Answered Essay: Arizona Health Services (AHS), a large hospital system, dispenses 250,000 bottles of brand name

Arizona Health Services (AHS), a large hospital system, dispenses 250,000 bottles of brand name pharmaceuticals annually in one of its hospitals (assume a constant daily demand). The optimal safety stock, which is on hand initially, is 1,000 bottles. Each bottle costs $10, the holding cost is $0.10/unit, and the cost of placing an order with the supplier is $175. Assume an interest rate of 5% and a lag time of 5 days. What is the total cost of the pharmaceuticals?

Expert Answer

Annual demand of bottles = D = 250,000

Order placement cost = Co = $175

Holding cost per unit per year = Ch = $0.10

Therefore ,

Economic Order Quantity ( EOQ )

= square root ( 2 x Co x D/Ch )

= square root ( 2 x 175 x 250,000 / 0.10)

= 29580.39 ( 29580 rounded to nearest whole number )


Annual ordering cost

= Ordering cost per order x Number of orders

= Ordering cost per order x Annual demand/EOQ

= $ 175 X 250000/29580

= $1479.03 ( $1479 rounded to nearest integer)

Annual inventory holding cost

= Holding cost per unit per year x average inventory

= Holding cost per unit per year x ( EOQ/2 + safety stock)

= $0.10 x ( 29580 /2 + 1000)

= $0.10 x ( 14790+ 1000)

= $0.10 x 15790

= $1579

Annual cost of bottles

= Cost/ bottle x annual demand of bottles

= $10 x 250,000

= $2500,000

It is to be noted that “Total cost of pharmaceuticals” has not been defined in the problem.

Therefore , we define :

Total cost of pharmaceuticals

=   Annual ordering cost + Annual inventory holding cost + annual cost of bottles


Total cost of pharmaceuticals

= $ 1479 + $1579 + $ 2500,000

= $2503058

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