Problem 1: Economic Order Quantity
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.
a) 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)
b) How many units of blood should the hospital order each time? (Hint: use the EOQ)
c) How many orders will be placed each year?
d) What is the total holding cost for the year?
Problem 2: Quantity Discounts
The hospital also buys plasma for use in surgical procedures. The demand for plasma is 2,028units per year. There is a $40cost to place an order and thecost per unit of plasma to hold it in inventory for the year is $60.
a) What is the economic order quantity?
For part b) assume the cost of a unit of plasma is based on the quantity ordered at one time. If less than 25units 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 if 101or more units of plasma are ordered the unit price is $59.55.
b) What order quantity will result in the lowest total annual cost forthe hospital? Be sure to show your work for full credit.
Problem 3: Periodic Review System
The hospital gift shop orders get well cards and uses a weekly periodic inventory system to maintain the inventory. Below is the number of cards sold for the last 5weeks.
|
Week of
|
3/6/16
|
3/13/16
|
3/20/16
|
3/27/16
|
4/3/16
|
|
Units Sold
|
101
|
94
|
82
|
97
|
106
|
a) What is the hospital'saverage weekly demand for get well cards?
b) Assume the standard deviation of demand is 9.03 cards and the hospital wants to be in stock at least 95% of the time. What is the appropriate restocking level?
c) If there are currently 30get well cards on hand when the order is placed on 4/10/16, how manycardsshould be ordered?
Problem 4: Single-Period Inventory System
The hospital cafeteria makes one large batch of macaroni and cheese each morning. If the cafeteria runs out of macaroni and cheese, the last few customers are less than satisfied, but if the cafeteria makes too much, itcan be sold to the local hog farmer for feed. Every serving costs $1.25 to make and can be sold for $7.00 to customers. The cafeteria has to pay $0.45 per serving to transport the extra servings to the hog farmer, but the hog farmer will pay $0.71 per serving. The average daily demand is 96 servings with a standard deviation of 19 servings.
a) What is the target service level?
b) How many servings of macaroni and cheeseshould the cafeteria make each day to meet this service level?