Consider the inventory of disposable food trays at a hospital, which are ordered
ID: 416680 • Letter: C
Question
Consider the inventory of disposable food trays at a hospital, which are ordered once a month. The demand for these trays, which cost the hospital $0.75 apiece, is forecasted to be 25,000 units per month (with a CV of 10%). The annual holding cost rate used at the hospital is 20% and the ordering cost is estimated to be $25. The lead time from order to receipt is 1 month. The desired service level is 95%.
a. Calculate the order up to level (OUL).
b. Calculate the order quantity if there are 22,456 food trays in inventory and another 25,407 in transit.
Explanation / Answer
Coefficient of variation ( CV) IN % = Standard deviation of demand /Average demand x 100 = 10
Or, Standard deviation of demand / Average demand = 0.1
Or, Standard deviation of monthly demand / Average monthly demand of 25000 = 0.1
Or, Standard deviation of monthly demand = 25000 x 0.1 = 2500
Also to be noted :
Protection period = Order frequency + Lead time = 1 + 1 = 2 months
Standard deviation of demand during Protection period
= Standard deviation of monthly demand x Square root ( Protection period )
= 2500 x Square root ( 2 )
= 2500 x 1.414
= 3535
Z value corresponding to Service level of 95% = NORMSINV ( 0.95 ) = 1.6448
Therefore, Safety stock requirement
= Z value x Standard deviation of demand during protection period
= 1.6448 x 3535
= 5814.368 ( 5815 rounded to next higher whole number )
Thus , Order Upto Level ( OUL )
= average monthly demand x Protection period ( months) + safety stock
= 25000 x 2 + 5815
= 50000 + 5815
= 55815
ORDER UPTO LEVEL WILL BE 55815 UNITS
Order quantity
= Order upto level – Number of trays in transit – Number of trays in inventory
= 55815 – 25407 – 22456
= 7952
ORDER QUANTITY WILL BE 7952 FOOD TRAYS
ORDER UPTO LEVEL WILL BE 55815 UNITS