EOQ Analysis with Safety Stock Calculation

This assignment involves calculating the Economic Order Quantity (EOQ) and Reorder Point (ROP) for a given table of parameters, including demand rate, setup/ordering cost, holding cost, unit cost, lead time, and safety stock. The EOQ is found to be 149 units, while the ROP is initially calculated as 187 units due to zero safety stock allocation. To bring the ROP within or equal to the EOQ, some safety stock should be allocated. Additionally, the assignment calculates the standard deviation of demand during the lead time, expected demand during lead time, and required safety stock to achieve a service level of 99%. The total annual holding cost is calculated as $36,000.

The table given below shows the workings of EOQ
Parameter Value
Demand rate(D) 4000
Setup/Ordering cost(S) 25
Holding cost(H)@10% 9
Unit cost 90
Days per year (D/d) 300
Daily demand rate 13.33
Lead time (in days) 14
Safety stock 0
Optimal order quantity (Q*) 149.07
Maximum Inventory Level (Imax) 149.07
Average inventory 74.54
Orders per period(year) 26.83
Annual Setup cost 670.82
Annual Holding cost 670.82
Unit costs (PD) 360000

Total Cost 361341.7
Reorder point
186.67
units
a. The EOQ is 149 units
b. The ROP is 187 units
c. Here, the ROP is greater than the EOQ, and this is mainly due to zero units allotted to safety stock. So, we should allocate some units to
safety stock to make ROP less than or equal to EOQ.
d. The average inventory is $ 74.54 and the annual holding cost is $ 670.82
e. Approximately 27 orders should be placed in a year and the annual ordering cost is $ 675
Standard Deviation of demand during the lead time = Safety Stock/(Z1-α/2 * √LT) = 12/(2.33 * √5) = 2.3
Parameter Value
(Daily) Demand (d-bar) 12
(Daily) Demand std dev (sigma-
d) 4
Service level % 99

Lead time (in days) (L) 5
Lead time std dev (sigma L) 2.3
Z value 2.33
Expected demand during lead
time 60
Safety Stock 67.6
Reorder point 127.6
The safety stock should be at least 68 units
The total annual holding cost is $36000