Homework SourseConsider the case of a fabric cutting machine Prior to each
Consider the case of a fabric cutting machine. Prior to each cutting task, the fabrics need to be layered first. The layering step is therefore considered as the setup of the cutting process. After the fabrics are layered, the cutting begins, which takes on average 10 minutes for each batch, and it is independent of the batch size (simultaneous batching). There is one employee working on layering the fabrics. On average, it takes 20 seconds to layer one piece of fabric (the set up time is proportional to the batch size).
The batch size for each cutting task is first set as 10 layers/batch. Please calculate the processing rate of the cutting process.
The processing rate of the cutting process is .
Please show your analysis below:
Please calculate the processing rate again for two other batch sizes: batch size = 20 layers/batch, batch size = 30 layers/batch.
The processing rate of the cutting process with batch size = 20 layers/batch is .
The processing rate of the cutting process with batch size = 30 layers/batch is .
Please show your analysis below:
Comparing your results in (a) and (b), the processing rate of the cutting process is
as the batch size increases.
Please explain the trend you circled above. (Note: you need to provide the reason for the trend, NOT describe the trend).
Solution
The processing rate of the cutting process with batch size =10layer/batch
Total work in cycle = batch size = 10
Total time elapsed in cycle = set up time + processing time
= 20seconds/layer* 10 layers + 10 minutes
= 200 seconds + 10 minutes
= 200/60 minutes +10 minutes = 13.33 minutes
Processing rate of the cutting process = 10 layers/ 13.33 = 0.750 layers/ minutes.
Hence, the processing rate of the cutting process with batch size =10layer/batch is 0.750 layers/ minutes.
Now calculate processing rate of the cutting process with batch size = 20 layers/batch
Total work in cycle = batch size = 20
Total time elapsed in cycle = set up time + processing time
= 20seconds/layer* 20 layers + 10 minutes
= 400 seconds + 10 minutes
= 400/60 minutes +10 minutes = 16.66 minutes
Processing rate of the cutting process = 20 layers/ 16.66 = 1.20 layers/ minutes
Hence, the processing rate of the cutting process with batch size = 20 layers/batch is 1.20 layers/batch.
Now calculate processing rate of the cutting process with batch size = 30 layers/batch
Total work in cycle = batch size = 30
Total time elapsed in cycle = set up time + processing time
= 20seconds/layer* 30 layers + 10 minutes
= 600 seconds + 10 minutes
= 600/60 minutes +10 minutes = 20 minutes
Processing rate of the cutting process = 30 layers/ 20 = 1.5 layers/ minutes
Hence, the processing rate of the cutting process with batch size = 30 layers/batch is 1.5 layers/batch.
Hence, it is clear that the processing rate of the cutting process is increasing as the batch size increases.
