Question

10. Aquatica makes underwater camera housings for divers. The process begins with a solid rectangular block of aluminum that is used to make a single housing. A computer numeri- cally controlled (CNC) machine drills into the block to make the metal “frame” of the housing. Each block requires 15 minutes of drilling. The frame is then chemically treated in a series of baths. There is ample capacity in the treating stage. Finally, a worker must man- ually attach the various buttons and components to the metal housing. This assembly takes 120 minutes per housing per worker and Aquatica has 6 workers trained to do this task. The CNC machine requires a 30-minute setup time before the production of a batch can begin.

a. If the CNC machine produces 14 housings between setups, what would be its capacity

(in housings per hour)?

b. Assuming the process is supply-constrained, what is the utilization (as a number

between 0 and 1) of the CNC machine if it operates in batches of 14 housings?

c. Assuming the process is supply-constrained and operates with batches of 14 housings,

what is the average inventory of housings?

d. Aquatica actually makes five different housings. As already mentioned, the CNC

machine must be set up whenever production switches from one housing to the other. In each case, the setup time is 30 minutes and it takes 15 minutes to drill the block for each type of housing. Demands for the housings are given in Table 7.7.

Answer 1

Here in question(a) the capacity of CNC machine can be derived based on Batch size,setup time and process time so as per given values

Batch size=14 & Setup time =30 and processing time is 15(each block)×14

A)Capacity = Batch size/(set up time+processing time)

= 14/(30+15*14)

= 14/240 minutes

= (14/240)*60 hours = 3.5 hours

Capacity =3.5hrs

B)To find the utilization here we have to know about capacity to assembly it and assembly time for batch so 1st we need to find capacity for assembly and in question we have 120minutes per housing and total 6workers trained so

= 120/6 = 20/minute

= 60/20 = 3hours

Assembly time for batch of 14 housings = 14/3 hr = 4.667 hr

CNC time for batch = 30+14*15 = 240 minutes = 4 hr

Utilization of CNC = (14*15)/60/4.667 = 0.75(approx)

C)Average invertory is totally based on Batch size and capacity of assembly

Average inventory = 1/2 * batch size * (1-(capacity for assembly * 1/4))

Here batch size is 14 and capacity of assembly is 3hrs so

= 1/2*14*(1-(3/4) = 1.75

d)here in the question given that setup for five different housing so the setup time is 30 minutes and it takes 15 minutes to drill the block for each type of housing total demand offive housings is 0.4+0.5+0.6+0.7+0.8 = 3/hour

As per question Setup time per housing = 30/60 hr = 0.5 hr
So Setup time for 5 housings =5*each housing setuptime= 5*0.5 = 2.5 hr

So Processing time = 15/60 hr = 0.25 hr(we have to find for 15 housings)

Total batch size = (2.5*3)/(1-3*0.25) = 30

Hope you understood