EOQ Inventory Management

Wilson Inventory Calculator



Fill this form to calculate optimal order quantity and reorder point

Currency
Demand per year
Setup costs/ fixed cost per order
Unit holding cost (warehouse, insurance etc.)
Lead time in days
Working days per year



What does EOQ mean?

EOQ is the level of inventory that minimizes the total cost of holding and ordering inventory over a period of time.  Usually the time period is one year.
 

What is the Total Cost of Inventory?

The total cost of inventory is the sum of the purchase, ordering and holding costs.  As a formula:
TC = PC + OC + HC, where TC is the Total Cost; PC is Purchase Cost; OC is Ordering Cost; and HC is Holding Cost.

Assumptions

To determine the EOQ, these costs must be analyzed further.  Some assumptions are required:

Variables

We will use the following variables:

It is important to note which variables are annualized, which are per-order and which are per-unit.

Do the easy math

Using the variables, here are the components of the first equation (TC = PC + OC + HC):

PC = P x D :                       Purchase Cost = unit Purchase cost times the annual Demand
OC = (D x O) / Q :             Order Cost = annual Demand times cost per Order,
divided by the order Quantity (number of units)
HC = (H x Q) / 2:               Holding Cost = annual unit Holding cost times order Quantity (number of units),
divided by 2 (because throughout the year, on average the warehouse is half full).

So TC = PC + OC + HC =  (P x D) + ( (D x O) / Q) + ( (H x Q) / 2).

Use calculus to determine the minimum

To minimize TC for Q, determine the first derivative of this formula and solve for zero.

dTC(Q)/dQ  = d ( (P x D) + ( (D x O) / Q) + ( (H x Q) / 2) )/dQ
                                            = (H / 2) – (D x O) / ( Q2 ) )
                                            = zero

To solve for Q*: (the optimal order Quantity):

(H / 2) = (D x O) / ( Q*2 ) )

Therefore Q*2 = 2 x (D x O) / H.

Thus Q* = the square root of 2 x (D x O) / H, and does not depend on the unit purchase cost.

In English: the optimal order Quantity is the square root of 2 times the annual Demand times the cost of one Order divided by the annual cost to Hold one unit.


Oskar Olofsson, 2009





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