3. [10 pts] Consider the move batching example in class (Page 31 of Module 7). S

Question

3. [10 pts] Consider the move batching example in class (Page 31 of Module 7). Suppose the total cycle time of the system is 101 minutes when the batch size is 1 (no batch), and the total cycle time of the system is 200 minutes when the batch size is 100, what is the total cycle time of the system when the batch size is 200? Please show your steps.

Move Batching Problem: Two machines in series - First machine receives individual parts at rate r with of co(1) and puts out batches of size k. -First machine has mean process time of te(1) for one part with CV of c,(1) Second machine receives batches of k and puts out individual parts. How does cycle time depend on the batch size k? single jo batch

Explanation / Answer

Following formula is to be noted :

Cycle time of the system x Batch size = Batch set up time + Cycle time / unit x Batch size ( i.e. number of units in a batch )

Since cycle time of batch size 1 = 101 minutes,

Therefore cycle time / unit = 101 minutes

Given that ;

Cycle time of the system = 200 minutes when batch size = 100 .

Putting these values in above equation :

200 minutes x 100 = Batch set up time + 101 x 100

Or, Batch set up time = ( 200 – 101 ) x 100 minutes

Or, Batch set up time = 9900 minutes

Let ,

Cycle time of the system when batch size is 200 = C1

Therefore ( using formula mentioned above ) :

C1 x 200 = 9900 + 101 x 200

Or, 200.C1 = 9900 + 20200

Or, 200.C1 = 30100

Or, C1 = 150.5 minutes

CYCLE TIME OF THE SYSTEM WHEN BATCH SIZE IS 200 = 150.5 MINUTES

CYCLE TIME OF THE SYSTEM WHEN BATCH SIZE IS 200 = 150.5 MINUTES

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