Which three of the following are assumptions of the economic order quantity EOQ model?

Economic order quantity or EOQ model is the equation that helps compute order quantity of inventory accompanied by the minimum total holding and ordering costs.

The economic order quantity is derived from the total cost equation,

TC = p × D + D × K + H × QQ2

where p is a unit price, D is annual demand quantity, K is ordering cost, H is holding cost per unit, and Q is order quantity.

To find order quantity with the minimum total cost, we should calculate the derivative of the total cost function with respect to variable “Q” and set it equal to zero assuming that other variables are constant.

Solving the equation with respect to variable “Q” will give the economic order quantity.

Assumptions of EOQ model

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

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

Holding cost vs. ordering cost

The holding or carrying cost is the total cost for keeping and maintaining inventories in storage. Common examples are a rent fee for the storage space, depreciation, labor cost to operate storage, materials, equipment and its maintenance cost, shrinkage of stock, security expense, insurance, cost of capital, and other direct costs.

Ordering cost refers to the cost related to shipping and handling a new order, e.g., communication and transportation cost, and insurance. Please note that ordering cost doesn’t include cost of goods!

Holding cost and ordering cost move in opposite directions. To reduce ordering cost per unit, we should increase order quantity, but such a scenario leads to an increase in holding cost; in turn, reducing holding costs requires a smaller order quantity, which leads to an increase in ordering cost. This relationship is shown in the graph below.

Economic order quantity calculation example

A company manufacturing building materials has an annual demand in concrete of 150,000 tons. The price is $425 per ton, the ordering cost is $3,750, and the annual holding cost per ton is $48.25.

Let’s put all the data available in the formula above.

Thus, the economic order quantity of 4,829 tons provides the minimum total holding and ordering cost. To prove this, we calculate the total cost for EOQ and order quantity of 4,500 tons and 5,500 tons using the total cost equation above.

As we can see, the EOQ model is always the best solution.

If basic assumptions of the model are met, the graph of inventory consumption and restocking looks as follows:

The maximum stock balance equals the economic order quantity, and it is consuming at a constant rate until reaching zero. At this time, restocking is made by the whole batch.

As the name suggests, Economic order quantity (EOQ) model is the method that provides the company with an order quantity. This order quantity figure is where the record holding costs and ordering costs are minimized. By using this model, the companies can minimize the costs associated with the ordering and inventory holding. In 1913, Ford W. Harris developed this formula whereas R. H. Wilson is given credit for the application and in-depth analysis on this model.

Definition

The economic order quantity (EOQ) is a model that is used to calculate the optimal quantity that can be purchased or produced to minimize the cost of both the carrying inventory and the processing of purchase orders or production set-ups.

Formula

Following is the formula for the economic order quantity (EOQ) model:

Where Q = optimal order quantity

D = units of annual demand

S = cost incurred to place a single order or setup

H = carrying cost per unit

This formula is derived from the following cost function:

Total cost = purchase cost + ordering cost + holding cost

Limitations of the economic order quantity model:

It is necessary for the application of EOQ order that the demands remain constant throughout the year. It is also necessary that the inventory be delivered in full when the inventory levels reach zero.

Underlying assumption of the EOQ model

Following are the underlying assumptions for the EOQ model. Without these assumptions, the EOQ model cannot work to its optimal potential.

• The cost of the ordering remains constant.
• The demand rate for the year is known and evenly spread throughout the year.
• The lead time is not fluctuating (lead time is the latency time it takes a process to initiate and complete).
• No cash or settlement discounts are available, and the purchase price is constant for every item.
• The optimal plan is calculated for only one product.
• There is no delay in the replenishment of the stock, and the order is delivered in the quantity that was demanded, i.e. in whole batch.

These underlying assumptions are the key to the economic order quantity model, and these assumptions help the companies to understand the shortcomings they are incurring in the application of this model. 

Which of the following is an assumption of EOQ?

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