# EOQ, EOQ with Discounts

09/05/2020

Economic order quantity (EOQ) is the ideal order quantity a company should purchase for its inventory given a set cost of production, demand rate and other variables. This is done to minimize variable inventory costs, and the equation for EOQ takes into account storage, ordering costs and shortage costs.

The full equation is:

EOQ = √(2SD / H), or the square root of (2 x S x D / H).

S = Setup costs (per order, generally includes shipping and handling)

D = Demand rate (quantity sold per year)

H = Holding costs (per year, per unit)

EOQ applies only when demand for a product is constant over the year and each new order is delivered in full when inventory reaches zero. There is a fixed cost for each order placed, regardless of the number of units ordered. There is also a cost for each unit held in storage, commonly known as holding cost, sometimes expressed as a percentage of the purchase cost of the item.

The economic order quantity is computed by both manufacturing companies and merchandising companies. Manufacturing companies compute it to find the optimal order size of raw materials inventory and

merchandising companies compute it to find the optimal order size of ready to use merchandise inventory.

The ordering and holding costs

The two significant factors that are considered while determining the economic order quantity (EOQ) for any business are the ordering costs and the holding costs.

Ordering costs

The ordering costs are the costs that are incurred every time an order for inventory is placed with the supplier. Examples of these costs include telephone charges, delivery charges, invoice verification expenses and payment processing expenses etc. The total ordering cost usually varies according to the frequency of placing orders. Mostly, it is directly proportional to the number of orders placed during the year which means If the number of orders placed during the year increases, the annual ordering cost will also increase and if, on the other hand, the number of orders placed during the year decreases, the annual ordering cost will also decrease.

Holding costs

The holding costs (also known as carrying costs) are the costs that are incurred to hold the inventory in a store or warehouse. Examples of costs associated with holding of inventory include occupancy of storage space, rent, shrinkage, deterioration, obsolescence, insurance and property tax etc. The total holding cost usually depends upon the size of the order placed for inventory. Mostly, the larger the order size, the higher the annual holding cost and vice versa. The total holding cost is some time expressed as a percentage of total investment in inventory.

EOQ with Discounts

Quantity discount is a reduction in price offered by seller on orders of large quantities. Quantity discounts exist in different forms and in certain scenarios they may not be obvious. The well-known buy-1-get-1-free sale is actually a 50% quantity discount since you effectively purchase a unit at half the normal price.

Different forms of quantity discounts provide different purchase incentives to buyers. For example, the one discussed above has a tentency to compel the buyer to purchase more than they need at the moment i.e. the seller will not allow you to purchase just one unit at 50% of the full price. Another form of quantity discount which is based on the cumulative quantity purchased during a specific time period actually induces the buyer to continue purchasing from the current supplier and restricts switching to other suppliers.

#### Implication for Decision Making

When purchasers following Economic Order Quantity (EOQ) model for ordering inventory have the opportunity to avail a quantity discount on order sizes greaters than their EOQ, they need to base their decision, apart from qualitative factors, on the net effect of the decision on the their income. A typical quantity discount has the following three effects on the income of a purchaser:

1. A saving in the form of reduced price
2. A saving in the form of reduced ordering costs
3. A loss in the form of increased total holding costs of inventory

A decision to avail the quantity discount should be taken only if the net effect of the above components on the income is positive.

#### EOQ Assumptions

If the economic order quantity model is applied, the following assumptions should be met:

• The rate of demand is constant, and total demand is known in advance.
• The ordering cost is constant.
• The unit price of inventory is constant, i.e., no discount is applied depending on order quantity.
• Delivery time is constant.
• Replacement of defective units is instantaneous.
• There is no safety stock level, i.e., the minimum stock level is zero.
• Restocking is made by the whole batch

#### Limitations

• Erratic changes usages: the formula presumes the usage of materials is both predictable and evenly distributed. When this is not the case, the formula becomes useless.
• Faulty basic information: order cost varies from commodity to commodity and the carrying cost can vary with the company’s opportunity cost of capital. Thus the assumption that the ordering cost and the carrying cost remains constant is faulty and hence EOQ calculations are not correct.
• Costly calculations: the calculation required to find out EOQ is extremely time consuming. More elaborate formulae are even more expensive. In many cases, the cost of estimating the cost of possession and acquisition and calculating EOQ exceeds the savings made by buying that quantity.
• No formula is a substitute for common sense: sometimes the EOQ may suggest that we order a particular commodity every week (six-year supply) based on the assumption that we need it at the same rate for the next six years. However, we have to order it in the quantities according to our judgement. Some items can be ordered every week; some can be ordered monthly, depends on how feasible it is for the firm.
• EOQ ordering must be tempered with judgement: Sometimes guidelines provide a conflict in ordering. Where an order strategy conflicts with an operational goal, order strategy restrictions should be developed to permit honouring the goal.