how to derive eoq formula?
- Determine the demand in units.
- Determine the order cost (incremental cost to process and order)
- Determine the holding cost (incremental cost to hold one unit in inventory)
- Multiply the demand by 2, then multiply the result by the order cost.
- Divide the result by the holding cost.
To calculate the economic order quantity, you will need the following variables: demand rate, setup costs, and holding costs. The formula is: EOQ = square root of: [2(setup costs)(demand rate)] / holding costs.
The economic lot size of an order depends upon two types of costs:
i. Inventory carrying costs and
ii. Procurement or set up costs.
EQO gives the order level where total costs i.e., inventory carrying and procurement costs are minimum.
EOQ formula is based on certain assumptions:
i. Demand for the product is known and constant.
ii. Lead time is known and constant.
iii. The receipt of inventory is instantaneous.
iv. Quantity discounts are not availed.
v. Stock outs and shortages are not considered.
Let Q be the Economic Order Quantity (EOQ), R be the demand per unit time in units,
C3 be the procurement cost or set up cost per order,
C1 be the stock holding or inventory carrying cost per unit item per unit time.
Total Annual Inventory Cost:
= Total Ordering Cost + Total Inventory Carrying Cost … (1)
Total Ordering Cost:
Total Inventory Carrying Cost:
(From Fig. 4.1, if total quantity is OB i.e., Q, then average inventory=Q/2)
Putting expressions of (2) ad (3) in (1)
The objective is to determine the quantity to order which minimizes the total annual inventory cost.
So to minimize the total cost, differentiate Total Cost (TC) w.r.t. Q and equate to zero.
Example 1:
A dealer has to supply 1000 units of a product per year to his customer. The inventory holding cost is Rs.2.40 per unit per year and ordering cost per order is Rs.350. Determine EOQ.
Solution:
Example 2:
Given the annual consumption of material is 3600 units, ordering costs are Rs.4 per order. The unit price of material is 64 paise and storage costs are 50% per annum of stock value. Find the economic order quantity in units.
Variables:
T = Total annual inventory cost P = Purchase unit price, unit production cost Q = Order quantity Q* = Optimal order quantity D = Annual demand quantity K = Fixed cost per order, setup cost h = Annual holding cost per unit, also known to be carrying or storage cost
The single-item EOQ formula helps find the minimum point of the following cost function:
Total Cost = Purchase Cost or Production Cost + Ordering Cost + Holding Cost
Where,
To determine the minimum point of the total cost curve, calculate the derivative of the total cost with respect to Q (assume all other variables are constant) and set it equal to zero (0):
Solving for Q gives Q* (the optimal order quantity):
Therefore,
Can also be written as,
