Question

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:

a. A batch can consist of only one order; it cannot have other orders in it. (8 pts)
b. Three orders are combined to form a batch. (8 pts)
c. All orders can be combined into one batch. (8 pts)
d. What is the percent change in capacity as you go from (i) to (ii) to (iii)?

Answer 1

Given,

Setup time of machine= 150 min

0.0075 min/pc.

1 order =10,000 pcs.

1 day= 2 shifts X 450 min each

1 order per batch

10000 pcs per batch before setup required again

(150 min setup time) –> (75 min run time for 10000 pcs) –> (150 min setup time) –> (75 min run time for 10000 pcs) = 450 mins

Total for shift 1 = 20,000 pcs

Similarly, for Shift 2, total production cap = 20,000 pcs

So, total capacity in this case is 40,000 pieces/day

3 orders per batch

30,000 pcs per batch before setup required again

Shift 1: (150 min setup time) –> (225 min run time for 30,000 pcs) –> (75 min setup time) = 450 mins

Shift 2: (75 min setup time) –> (225 min run time for 30,000 pcs) –> (150 min setup time) = 450 mins

So, total capacity in this case is 60,000 pieces/day

All orders can be combined in one batch

No cap on number of orders in a batch

Shift 1: (150 min setup time) –> (300 min run time for 40,000 pcs) = 450 min

Shift 2: (450 min run time for 60,000 pcs) = 450 min

So, total capacity in this case is 100,000 pieces/day

From (i) to (ii) there is 50% increase in capacity

From (ii) to (iii) there is 66.67% increase in capacity