EOQ Analysis

Under the fixed order quantity system of inventory management, an order for supplies is placed when the existing order reaches reorder point. The relevant question now is – what should be the size of the order? Buying in large quantities has its virtues but, one of the problems associated with bulk buying is the high carrying cost. Similarly, buying in small quantities reduces holding cost but adds to ordering cost. Consequently materials manager is torn between a desire to keep inventories low by ordering in small quantities and a desire to reduce cost by buying large quantities.

Economic order quantity (EOQ) is the technique which solves the problem of the materials manager. EOQ or Q Opt (Optimum Quantity) is the order size at which the total cost, comprising ordering cost and plus carrying cost, is the least.

The following figure illustrates the EOQ graphically

Graphing the two costs, viz., carrying costs and ordering costs show exactly, where the total cost curve is at its lowest point. An examination of the two curves reveals that carrying cost curve is linear i.e., the more the inventory held in any period, greater will be the cost of holding it. Ordering cost curve, on the other hand, is different. Ordering in small quantities means more acquisition and higher ordering costs. The ordering costs decreases with increase in order sizes. A point where the carrying cost curve and the ordering cost curve meet represents the least total cost which incidentally is the economic order quantity or optimum quantity.

Assumptions

EOQ can be carrying with the help of a mathematical formula. Following assumptions are and implied in the calculation:

• Demand for the product is constant and uniform throughout the period,

• Lead time (time from ordering to receipt) constant,

• Price per unit of product is constant,

• Inventory holding cost is based on average inventory,

• Ordering costs are constant, and

• All demands for the product will be satisfied (no back orders are allowed).

  In constructing any inventory model, the first step is to develop a functional relationship between the variables of interest and the measure of effectiveness. As we are concerned with cost here, the following equation would pertain:

                                        TC = DC + DS/Q + QH/2

Where, TC - Total cost

D = Annual Demand

C=Purchase cost per unit

Q=Quantity to be ordered (the optimum amount is termed the EOQ or Q opt)

S = Cost of placing an order

H =Holding cost per unit of average inventory per annum.

    [C x percent carrying]

I=Cost of carrying inventory as percentage.

  On the right hand side of the equation, DC is the annual purchase cost for the units,(D/Q)S is the annual ordering cost (the actual number of orders placed, D/Q, times the each order, S), and (Q/2) H is the annual holding cost (the average inventory, Q/2, times the cost per unit for holding and storage, H). These cost relationships are shown graphically in above figure.

  The second step in the model development is to calculate order quantity Q, for which the total cost is the minimum. In the basic model, this may be done by simple algebra if we orgnanise that DC is not a decision variable and hence not a factor in the ordering decision. Then, with reference to above figure, total cost is minimum at the point where, the cost of ordering is equal to the cost of carrying, or

DS/Q=QH/2

Which in turn is solved as follows :

DS=Q2H OR   2DS= Q2H   OR   Q2=2DS/H

Q (optimum) or EOQ = √2DS/H

EOQ technique is highly useful in as much it answers the question of how much to order and in doing establishes the frequency with which orders are placed. EOQ is applicable to both single items and to any group of stock items with similar holding and procurement cost. Its use causes the sum of the two costs to be lower than under any other system of replenishment.