1. Your plant has three milling machines dedicated to production of a single product. Each batch...
1. Your plant has three milling machines dedicated to production of a single product. Each batch requires a setup time of 25 minutes per batch, the processing time per unit is 5 minutes, and the batch size is set at 100 units. Each machine processes an entire batch at one time. The machines are staffed 8 hours per day.
A. (10 points) If the average arrival rate to the plant is 2.5 batches per day, what is the average utilization of the machines? Show calculations using two of the three utilization methods.
Homework Answers
milling machines in the plant – 3 units
Setup Time - 25 minutes.
Processing time for each unit - 5 minutes.
Batch Size - 100 Units
Working hours - 8 hr.
Total time needed by a single machine in processing one batch - (100 X 5) + 25 = 525 Minutes.
525 min= 525 / 60 = 8.75 Hours.
Therefore, 8.75 hrs are needed for processing 100 Units.
Number of units processed in a day( 8 Hours )by one machine –
(100 X 8) / 8.75 = 91.4 Units.
Total Units processed by 3 machines in 8 Hours - 91.4 x 3 = 274 Units.
As mentioned, average arrival rate of the plant - 2.5 Batches = 250 Units.
Utilization percentage of the plant = (250 / 274) * 100
= 91.2%
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