a)
|
Daily Demand |
µD |
= |
|
100 |
|
Standard Deviation of Daily Demand |
σD |
= |
|
30 |
| Working
days per year |
n |
= |
|
300 |
|
Annual Demand |
D |
= |
n*µD |
30,000 |
| Lead Time
(Days) |
L |
= |
|
10 |
| Desired
Service level |
α |
= |
|
90% |
|
Z-value corresponding to Service Level |
Zα |
= |
NORMSINV(α) |
1.28 |
|
Safety stock |
ss |
= |
ZασD
√L |
121 |
|
Reorder Point |
R |
= |
µD*L
+ ss |
1,121 |
| Annual
Holding Cost per Unit |
H |
= |
|
$0.90 |
| Ordering
Cost per Order |
S |
= |
|
$100 |
|
Optimal Order Qty |
Q* |
= |
√(2SD/H) |
2,582 |
Optimal reorder point, R = 1121
EOQ = 2582
-------------------------------------------------------------------------------------------------------
b)
Average inventory = EOQ/2 + Safety stock
= 2582/2 + 121
= 1412
-------------------------------------------------------------------------------------------------------
c)
New lead time, L = 3 days
Revised safety stock = 1.28*30*sqrt(3)
= 67
EOQ remains unchanged.
New average inventory = 2582/2+67
= 1358
Reduction in average inventory = 1412 - 1358
= 54
Savings = 54*0.9
= $ 48.6
