Question

Brooke Army Medical Center dispenses 250,000 bottles of brand name pharmaceutical annually. The optimal safety stock (which is on hand initially) is 1,000 bottles. Each bottle costs the center $10, inventory carrying costs are 30 percent, and the cost of placing an order with its supplier is $175. Orders can be placed only in multiples of 100 units.

a. What is the economic order quantity?

b. How many orders will be placed annually?

Please show work in Excel!

Answer 1

Annual demand (A)=    250000   units
Bottle cost =   $10  
Annual holding cost (C)= 30%*10=   $3   per unit
Ordering cost (o)=    $175  

Economic order quantity (EOQ) = √(2*A*O/C)      
√((2*250000*175)/3)      
5400.617249   or 5500 units  
      
So, EOQ quantity is 5500 units.      

(units are rounded off in 100 units. So quantity will be 5500 bottles. As optimal quantity is 5400.61 or 5401. But optimal order quantity cannot be less than 5401. So EOQ will be 5500 units.

  
(b) No of orders placed in year = Annual demand/EOQ      
250000/5500=   45.45454545   or 46 orders
      
So, no of orders is 46.       
(orders cannot be in round quantity. So it will be round up)