A sporting goods company has a distribution center that maintains inventory of fishing rods. The fishing rods have the following demand, lead time, and cost characteristics:
Average demand = 95 units per day, with a standard deviation of 18 units
Average lead time = 14 days with a standard deviation of 2 days
250 days per year
Unit cost = $30
Desired service level = 95%
Ordering cost = $55
Inventory carrying cost = 20%
What is the???
Annual ordering cost
Annual inventory carrying cost
Annual product cost
Total cost
Average cycle stock
Average inventory
To calculate the various costs and inventory metrics, we need to understand a few key concepts and formulas. Let's break down each metric and how to calculate it:
1. Annual Ordering Cost:
The annual ordering cost represents the total cost incurred to place orders for fishing rods throughout the year. It can be calculated using the following formula:
Annual Ordering Cost = (Number of orders per year) x (Cost per order)
To find the number of orders per year, we need to calculate the economic order quantity (EOQ). The EOQ is the optimal order quantity that minimizes the total ordering and carrying costs. The formula for EOQ is:
EOQ = √[(2 x Average demand x Cost per order) / Annual carrying cost per unit]
Given:
Average demand (D) = 95 units per day
Cost per order = $55
Annual carrying cost per unit = 20% of unit cost = (0.20) x ($30) = $6
Using the above values, we can calculate the EOQ:
EOQ = √[(2 x 95 x $55) / $6]
Once we've calculated the EOQ, we can find the number of orders per year by dividing the total annual demand by the EOQ:
Number of orders per year = (Total demand per year) / EOQ
Total demand per year = Average demand (D) x Number of working days (250 days)
Now, substitute the values into the formula for the annual ordering cost:
Annual Ordering Cost = (Number of orders per year) x (Cost per order)
2. Annual Inventory Carrying Cost:
The annual inventory carrying cost represents the cost of holding the fishing rods in inventory for a year. It includes costs such as warehousing, insurance, and obsolescence. The formula for the annual carrying cost is:
Annual Inventory Carrying Cost = (Average inventory level) x (Carrying cost per unit)
To find the average inventory level, we can use the EOQ formula:
Average inventory level = (EOQ) / 2
Now, substitute the values into the formula for the annual inventory carrying cost:
Annual Inventory Carrying Cost = (Average inventory level) x (Carrying cost per unit)
3. Annual Product Cost:
The annual product cost represents the cost of purchasing the fishing rods for a year. It is calculated by multiplying the unit cost by the total annual demand:
Annual Product Cost = Unit cost x Total demand per year
4. Total Cost:
The total cost is the sum of the annual ordering cost, annual inventory carrying cost, and annual product cost:
Total Cost = Annual Ordering Cost + Annual Inventory Carrying Cost + Annual Product Cost
5. Average Cycle Stock:
The average cycle stock represents the average inventory level during one complete cycle of ordering and receiving a new batch of fishing rods. It can be calculated using the EOQ formula:
Average Cycle Stock = (EOQ) / 2
6. Average Inventory:
The average inventory is the average amount of inventory held during a year. It can be calculated as:
Average Inventory = Average Cycle Stock + Safety Stock
However, the safety stock is not provided in the given information, so we won't be able to calculate it.
Now, you can use the provided information and the formulas above to calculate the values for each metric.