To develop a model for total cost, we need to formulate mathematical functions for annual ordering costs and annual holding costs based on the average inventory held throughout the year.
1. Annual Ordering Cost:
The annual ordering cost refers to the cost incurred each time an order is placed for new inventory. It includes expenses such as order processing, transportation, and paperwork. The formula to calculate the annual ordering cost can be given as:
Annual Ordering Cost = Demand (D) * Ordering Cost per Order (S)
Where:
- Demand (D) is the total quantity of inventory demanded in a year.
- Ordering Cost per Order (S) is the cost incurred for placing a single order.
2. Annual Holding Cost:
The annual holding cost represents the expenses associated with holding or storing inventory over a one-year period. This includes costs such as warehousing, insurance, taxes, depreciation, and opportunity cost. The formula to calculate the annual holding cost can be expressed as:
Annual Holding Cost = Average Inventory (Q/2) * Holding Cost per Unit (H)
Where:
- Average Inventory (Q/2) is half of the total inventory quantity held on average throughout the year.
- Holding Cost per Unit (H) is the cost to hold one unit of inventory for a year.
3. Total Cost Model:
To calculate the total cost, we need to sum the annual ordering cost and the annual holding cost. The formula for the total cost (TC) can be represented as:
Total Cost (TC) = Annual Ordering Cost + Annual Holding Cost
Substituting the formulas we derived earlier, we get:
TC = D * S + (Q/2) * H, where
- TC is the total cost.
- D is the demand or total quantity of inventory demanded in a year.
- S is the ordering cost per order.
- Q is the total inventory quantity held on average throughout the year.
- H is the holding cost per unit.
By using this model, you can estimate the total cost based on the given demand, ordering cost, and holding cost.