Economic Order Quantity - YouTube

This lecture is a very brief introduction  to the Economic Order Quantity model. 

The Economic Order Quantity model, EOQ,  was introduced in 1913 by Ford W. Harris,  

in his work How Many Parts to Make at Once.

It was a very early application of mathematical  modelling to scientific management. 

Recall that EOQ is a basic reorder level system where one orders a set amount  

of materials or parts when the reorder point is met.

The basic assumptions of  the original EOQ model are 

that we have a known and constant demand,  and a known and constant lead time. 

In this simple model we also assume instantaneous receipts of materials from suppliers. 

We do not allow quantity discounts,  and assumes the prices are constant. 

We only consider two involved costs: 

the order cost, which is  a fixed cost for every order, 

and an inventory holding cost, calculated per part. 

Finally, we assume that our model  will never lead to a stock-out.

Let's derive the Economic Order Quantity graphically. 

Consider this coordination system: along the horizontal axis,  

we have the Order Quantity. In other words, the amount of goods we order  

each time we put in an order. Along the vertical axis,  

we have the total Annual Costs. Recall, we only consider two costs: 

first, the Order Cost is a fixed sum  we pay every time we put in an order. 

In Switzerland, this sum is often arbitrary, set to 200 or 300 CHF.

Now, the more products we order at the same time, the fewer times we have to put in an order. 

If we order only one product at the time, the annual costs are very high. 

If we order a big batch of all we need for a year, we only incur the order setup cost once,  

as shown with this exponentially declining curve.

The other cost was the Inventory Holding Cost,  

which increases linearly with the average number of goods we hold on inventory. 

If we hold on average zero stocks, the cost is zero. 

If we, on average, hold half of the year's consumption, the holding cost is very high. 

It is the holding costs, which prompt us to hold low inventory, and by that,  

order small quantities, often. But the ordering cost prompts us instead 

to order only a few times,  and hold larger amounts of inventory. 

We must, of course, look at the Total Costs, 

which is simply calculated by  adding the two cost curves:

the Economic Order Quantity, that is the  amount of goods we should order each time,  

is now given by the lowest point in the cost curve.

The Economic Order Quantity  formula can, of course,  

also be derived mathematically  by simple derivation, and optimization. 

If you let D be the annual demand in units, Q be the order quantity, 

Cs be the setup cost per order,  and Ch be the inventory holding cost, 

the Economic Order Quantity is given by  the square root of 2, times annual demand, 

times order setup cost, over inventory holding cost.

So that's the classic EOQ formula!

And now we can use the EOQ formula to understand  what will happen when external factors change.

For example, what will happen if  order processing is fully automated?

Yes! Cs will drop towards zero, making the EOQ smaller, 

hence more frequent orders of smaller quantities.

Now, what will happen if warehouse costs drop?

Correct! Ch is reduced, which  will lead to higher EOQ, 

hence encouraging larger stocks, and fewer orders.

And what will happen if competitive products are introduced?

The Demand may drop, hence reducing  the Economic Order Quantity 

and encouraging more frequent deliveries of smaller quantities.

If you think the EOQ formula seems far too simple for real life, then no problem. 

Operations research has developed  inventory models for almost any situation. 

Examples include: the  Economic Production Lot model, 

which accounts for production lead times, or the Extended EOQ model, 

which accounts for safety stocks and delivery lead time, 

or the Wagner-Within model, which accounts for demand variation  

and allows dynamic lot sizing, the Newsvendor model, 

which accounts for dynamic or unknown demand, and (Q,r) models, 

which accounts for dynamic demands and multiple products. 

Luckily, most of these models  are codified in ERP systems, 

so all we usually have to do is  to select the model we want to use 

and enter the parameters. Then the rest is done by the software.

And now, you heard about the  Economic Order Quantity model.