In: Operations Management
The normal scrap loss for four successive operations is 5%, 3%, 15% and 10% respectively. How many units should be started through in order to finish with 1,200 pieces? Find:
a) The total machine time needed if the operation times are 3, 6,
4, and 5 minutes, respectively.
b) The total cost if the cost per unit for each successive
operation is $2, $5, $3, and $1, respectively.
operations |
normal scrap loss |
1-loss % |
1 |
5% |
95% |
2 |
3% |
97% |
3 |
15% |
85% |
4 |
10% |
90% |
required output |
1,200 |
pieces |
Output Required=Input Given *(1-Loss1%)*(1-Loss2%)*(1-Loss3%)*(1-Loss4%) |
||
1200 = input *(1-0.05)*(1-0.03)*(1-0.15)*(1-0.10) |
||
solve for input: |
||
input = 1200/(95%*97%*85%*90%) |
||
input |
1702 |
pieces |
(rounding off) |
||
a) |
||
operations |
time/unit (min) |
time |
1 |
3 |
5107 |
2 |
6 |
9703 |
3 |
4 |
6275 |
4 |
5 |
6667 |
total time |
27751 |
|
min |
||
b) |
||
operations |
cost/unit |
cost |
1 |
$ 2 |
$ 3,404.51 |
2 |
$ 5 |
$ 8,085.71 |
3 |
$ 3 |
$ 4,705.88 |
4 |
$ 1 |
$ 1,333.33 |
total cost |
$ 17,529.43 |
formulae used: