1)A four-step process is used to make a product. The first resource takes 8 minutes per unit, the second takes 7 minutes per unit, the third takes 2 minutes per unit, and the fourth takes 10 minutes per unit. 20% of all units have to be reworked. For that, they have to revisit the third and fourth resources. Each resource is staffed by one worker. Rework takes the same processing times as the first pass and always fixes the problem. Where is the bottleneck? A. Resource 3 B. Resource 4 C. Resource 1 D. Resource 2

2. C&A uses a two-step process to make a part. The first step involves cutting with a machine that requires a 40-minute setup time before the production of each batch. The cutting takes 30 minutes per part. The second step is polishing the parts from cutting. The polishing takes 40 minutes per part. Assume demand is unlimited. What is the ideal batch size of the parts? A. 8 B. 10 C. 4 D. Cannot be determined

3. C&A Printing takes 10 seconds to print a page in color, but after 500 pages, the printer must be cooled down for 15 minutes. No pages can be printed while the printer is cooling down. C&A’s demand rate is 3 pages per minute. What is the smallest batch size to ensure the process is demand-constrained? A. Cannot be determined B. 90 C. 64 D. 500

4. Packages arrive at a facility at a rate of 30 per hour and are processed continuously at a rate of 25 per hour. The facility is open from 8 a.m. to 4 p.m. How long does the last package wait before it is processed?   A. 1.75 hours B. 1.20 hours C. 1.33 hours D. 1.60 hours

Answer to question 1 :

Effective processing time of any resource = Processing time / unit x ( 1 + percentage of units reworked/ 100 )

Effective processing time of first resource = 8 minutes/ unit

Effective processing time for second resource = 7 minutes/ unit

Effective processing time for third resource = 2 x (1 + 20/100) = 2 x 1.2 minutes = 2.4 minutes /unit

Effective processing time for 4th resource = 10 x ( 1 + 20/100) = 10 x 1.2 = 12 minutes/ unit

Since effective processing time is highest at 4th resource, bottleneck lies there

Answer to question 2 :

Let, the ideal batch size = N

At ideal batch size, Total processing time for cutting = Total processing time for Polishing ( so that the system is in equilibrium and there is no build up of bottleneck between two processes)

Total processing time for cutting for N units

= Set up time + Total cutting time

= set up time + Cutting time / unit x Number of units

= 40 + 30.N

Total processing time for polishing N units

= Polishing time / unit x Number of units

= 40.N

Therefore, for ideal batch size :

40 + 30.N = 40.N

Or, 10.N = 40

Or, N = 4

Answer to question 3 :

To find out the smallest batch size to ensure that the process is demand constrained , we have to find out the batch size and corresponding capacity which at least meets the demand rate of 3 pages per minute or more. ( i.e. Capacity > demand)

Demand rate = 3 pages per minute = 20 seconds / page

Cooling down period for every 500 pages = 15 minutes = 900 seconds

Or , Average cooling down period per page = 900/ 500 = 1.8 seconds / page

Time taken to print per page = 10 seconds

Let the corresponding batch size = N units

Time to print a batch size of N = ( average cooling down period / page + time to print / page ) x N = ( 1.8 + 10 ) x N = 11.8N seconds

Time taken to generate demand for N units = 20.N

Since Capacity should be > Time of corresponding demand of N units,

Total time to print N units < Total time during which demand for N units is generated

11.8N < 20.N

We however cannot determine value of N from above

Answer to question 4:

Duration of time when process is open ( 8 AM to 4 PM ) = 8 hours

Total arrival during 8 hours = 30 / hour x 8 hours = 240 packages

Total processed during same 8 hours = 25 / hour x 8 hours = 200 packages

Thus , backlog created after processing for 8 hours i.e. at 4 PM = 240 – 200 = 40 units

Since processing time is 25/hour, time to process this backlog of 40 units = 40 / 25 hour = 1.6 hour

Therefore, last package must wait for 1.6 hours before it is processed