Question

PA 7-10 Aquatica makes underwater camera housings Aquatica makes underwater camera housings for divers. The prooass begins with a solid rectangular block of aluminum which is used to make a single housing. A Computer Numerically 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 treatad in a seres of baths. There is ample capacity in the treating stage. Finaly, a worker must manually attach the various buttons and components to the metal houaing. This essembly takas 120 minutes per houaing per worker and Aquatica has 6 workers trained to do thia tsak. The CNC machine raquires a 30 minute setup time before the production of a batch can begin. Demand rate Housing type (housings per hour) D7000 0.4 5DS Mark III 0.5 AN-Sn 0.6 D300 0.7 T2i 0.8 Round your answer to 1 decimal place. If the CNC machine produces 14 housing between setups, what would be its capacity in housings per hour)? housings per hour h Assuming the process is supply constrained, what is the utilization (as a percentage) of the CNC machine if it operates in batches of 14 housings? (Round your answer to 2 decimal places.) Assuming the processis supply constrained and operates with batches of 14 housings, what is the average invetory of housings? number of housings Aquatica actually makes 5 different housings. As already mentioned, the CNC machine must be setup 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 the table above. If they wiah to minimize inventory while satisfying their demand, how many DYDCo housings should they produce in each batch? number of housings

Answer 1

a.

Capacity = Batch size/(set up time + processing time) = 14/(30+15*14) = 14/240 minutes = (14/240)*60 hours = 3.5 hours

b.

Capacity for assembly = 120/6 = 20/minute = 60/20 = 3/hour as assembly takes 120 minutes per housing per worker and 6 workers are working at the moment

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 = 0.749946432 = 0.75 (Rounded to 2 decimal places)

c.

Average inventory = 1/2 * batch size * (1-(capacity for assembly * 1/4)) = 1/2*14*(1-(3/4) = 1.75

d.

Total demand of all the housings = 0.4+0.5+0.6+0.7+0.8 = 3/hour

Setup time per housing = 30/60 hr = 0.5 hr
Setup time for 5 housings = 5*0.5 = 2.5 hr

Processing time = 15/60 hr = 0.25 hr

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

Batch size of D700 = 30*(0.4/3) = 4