Problem 1: Economic Order Quantity (8 points) A hospital buys blood from the loc
ID: 450925 • Letter: P
Question
Problem 1: Economic Order Quantity (8 points)
A hospital buys blood from the local blood bank and because this is a critical item the inventory supply of blood at the hospital is constantly monitored. An EOQ inventory model is used to determine when to order and how much blood to order (blood is measured in “units” and one unit of blood is about 525 mL). Since the shelf life of a unit of blood is short (42 days or less) the hospital has a high holding cost of $90 per year per unit of blood. It costs the hospital $50 to place an order and the hospital uses 4,410 units of blood annually. The average lead time to deliver blood to the hospital is 2 days and since the demand for blood and lead time are both variable, the hospital keeps a safety stock of 80 units of blood on hand.
The next order should be placed when blood inventory drops to how many units of blood? (assume 365 days in one year for converting annual demand to daily demand. You may leave your final answer as a decimal) (2 points)
How many units of blood should the hospital order each time? (Hint: use the EOQ) (2 points)
How many orders will be placed each year? (2 points)
What is the total holding cost for the year? (2 points)
Problem 2: Quantity Discounts (5 points)
The hospital also buys plasma for use in surgical procedures. The demand for plasma is 2,028 units per year. There is a $40 cost to place an order and the cost per unit of plasma to hold it in inventory for the year is $60.
What is the economic order quantity? (2 points)
For part b) assume the cost of a unit of plasma is based on the quantity ordered at one time. If less than 25 units of plasma are ordered the unit price is $60; if 26-75 units of plasma are ordered the unit price is $59.85; if 76-100 units of plasma are ordered the unit price is $59.70; and if101 or more units of plasma are ordered the unit price is $59.55.
What order quantity will result in the lowest total annual cost for the hospital? Be sure to show your work for full credit. (3 points)
Explanation / Answer
1- Annual Holding Cost=H=90
Ordering Cost=O=50
Annual Demand=D=4410, daily demand=d=4410/365=12.1
L=2
Safety Stock=S=80
Q-1=Reorder point=dL+safety stock=12.1*2+80=94.2
Q-2=EOQ=Sqrt(2*D*O/H)=sqrt(2*4410*50/90)=70
Q-3 number of orders=4410/70=63
Q-4 total holding cost= EOQ*H/2=70*90/2=3150