UC-25 Uncertain Demand Rc:o HC 2 x 25 After one year of operations, the Nawras E

Question

UC-25 Uncertain Demand Rc:o HC 2 x 25 After one year of operations, the Nawras Electronics Company reached agreement wi suppliers to ensure a constant lead time of 7 days. However, the company also realized that daily demand for laptops exhibited some variability, with the mean annual demand still at 3200 units, but with a standard deviation of 150 laptops. th 21. The company has decided on a service level of 95%. Accordingly, what size or safety stock should be kept to cope with uncertainty? 22, Determine the total annual inventory cost under this 95% service level inventory policy 23. In a first assessment of the new policy, the company managers concluded that the . type I service level is not enough information encompassing. What is meant by this? 24. Calculate the fill rate for a reorder level of 725 screens? 25. What is the expected number of units short per cycle? 26. The Nawras Electronics Company is planning to switch to a periodic review system whose replenishment period is based on the same time parameters as the existing continuous review system Analyze the prospective inventory system and help the company decide whether or not to shift to a periodic review system. Order cost-70 Unit cost-25 Holding cost 2x 25-5

Explanation / Answer

(21)

Safety Stock = Z.d.sqrt(L)
Average lead time = L = 7 days = 7/365 years
Z at 95% service level = NORMSINV(95%)=1.645
Safety stock = 1.645 x 150 x sqrt(7/365) = 34.17 or 34

[Note: 150 is the std. deviation of yearly demand and that it why we need to write lead time in years]

(22)

D = annual demand = 3200 units
S = ordering cost = 70
H = holding cost = 5

EOQ = Q* = (2.D.S / H)1/2 = sqrt(2*3200*70/5) = 299.33 or 300 units (rounded off)

Holding cost for cycle stock = Q* x H/2 = 300*5/2 = $750
Holding cost for safety stock = Safety stock x 5 = 34 x 5 = $170

Total holding cost = $750+$170 = $920

(23)

The type-I level service level is the customer service level which determines the probability of stockput in a complete cycle i.e. the proportion of cycles in which no stockouts occur. This may be misleading because it does not account for the proportion of service delivery missed out. For example, if in a particular order, 50% was delivered, then the type-I service level will still be zero becasue the order was not completely fulfilled. A type-II service level i.e. the fill rate will measure this adequately as it determines the proportion of demand satisfied on time. It will show the above example as 50%.

(24)

Reorder point = 725

Average lead time demand = (7/365) x 3200 = 61.37

So, safety stock = ROP - Average lead time demand = 725 - 61.37 = 663.63 (very absurd, but can't help)

So, Z.d.sqrt(L) = 663.63
or, Z = 663.63 / (150*sqrt(7/365)) = 31.95 (very absurd, but can't help)

Corresponding loss function, L(z) = 0

Fill rate = 1 - L(z)*d.sqrt(L)/Q* = 1 - 0 = 100%

[Note: please check the demand figure, is 3200 the annual demand or daily demand? If it's annual demand, the above absurdity will come]

(25)

Expected number of units short in a cycle = L(z)*d.sqrt(L) = 0 as L(z) is zero

(26)

Time between order = P = EOQ/average daily demand = 300 / (3200/365) = 34.2 days
Average lead time = L = 7 days

Safety Stock = Z.d.sqrt(L+P) = 1.645 x 150 x sqrt(34.2+7) = 1584

Note that the safety stock will become too high in the case of periodic review system with very little advantage.

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