied utilization for the bottleneck resource?

• 0.69
• 1.04
• 0.28
• 1.67

Answer 1

Total available time for each machine ( 9 AM TO 5 PM) = 8 hours = 480 minutes

Thus maximum capacity of machine 1 during above time ( 0.4 unit per minute) = 480 x 0.4 = 192 units

Maximum capacity of Machine 2 during above time ( 0.12 unit per minute) = 480 x 0.12 = 57.6 units

Maximum capacity of machine 3 during above time ( 0.2 unit per minute) = 480 x 0.2 = 96 units

Maximum capacity of machine 4 during above time ( 0.3 unit per minute) = 480 x 0.3 = 144 units

Against above capacity, number of units which must pass through each machine for 40 units of Product A and 160 units of Product B :

Machine	Maximum capacity	Number of units which must pass through
1	192	40 +160 = 200
2	57.6	40
3	96	160
4	144	40

The bottleneck capacities are those , when:

Number of units which must pass through > Maximum capacity

Accordingly Bottleneck machines are : Machine 1 and Machine 3

Implied utilization of such bottleneck machine

= Number of units which must pass through/ Maximum capacity

Thus Bottleneck capacity of Machine 1 = 200/192 = 1.04 ( rounded to 2 decimal places)

Bottleneck capacity of Machine 3 = 160/96 = 1.67 ( rounded to 2 decimal places )

Thus largest bottleneck from above data is Machine 3 with implied utilization of 1.67

IMPLIED UTILIZATION FOR THE BOTTLENECK RESOURCE = 1.67