I am confused with this question. I calculated that for the 10,000 piece batch s

Question

I am confused with this question. I calculated that for the 10,000 piece batch size there was 225 min. per batch (Hopefully i got this right)

I then calculated since there is 2 shifts it would be a 15-hr day between the two shifts ((450*2)/60)) = 15 hrs,

Then I cam up with the capacity of the 10,000 piece having 4 batches: 900/225= 4

Which then comes to 4*10,000 = 40,000 pieces.

However, after this part I am stuck (but hopefully I did the first part right) Please show work, because I want to know how to do this correctly.

A machine has a setup time of 150 minutes and run time of 0.0075 minutes per piece. Order sizes are typically 10,000 pieces. After a batch is processed, the process has to be stopped and the machine has to be setup before the next batch can be processed. Assume that a day consists of two shifts and each shift is 450 minutes long. Find the capacity in pieces per day for this machine under the following assumptions: Ö) A batch can consist of only one order; it cannot have other orders in it. (ii) Three orders are combined to form a batch. (iii) All orders can be combined into one batch. (iv) What is the percent change in capacity as you go from (i) to (ii) to (ii)?

Explanation / Answer

(i) the 1st part done by you is correct, we can do 40000 pieces in a day if we do only one order in one batch. Since all orders take 225 minutes to complete.

(ii) If 3 orders combined, pieces in a batch = 10000*3 = 30000

time taken for a batch = setup +run time = 150 + 30000*0.0075 = 150+ 225 = 375

a day consist of 900 minutes.

total batches = 900/375 = 2.4

2 batches take 375+375 = 750 minutes

another setup = 150 minutes

which completes 900 minutes.

Hence total pieces = 6 batches = 60000 pieces.

(iii) all orders combined in 1 batch:

here we have total 900 minutes in day. 150 minutes used for setup, rest time used for processing.

time remaining = 900 - 150 = 750

pieces possible in 750 minutes = 750/0.0075 = 100000 pieces.

(iv) % change from 1 to 2:

40000 to 60000

increase = 20000

change = 20000/40000 = 0.5 = 50%

2 to 3:

60000 to 100000

change = 40000

% change = 40000/ 60000 = 0.6667 = 66.67%

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