The Optimal Order Quantity for the Manufacturer
A furniture manufacturer uses 20,000 square feet of plywood per month. The holding costs are estimated to be 20% per year and fixed cost of each order is $400 regardless of the quantity ordered. The supplier charges $2.00 per square foot if you order less than 20,000 square feet, $1.80 per square foot for orders 20,000 square feet but less than 50,000 square feet, and $1.70 per square foot for all orders of 50,000 square feet or more.
a) What will be the optimal order quantity for the manufacturer given this pricing structure? What will be the cycle inventory and the annual inventory cost and annual item cost?
b) How many orders will be placed each year?
The Optimal Order Quantity for the Manufacturer
To determine the optimal order quantity for the manufacturer, we need to consider the pricing structure provided by the supplier and the holding costs associated with inventory. We can calculate the total cost for different order quantities and select the one with the minimum cost.
Let's start by calculating the total cost for different order quantities:
Order Quantity: Less than 20,000 square feet
Cost per square foot: $2.00
Total cost: $2.00 * 20,000 = $40,000
Order Quantity: 20,000 to 49,999 square feet
Cost per square foot: $1.80
Total cost: $1.80 * Order Quantity
Order Quantity: 50,000 square feet or more
Cost per square foot: $1.70
Total cost: $1.70 * Order Quantity
Now, let's calculate the cycle inventory and annual inventory cost for each order quantity:
Cycle Inventory
Cycle inventory refers to the average amount of inventory held during a production cycle. In this case, the production cycle is one month.
Order Quantity: Less than 20,000 square feet
Cycle inventory: (Order Quantity / 2) = (20,000 / 2) = 10,000 square feet
Order Quantity: 20,000 to 49,999 square feet
Cycle inventory: (Order Quantity / 2) = (Order Quantity / 2)
Order Quantity: 50,000 square feet or more
Cycle inventory: (Order Quantity / 2) = (Order Quantity / 2)
Annual Inventory Cost
Annual inventory cost is the product of cycle inventory and holding cost per square foot.
Holding cost per square foot: 20% per year
Order Quantity: Less than 20,000 square feet
Annual inventory cost: (Cycle Inventory * Holding Cost per Square Foot) = (10,000 * $0.20)
Order Quantity: 20,000 to 49,999 square feet
Annual inventory cost: (Cycle Inventory * Holding Cost per Square Foot)
Order Quantity: 50,000 square feet or more
Annual inventory cost: (Cycle Inventory * Holding Cost per Square Foot)
Annual Item Cost
Annual item cost is the product of order quantity and unit cost per square foot.
Order Quantity: Less than 20,000 square feet
Annual item cost: (Order Quantity * Cost per Square Foot) = (20,000 * $2.00)
Order Quantity: 20,000 to 49,999 square feet
Annual item cost: (Order Quantity * Cost per Square Foot)
Order Quantity: 50,000 square feet or more
Annual item cost: (Order Quantity * Cost per Square Foot)
Now that we have calculated the different costs for each order quantity, we can compare them to find the optimal order quantity.
Once we determine the optimal order quantity, we can calculate the number of orders placed each year by dividing the total usage (20,000 square feet) by the optimal order quantity.
By analyzing these costs and quantities, we can provide a comprehensive answer to both parts of the question.