Eoq Application in Our Company
Eoq Application in Our Company
1 Introduction of EOQ
1.1 Economic order quantity (EOQ)
Economic order quantity is the level of inventory that minimizes the total inventory holding costs and ordering costs. It is one of the oldest classical production scheduling models. The framework used to determine this order quantity is also known as Wilson EOQ Model or Wilson Formula. The model was developed by F. W. Harris in 1913, but R. H. Wilson, a consultant who applied it extensively, is given credit for his early in-depth analysis of it. [1]
1.2 EOQ Modeling Assumptions
Under these conditions, our company can use EOQ formula to determine the optimal order quantity.
1. Production is instantaneous – there is no capacity constraint and the entire lot is produced simultaneously.
2. Delivery is immediate – there is no time lag between production and availability to satisfy demand.
3. Demand is deterministic – there is no uncertainty about the quantity or timing of demand.
4. Demand is constant over time – in fact, it can be represented as a straight line, so that if annual demand is 365 units this translates into a daily demand of one unit.
5. A production run incurs a fixed setup cost – regardless of the size of the lot or the status of the factory, the setup cost is constant.
6. Products can be analyzed singly – either there is only a single product or conditions exist that ensure separability of products.
EOQ is the quantity to order, so that ordering cost + carrying cost finds its minimum. (A common misunderstanding is that the formula tries to find when these are equal.)
2. How to obtain the EOQ formula
2.1 Variables
Q = order quantity
Q * = optimal order quantity
D = annual demand quantity of the product
P = purchase cost per unit
S = fixed cost per order (not per unit, in addition to unit cost)
H = annual holding cost per unit (also known as carrying cost or storage cost) (warehouse space, refrigeration, insurance, etc. usually not related to the unit cost)
2.2 The Total Cost function
The single-item EOQ formula finds the minimum point of the following cost function:
Total Cost = purchase cost + ordering cost + holding cost
– Purchase cost: This is the variable cost of goods: purchase unit price Ă— annual demand quantity. This is PĂ—D
– Ordering cost: This is the cost of placing orders: each order has a fixed cost S, and we need to order D/Q times per year. This is S Ă— D/Q
– Holding cost: the average quantity in stock (between fully replenished and empty) is Q/2, so this cost is H Ă— Q/2
To determine the minimum point of the total cost curve, set the ordering cost equal to the holding cost:
Solving for Q gives Q* (the optimal order quantity):
Therefore: .
Note that interestingly, Q* is independent of P; it is a function of only S, D, H.
3. How to use formula to Calculate EOQ
1. Understand the formula.
The basic formula for EOQ is: [2 * (Annual Usage in Units * Order Cost) / Annual Carrying Cost per Unit] ^ (1/2).
2. Define the variables.
The most difficult part about calculating the EOQ is defining the variables. Annual usage is expressed in units and is usually a forecast. Lets use 100 for this example. Order cost is the purchase cost or the sum of the “fixed costs” associated