Dear Juan,

As you truly mentioned, safety stock is very important in today's competitive markets. Operation management books usually suggest simple methods cause they aim to teach fundamental concepts. In real world, it is better to consider lead time forecast demand error to be more similar to real situation.

Dear Juan, I think that it is more correct to consider the forecasting error distribution instead of the demand distribution (during lead time). The two alternatives would be equivalent if you use, as forecasting method, the simple mean over all the hystorical data. In this case the estimate coming from the forecasting method is exactly the mean value of the demand during the lead time.

But if you use any other forecasting method (like moving averages, or exponential smoothing) to estimate demand during lead time, your estimate will be different than the simple mean over the periods. Because you use a forecasting method to estimate demand during lead time, you have to protect against errors in forecasating demand. This is why you have to consider the standard deviation of forecasting errors to calculate the required safty stocks.

In summary, the books that consider standard deviation of demand instead of s.d. of forecasting error do not consider the link between inventory control and forecasting method.

Dear Juan.

it is best way to use s.d. of forecasting errors as all your all plans are based on the forecasted data. At this point, you should also know that s.d. of forecast errors are greater than s.d. of demand.  

Juan, most books on inventory management assume that you know the demand distribution, and don't really deal with the problem of estimating a demand distribution (i.e. forecasting).

Most forecasting methods have a theoretical basis to calculate the inherent uncertainty in the forecast; for one-step-ahead forecasts, the forecast error distribution can approximate this uncertainty well (see https://www.otexts.org/fpp/2/7).

The only time using the standard deviation of forecast errors would be equivalent to the standard deviation of demand is if demand is just 'noise around a mean'. Anytime you have embedded random walks, seasonality, etc., your forecast errors should be less than the standard deviation of demand, since the purpose of the forecasting method is to help you filter out predictable variation in the demand data. The only exceptions I can think of is if demand volatility is increasing in time, and if you use a very ineffective forecasting method (which adds noise, rather than reducing it).

Dear Juan,

The decision is quite depends on the present inventory policy. If the shortages are backlogged and backlog costs are rather high, regarding the holding costs, it would be optimal to apply the decision that make a cost balance on  the expected total  annual cost ( this cost must be computed for the two methods) Otherwise, it makes no important difference.    

Lead time forecast error demand distribution is better methods as it takes into account forecast values and gives better estimate.

Lead time forecast error is ggod enough even in the situation which Salehi is talking about.

It also depends on existing product or newly launch product.

In order to introduce the students to inventory management field, I think that is better begin with sd of demand, but always is important to remind that the value that should be used is sd of forecast error. Now, as someone mention before, you can explain the concept of sd of forecast error using the mean forecast model, so in this case the sd of demand and the sd of forecast models are equals. Finally I believe that sd of demand is always greater than sd of forecasting errors  

Thank you very much for all your answers. I think it is an interesting debate. I see that most of you agree that forecasting error standard deviation should be used. I understand that it is difficult to introduce these concepts to students and we can be tempted to simplify with the use of the demand s.d. insteand of forecasts. However, if I do not explain in that way, I feel I'll will be contributing to the creation of misunderstandings among students. Additionally, I agree with Enno's and Lorenzo's comments  about the importance of linking the inventory control theory and the forecasts; and about the idea that not always the s.d. of demand is higher than s.d. of forecasting errors. Please, I've made some simulations and you are invited to take a look at my blog

(http://blog.uclm.es/juanramontrapero/2015/03/02/how-to-compute-the-safety-stock-shall-i-use-the-demand-distribution-or-the-forecast-demand-error-distribution/)

In cases that the demand is seasonal or there exist level-drifts or other predictable variations, the demand s.d. can be higher than the demand forecast error s.d. (during lead time). 

Thank you very much again!

Dear Juan,

your blog is very interesting and the example about the case in which the demand s.d. is higher than the forecast error s.d. is very clear.

However, I am not sure that using a seasonal demand pattern in the example is completely appropriate. In fact, one of the assumption of inventory control policies in which the calculation of s.d. during lead time is needed (such as continuous review (s,Q) or periodic review (R,S)) is that demand is stationary, i.e. no trend and seasonality  are observed.

In general, in the case of stationary demand, I think it could be difficult to find an example in which the demand s.d. is higher than the forecast error s.d.

In the book "Production and Operations Analysis" from S. Nahamias it is demonstrated that when using moving averages or simple exponential smoothing the forecast error s.d.is always higher than demand s.d., if demand is stationary. The reason is that the process of forecasting introduces sampling error into the estimation process.

Finally, concerning the importance of linking the inventory control theory and forecasting, I just wanted to signal you a publication of mines about this interesting issue.

L. Tiacci, S. Saetta "An approach to evaluate the impact of interaction between demand forecasting method and stock control policy on the inventory system performances", International Journal of Production Economics, 2009; 118:63-71. http://dx.doi.org/10.1016/j.ijpe.2008.08.010