Derivation of the Economic Order Quantity (EOQ) Model: 1. Assumptions: Demand is known and constant. Lead time is constant. Inventory setup costs a...
1. Assumptions:
Demand is known and constant.
Lead time is constant.
Inventory setup costs are negligible.
Cost of holding inventory is constant.
2. Objective:
3. Steps:
Define:
Q: The optimal order quantity to order.
R: The lead time required to receive an order.
D: The known demand per unit of time.
H: The holding cost per unit of time.
p: The cost per unit of order.
Minimize:
Total cost: Cp = (D/Q) * p - (R/Q) * H.
Differentiate:
Total cost with respect to Q and solve for the critical point that minimizes total cost.
Critical point represents the optimal order quantity.
4. Solution:
The EOQ model finds the optimal order quantity by balancing the cost of ordering (pQ) with the cost of holding inventory (H).
The optimal order quantity is approximately equal to the lead time multiplied by the demand per unit of time.
The model suggests that ordering more than the optimal quantity would result in higher holding costs, while ordering less would lead to lower costs but potentially higher lead times.
5. Example:
Suppose a company has a demand of 10 units per week, a lead time of 5 weeks, and the cost of holding inventory is 5. Using the EOQ model, the optimal order quantity would be 5 units.
6. Implications:
EOQ is widely used in inventory and warehouse management to optimize ordering and inventory levels.
It helps balance the costs of ordering, holding, and lost sales.
Understanding the EOQ model is crucial for professionals involved in inventory management