2 Question 75 in Cachon Terwiesch 2013 Consider the followin

2. [Question 7.5 in Cachon, Terwiesch 2013] Consider the following batch-flow process consisting of three process steps performed by three machines: Work is processed in batches at each step. Before a batch is processed at Step 1, the machine has to be set up. During a setup, the machine is unable to process any product.

a. Assume that the batch size is 50 parts. What is the capacity of the process?

b. For a batch size of 10 parts, which step is the bottleneck of the process?

c. Using the current production batch size of 50 parts, how long would it take to produce the first 10 parts starting with an empty system? Assume that the units in the batch have to stay together when transferred to Step 2 and Step 3. This means all the parts in the batch (i.e., all 50 parts) must complete at Step 2 and then the entire batch is moved to Step 3. A unit can leave the system at the moment it is completed at Step 3. Assume Step 1 needs to be setup before the production.

d. Using the current production batch size of 50 parts, how long would it take to produce 20 parts starting with an empty system? Assume that the units in the batch DO NOT have to stay together. Specifically, each unit is transferred to the next step the moment it is completed at any step. Assume Step 1 needs to be setup before the production.

e. What batch size would you choose, assuming that all units of a batch to stay together for the entire process?

Please explain how you got your answer.

Solution

a.

Calculate Capacity (units/min) of the process-

Step 1

B/(S+B*p)

= 50/(20+50*1) = 0.714

Step 2

½ = 0.5

Step 3

1/1.5 = 0.667

Step 2 is the bottleneck k, and the capacity   of the process is 0.5 uits/min.

b.

capacity of step 2 and step 3 are not affected by the size of bottle.

Capacity of step 1 given batch size 10 is 10(20+10*1) = 0.333 units/min

Hence, step 1 is bottleneck for the process.

c.

the total time to process through step 1 = 20 minutes for set up + 50 minutes for processing = 70 minutes.

The total time to process the batch size through step 2 = 100 minutes. So the bath size takes 170 minutes through the first two steps.

At step 3, need to process the 20 parts takes 30 minutes.

Under this situation it takes of 200 minutes to process 20 parts.