EOQ

How to Best Figure Out Ordering Quantity and Ordering Frequency

Executive Summary

  • Ordering quantities are often the focus of supply chain planning as they directly impact the frequency with which things are done.
  • We cover determining ordering quantities.

Introduction to The Safety Stock and Ordering Quantity and Frequency Scenarios

While not often discussed, ordering frequency is linked to all of the other subjects that are frequently discussed in the area of supply chain planning. Order frequency can be viewed as the inverse of order frequency. Every order quantity is also a type of order frequency, so when you set an order quantity, you are also setting an order frequency. The higher the order quantity, given the same demand, the lower is the order frequency. You will learn about the relationship of order frequency with other important supply chain planning concepts.

Our References for This Article

If you want to see our references for this article and related Brightwork articles, see this link.

Subjects Connected to Order Frequency

The subjects connected to order frequency include items such as:

  • EOQ
  • Safety Stock
  • Min Lot Size

That is, quantities are much more often a focus of discussions in supply chain planning. It directly affects the frequency with which things are done.

See our references for this article and related articles at this link.

An excellent place to start this analysis is to look at a straightforward ordering pattern. This occurs with a level demand, as is shown in the graphic below.

Safety Stock and Order Frequency

Safety stock is one of the best-known concepts in supply chain management. Every MRP application and advanced planning application on the market has either a safety stock field or can calculate safety stock.

Notice that safety stock is not required because of lead-times or because of the volume of a forecast – it is because of the variability of either of these two components.

The second most important thing to understand about safety stock is that variability is projected – it is probabilistic and, therefore, subject to error or, more specifically, variability. If the variability was predictable, a lower level of safety stock could be maintained – however, variability is generally not predictable.

Economic Order Quantity and Order Frequency

The reorder point tells the system when to reorder, while the economic order quantity tells the system how much to order; as such, they are necessarily highly integrated values.

EOQ is one method for performing what is generally known as lot sizing. The lot size is the quantity in which the item is produced or procured, and therefore it is set at the production location combination in the product master. Here it is in Demand Works Smoothie on their Policies Tab.

All supply planning systems store these values. 

Here are some of the similar values in SAP ECC. 

Min Lot Size

The creation of lot sizes (discrete quantities of a good to be produced or purchased at a given time or per order) is based on the selected lot-sizing procedure. The exact sizes matter because, in each production level, the lots are usually produced entirely before being passed on for further processing.

Scenario 1: No Forecast Error or Supply Variability

  • Because the demand is entirely level and zero forecast error, a mere economic ordering quantity if (EOQ) of 750 units can be placed once every three months. This is true even though the lead time is only for two weeks. The orange line represents this ordering quantity. This quantity is received into inventory every three months.
  • Because there are both zero forecast error and zero supply variability, there is also zero safety stock.

Now that we have covered a scenario with no variability let us add variability and see what happens to safety stock.

Scenario 2: Forecast Error and Supply Variability

Now we will change the scenario to include variability. This product’s forecast error is now 14.6%, and the lead time variability has been modified to 7.4%. Both errors apply to the procurement/production (supply) lead time. However, safety stock is only necessary under the following scenarios:

  1. When actual demand exceeds the forecast.
  2. When the supply leads time exceeds the actual lead time.

If the reverse happens, then we are only left with excess stock.

Notice how the forecast error changes when we are only concerned with negative forecast error.

Both errors or variations are averages.

If we put together a sample of forecast error and procurement/production lead time history, it might look like this.

History of Forecast Error and Lead Time Variability

Lead time and forecast error history and variability.
JanFebMarAprMayAverage ErrorAverage Error for Safety Stock Purposes
Lead Time Variabiltiy5%-15%0-10%25%7.4%-5%
Forecast Error History20%-25%+15%+10%-3%14.6%-5.6%
  1. The error is much smaller when we do not consider errors that do not pull from stock.
  2. This is what we will increase our starting stock level for, which is -5.6% + -5% = -10%, or 10%.

The safety stock here is not statistically calculated in this scenario. Instead, it is a mean error — or a service level at precisely the 50th percentile. This means we need to add the twin variabilities that sum up to 10%.

This is how much we have to increase in stock. The stock is required to cover the possibility that both the supply is late and the forecast is in error. If both of these events do not occur, then we will have carried excess stock.

The next question is, what should this increase be calculated over.

There are two options:

  1. Lead Time Demand
  2. Demand Between Replenishments

Let us discuss each in detail using a scenario.

How to Understand Lead Time Demand

The standard answer is that the bump in stock should be over lead time demand.

If the order frequency is once every three months — but the lead time is two weeks. Enough safety stock is necessary to cover the two-week lead time. If demand spiked, we could place an order before the next regular order date.

Let us review the following math associated with this scenario.

  • If the lead time is two weeks, and the average monthly demand is (roughly) 250. Therefore 250 units are one of the parts of the formula.
  • The 50th percentile sums to 10%.
  • Therefore 10% should be multiplied by 1/2 * 250 or 125.
  • This brings a safety stock of 12.5.

Demand Between Replenishments

The EOQ was already calculated, and it was determined that this product at this location should be ordered once every three months. With a 1/2 month replenishment time, the flexibility does exist to keep a little safety stock, but only by taking on a risk that the order will have to be placed on the next standard order date or reorder date, and that is less economical.

  • To enforce the EOQ, the 10% increase would be applied to the three-month demand of 750 units, which would bring the safety stock to 75 units.
  • Because the safety stock is 75 units, the plan is for that 75 units to be carried throughout the duration, and therefore this bumps up the ending inventory of each month by 75 units.

Now we are ready to make the safety stock statistical, which means using a service level.

Scenario 3: Forecast Error and Supply Variability + Service Level

Scenario 2 would only offer the appropriate safety stock for up to 50% of cases or the 50th percentile on a standard distribution curve. However, in most cases, companies have a service level, which means moving up the distribution curve, which, of course, gets more expensive. 95% is a common service goal, so let us apply this service level to our safety stock.

This will mean converting 95% to an inverse value — which happens to be 1.644.

  • So now we take the 75 units and multiply them by 1.644, which yields 123.3.
  • Because our error is a composite value of both demand and supply variability, this safety stock level should cover us for 95% of the scenarios.

How Should EOQ and Other Supply Planning Parameters be Calculated?

One would be able to, for example:

Item #1: Simulation

Set the supply planning parameters in a way that one can simulate the impact on the overall supply plan. When using supply planning systems, inventory parameters are typically managed on a "one by one" basis. This leads to individual planners entering values without considering how inventory parameters are set across the supply network.

Item #2: Interactivity of Changes

This is the ability to see the relationship between changes to service levels and the simulated output.

Item #3: Seeing Financial Implications

This is the ability to see the impact on the dollarized inventory for different aggregate settings.

Item #4: Mass Change for Efficient Maintenance

This allow the parameters to be changed en mass or as a mass change function. Both supply planning systems are designed to receive parameters; they are not designed to develop the parameters.

Getting to a Better Parameter Setting Capability

We developed an approach where EOQ and reorder points are calculated externally, which allows for a higher degree of control. And for the average inventory to be coestimated in a way that provides an observable total system inventory, holding cost, service level, and a picture of what is happening to the overall system. Calculating individual parameters like EOQ without an appreciation for the systemwide does not make any sense. Also, in many, perhaps even most cases, there is no reason to use EOQ for the purposes given above. Instead, an alternative custom order batching method can be created to replace EOQ. There is nothing magical about EOQ. It is not a "best practice." It will not provide you with "digital transformation." It is not "Six Sigma." You will not get a "black belt" for using it.

After observing ineffective and non-comparative supply planning parameter setting at so many companies, we developed, in part, a purpose-built supply planning parameter calculation application called the Brightwork Explorer to meet these requirements.

Few companies will ever use our Brightwork Explorer or have us use it for them. However, the lessons from the approach followed in requirements development for supply planning parameter maintenance are important for anyone who wants to improve order batching and supply parameters.

Conclusion

This article was all about showing the trade-offs on order frequency, order quantity (EOQ), and safety stock. The order frequency is as important as the order quantity. The order frequency is the order’s timing, and the order frequency accuracy can be tested and checked historically.

This article used statistical safety stock, but not the standard formula — because we prefer our own, as is explained at the following link.

Also, learn about the limitations of EOQ at this link.