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. An office building that operates 365 days per year maintains inventories of office supplies, including a specialized paper. Currently, this paper is ordered once every two weeks. Over the course of a year, its average rate of usage is 75 reams per week (with a forecast CV is 20%). The paper costs $20 per ream, and the holding rate is 15% annually. The fixed ordering cost is $35 and the lead time for receiving an order is 4 weeks. Target cycle service level is 93%. a. Calculate the preferred order up to level (OUL). b. If the manager switched to a fixed order quantity system with an optimal EOQ, how frequently would orders be placed? c. Do the results imply that daily ordering is too frequent?

Coefficient of variation ( CV ) = (Standard deviation / Mean or average rate ) x 100 = 20
Given , Average rate = 75 reams per week
Therefore ,
(Standard deviation / 75 ) x 100 = 20
Or, Standard deviation of weekly demand = 15
It is to be Noted that :
Protection period = Ordering frequency + Lead time = 2 weeks + 4 weeks = 6 weeks
Standard deviation of demand during Protection period
= Standard deviation of weekly demand x Square root ( Protection period )
= 15 x Square root ( 6 )
= 15 x 2.449
= 36.735
Z value for cycle service level of 93% = NORMSINV ( 0.93 ) = 1.475
Therefore , safety stock requirement = Z value x Standard deviation of demand during protection period = 1.475 x 36.735= 54.18 ( 54 rounded to nearest whole number )
Thus,
Order upto level = Average weekly demand x Protection period ( weeks ) + safety stock = 75 x 6 + 54 = 450 + 54 = 504
PREFERRED ORDER UPTO LEVEL = 504 REAMS
Optimum EOQ = Square root ( 2 x Co x D / Ch )
Where,
Co = Ordering cost = $35
D = Annual demand = 75 reams / week x 52 weeks = 3900 reams
Ch = Holding cost per unit per annum = 15% of $20 = $3
Therefore,
EOQ = Square root ( 2 x 35 x 3900 / 3 ) = 301.66 ( 302 rounded to nearest whole number )
Frequency at which order should be placed = EOQ / Average weekly requirement = 302/75 = 4.026 weeks
ORDER SHOULD BE PLACED ONCE IN EVERY 4.026 WEEKS
Daily ordering is considered too frequent, since total annual ordering cost + total annual holding cost incurred for daily ordering system will be more than similar total cost incurred basis EOQ ordering system
 
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