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:
