One particular situation fits the wholesale magazine industry to a tee. In fact it is nicknamed the "newsboy problem" because the example always used to describe the formula is "how many newspapers should a newsboy order each day?". A more formal description is "single period forecasting" in which the formula is designed to calculate the proper order quantity to cover one demand period.
 

The formula uses Mean Average Deviation (MAD) and marginal analysis to arrive at the optimal number of copies draw.

MAD (Mean Average Deviation) is one of the differences between the forecasting formula and all other O/R formulae. This is the data that keeps track of the difference between the forecast and the actual sale. In order to make a good forecast the formula looks at past forecasts, decides how far off it was and makes adjustments. These adjustments bring the forecast closer and closer to actual sale. MAD as the name implies is the statistical averaging of the error (deviation) between the forecast and the sale. As the forecast gets better the MAD reduces. In the instances where the demand (net sale) of each issue fluctuates widely, the MAD will remain high indicating volatile demand and a resulting higher copy forecast to cover the swing in sales from one issue to another.

The optimal copies draw decision, using marginal analysis, occurs at the point where the benefits derived from increasing the number of copies by one more copy are less than the costs for that copy. In other words, the most profitable number of copies to deliver is that when the profit from the last copy sold is equal to or greater than the loss if the last copy remains unsold. In symbolic terms this is the condition where:

MP >= ML
MP is marginal profit (your selling price - your purchase cost)
ML is marginal loss (your handling and/or carrying costs)

Since the copies are fully returnable your loss is limited to what it cost you to handle the copies (pick, deliver, stack, pull down, and return) and carrying costs (the float between when you pay and when you get paid).

Marginal analysis is also valid when we are dealing with probabilities of occurrence. Then we are looking at expected profits and expected losses. By introducing probabilities into the equation it becomes:

(P)MP >= (1-P)ML
P is the probability of a copy being sold
1-P is the probability of the copy not being sold

Solving for P we get P >= ML/(MP + ML) which says that we should keep increasing the number of copies of draw so long as the probability of selling that copy is greater than or equal to the ratio of ML/MP + ML.

Let's use numbers for an example. You buy a magazine for .70 and sell it for 1.00 so you make .30 on a copy. For example purposes only let's say that it costs you .10 to handle each copy. In our formula we use mean average deviation to forecast a sale of 37.5 copies.
 

Exhibit 1
Demand and Cumulative Probabilities

Exhibit 2
Formula Calculation
P >= 10/(30 + 10)
P >= .25

Exhibit 3
Marginal Copy Draw Analysis

As you can see using these artificial numbers after 39 copies you start losing money on each copy so the optimum draw quantity should be 39.

The draw figure is arrived at after due consideration of your profits and your costs. Using the copy range percent multiplier to add additional copies to protect the rack space for the title you arrive at the true number of copies to deliver to each retailer. This becomes the draw in the DPS System.