The first major decision in managing goods for sale is deciding how much of a given product to order. A firm can use the Economic Order Quantity (EOQ) procurement model to calculate the optimal quantity of inventory to order.

This model has various assumptions. However, the presence of these assumptions does not mean that the model cannot be used in practice. There are many situations in which this model will produce good results.

For example, these models have been effectively employed in automotive, pharmaceutical, and retail sectors of the economy for many years.

**Assumptions of EOQ Model**

To be able to calculate a basic EOQ certain assumptions are necessary.

- Demand arrives continuously at a constant and known rate of λ units per year. Arrival of demand at a continuous rate implies that the optimal order quantity may be non-integer. The fractional nature of the optimal order quantity is not a significant problem so long as the order quantity is not very small; in practice, one simply rounds off the order quantity. Similarly, the assumption that demand arrives at a constant and known rate is rarely satisfied in practice. However, the model produces good results where demand is relatively stable over time.
- Whenever an order is placed, a fixed cost K is incurred. Each unit of inventory costs I to stock per year per rupee invested in inventory. Therefore, if a unit’s purchasing cost is C, it will cost I ·C to stock one unit of that item for a year.
- The order arrives τ years after the placement of the order. We assume that τ is deterministic and known.
- All the model parameters are unchanging over time.
- The length of the planning horizon is infinite.
- All the demand is satisfied on time

Economic Order Quantity is one of the inventory control models that deal with the first category of inventory. It is a quantity of materials to be ordered which takes into account the optimum combination of:

- Bulk discounts from high volume purchases
- Usage rate
- Stock holding costs
- Order delivery time
- Cost of processing the order

In simple words, Economic order quantity ie the quantity fixed at the point where the total cost of ordering and the cost of carrying the inventory will be the minimum.

The major objective of managing inventory is to discover and maintain the optimum level of investment in inventory. The optimum level will be that quantity which minimizes the total costs associated with inventory.

The simplest version of this model incorporates only ordering costs and carrying costs into the calculation.

**Costs of ordering stocks**

Ordering cost is the cost of placing an order to the supplier for inventory. It includes:

- Preparation of purchase order.
- Costs for receiving goods.
- Documentation processing costs.
- Transport costs.
- Intermittent costs of chasing orders, rejecting faulty goods.
- Additional costs of frequent or small quantity orders.

**Costs of carrying stocks**

Carrying cost is also called holding cost . Carrying cost refers to the cost of holding stocks in storage over a period of time. It includes:

- Storage costs (rent, lighting, heating, refrigeration, etc).
- Stores staffing, equipment maintenance, and running costs.
- Handing costs.
- Audit, stock taking or perpetual inventory costs.
- Insurance and security costs.
- Pilferage and damage costs.

The optimum size of the order for an item is known as the Economic Order Quantity (EOQ). It is calculated so that total inventory costs are at a minimum for that particular stock item.

Total inventory costs for an item of stock are computed for a given period usually an accounting year by combining the costs of ordering and the costs of carrying that item.

**Total inventory costs = Costs of ordering + Costs of carrying**

The pattern of supply and demand for the item is assumed to be known with certainty and various costs are assumed constant over the period under review.

The cost of ordering is the cost of placing as separate order multiplied by the number of separate orders placed in the period.

The carrying costs can be calculated on the assumption that the annual cost of carrying one stock item on average, half the stock is on hand all the time in addition to the safety or buffer stock.

The fewer the orders, the lower the costs of ordering but the greater the size of the order, the greater the cost of carrying.

The ordering costs are inversely related to the inventory carrying costs, i.e. the lower the carrying costs, the higher the ordering costs.

It is possible to compute the Economic Order Quantity algebraically. The following EOQ formula is widely used in practice.

**Where, **

**EOQ = Economic Order Quantity**

**A = Annual Consumption**

**B = Buying Cost Per Order**

**C = Cost Per Unit**

**S = Carrying Cost**

**EOQ Exercises & Answers**

**Illustration: 1** Annual usage of a material is 3000 units and it costs Rs. 150 to handle an order for this material. The price is Rs. 450 per unit regardless of the quantity purchased and carrying cost of inventory is 18% per annum. calculate EOQ.

**Solution:**

A = 3000 units

B = Rs. 150 per order

C = Rs. 450 per unit

S = 18% p.a.

**When to Order, Assuming Certainty**

The second major decision in dealing with cost of goods available for sale is when to order. The reorder level is the quantity level of the inventory on hand that triggers a new order. The reorder level is simple to compute:

**Reorder Level = Maximum usage X Maximum lead time**

The length of time between the placement of an order on a supplier and its receipt is called a lead time.