Manage improved return-rate/availability outcomes

The statistical analysis of supply and demand is the cornerstone of an efficient distribution operation. Got right, it can affect both an increase in sales and a reduction in costs. Jim McArdle looks at the relationship between some of the key variables.

By Jim McArdle

This piece develops analytical ideas and methods relevant to controlling the return-rate/availability outcomes of regularly produced printed media; a topic of concern to publishers where sales via the domestic retail network under sale-or-return (SOR) or limited SOR conditions account for at least a significant proportion of total sales. The content applies equally to national and regional newspapers and to magazines, whatever the publishing frequency in any of these cases.

The overall purpose is to make sense of, and bring order to, a complex process; the distribution of printed media. Sales volumes, supply volumes and return-rate and availability readings all vary per issue date. Return-rate and availability averages per area frequently bear little relation to each other. Management by exception, identifying and attending to obvious supply anomalies, always has its place, but, given this mix of variability, how do we set benchmarks? What return-rate/availability target is appropriate to a particular area? How do we identify persistent over- or under-supply? These questions are all the more urgent against the usual background of fleeting shelf lives.

We briefly explore three relationships;

* retail outlet sales variation v average sales volume
* availability v return rate
* return rate v average sales volume

The main message is that, in each case, the two variables are connected. Individually, the relationships prompt useful insights. Taken together, they enable an ordered approach to managing distribution.

Terms and background

Return rate: (Number of copies returned unsold)/(Number of copies supplied). The ratio is usually expressed as a percentage.
Sell-out ratio: (Number of sell-out events)/(Number of delivery events)
Availability: [(Number of delivery events) - (Number of sell-out events)]/(Number of delivery events) = 1 minus sell-out ratio. The ratio is usually expressed as a percentage.
Variation: The amount of variation or scatter in a set of observed values is quantified by various statistical measures (eg. the variance, and the coefficient of variation (C), which is the ratio of the standard deviation to the mean). In this context, we are concerned mainly with the variation inherent in sales values observed over time. Retail outlet sales per issue date, and summations of the latter (eg. by wholesale outlet or area), are examples of time series. High variation in a time series does not necessarily mean that it is incapable of prediction within workable bounds of accuracy. We might find, for example, that sales fluctuate greatly when viewed across all weekdays, but little on the same weekday. After isolating variation which exhibits a pattern, usually we are left with variation which exhibits no regularity at all, and, although we might surmise about its causes, are forced to recognise its unpredictability. Statisticians call this type of variation random, and quickly move on. We have to cope with it though. The word ‘volatility’ is much used in the industry. Perhaps volatility is best taken synonymously with ‘unpredictability’, referring to random variation.
Sales and sales/variation classification schemes: To illustrate the relationships explored in this article, I have used retail outlet sales and sales/variation classification schemes. Firstly, I grouped retail outlets by average daily sales volume. The classes progress from 01 (average sales less than or equal to 5 copies) through to 15 (average sales of 800 plus). I then split each class into two sub-groups, LV and HV, containing outlets showing relatively low and high sales variation respectively.

Relationship # 1: Retail outlet sales variation v average sales volume

The connection between sales variation and average sales volume is that variation is inversely proportional to average sales volume. The relationship applies directly at the point of sale level. In the real world which we have to contend with, exceptions do, of course, present themselves. For example, you might have come across a retail outlet where title sales are constant at three copies, say, even when supplies are greater than that. However, exceptions neither negate nor weaken the general law.

Figure 1 illustrates the phenomenon in the case of a national title. The plot is of average sales variation by sales class on a particular day of the week over a number of weeks, thereby excluding fluctuation across weekdays. Variation is fierce at the low-volume end of the sales range, but once average sales reach around 30 copies per day the worst is left behind and variation continues to decline with increasing average issue-date sales.

Variation readings certainly differ from one title to the next, but the principle applies universally, and is important strategically. The expectation that, across titles, retail outlet sales variation declines as average sales volume increases is usually borne out.

Relationship # 2: Availability v return rate

The observation that availability increases with the return rate in a predictable manner is true of any title and retail population, or sizeable sub-set of it, provided that distribution is reasonably efficient.

No doubt, we are all familiar with the results of overestimating demand: the return rate soars, the single consolation being that the sell-out ratio falls at the same time. Perhaps we did make an incremental sales gain, but at what return-rate cost? However, the relationship between availability and the return rate per product, itself influenced by the supply allocation process, is less obvious. In general, there is, and ought to be, high positive correlation between the two variables. If, for example, as the return rate increases, availability increments are weak, then little benefit is being derived from the greater return rates, which themselves imply increasingly generous supply levels relative to demand.

As the focus sharpens from viewing a retail population taken as a whole to groups of retail outlets having like average sales volumes and variation levels, the association between availability and the return rate tends to strengthen, prompting the realisation that the return rate may be taken as the cost of availability, the two increasing in tandem. An availability reading of 75%, say, gives the assurance that 75% of allocations resulted in total point of sale demand being met. However, the measure says nothing about the proportion of demand which we might reasonably assume was lost on the occurrence of sell-outs in the remaining 25% of the population. To make matters worse, usually there is no direct connection to be found between availability and sales volume; surges in demand cannot always be anticipated, whereupon availability invariably falls with the resulting increases in sales, contrary to the effect which we might hope to show.

So, how much are you prepared to pay in return-rate terms for your comfort zone? More to the point, does an increase in availability of five percentage points, say, deliver an economic sales benefit, given a quantifiable return-rate cost? It is possible to estimate the sales effect of successive gains in availability via use of an allocation system. The trick is to allocate retrospectively, using steadily increasing supply totals, and calculate system availability and the percentage of actual sales realised on each run. The resulting relationship is specific to the individual title and the allocation system at work. Suffice to say that, provided that the allocation operation is competent and consistent, gains in availability do deliver regular increases in the percentage of total demand translated into sales. There comes a point, though, at which the rate of increase of the return rate accelerates; the law of diminishing returns kicks in.

Relationship # 3: Return rate v average retail outlet sales volume

The statement that, within normally acceptable availability ranges, the return-rate is inversely proportional to average retail outlet sales volume, will not be altogether unexpected – music to the ears of some, but disconcerting where a title with low average retail outlet sales is unable to command a price in the market sufficient to offset relatively high return-rate costs.

We have seen already how sales variation declines as average retail outlet sales volume increases. This, with the inevitability that within usual bounds of availability the return rate increases with the amount of random variation in a sales series, corroborates the return rate/average sales volume relationship. Figure 2 charts, in the case of a national title, the decline in the return rate as average retail outlet sales volume increases. Readings for the high variation sub-sets of each sales class are to the right of the low variation values. Note how return-rate averages for the high-variation classes are generally significantly higher than those for the corresponding low-variation classes. Insofar as return-rate costs are important to profitability, the rule has clear implications.


Classification of consumers and retail outlets is crucial to discovering and understanding patterns of consumption and other factors which influence business performance. As knowledge develops, marketing strategies evolve and classification schemes stay relevant as a guide to targeting effort and monitoring results. We might employ several different classification schemes in connection with different routes of enquiry or in pursuing distinct business objectives. The general principle is to assemble population members into groups in such a way as to ensure that intra-group consistency, with respect to some characteristic, is greater than across the entire population. If we wish to examine an effect or relationship, then provided that the classification criteria are germane, we shall see stronger connections within classes than otherwise. If the classification scheme does not deliver this, it is ineffective.

Management control

The relationships discussed underpin the commonsense view that the generality of retail outlets with comparable average sales and variation levels ought ideally to produce closely grouped return-rate/availability results. This standpoint provides a basis for targeting and managing the distribution chain. Suppose, for example, that we take a sales/variation class and calculate return rate and availability averages for (a) the entire retail population, and (b) area retail populations. The immediate consequence of the analysis is to highlight any areas where the return rate is consistently either unusually high or low relative to the population class average. Usually, as we have seen, high return rates are accompanied by high availability and unusually low return rates by correspondingly low availability. The point of the analysis is to identify readily, and remedy, any extreme and unwarranted departures from the norm. Once questionable area/class results have been identified, the return-rate and availability averages of the constituent retail outlets should be inspected for acceptance or action.

Adjustments to supply practices based on this methodology have the potential to reduce return rates and sell-out ratios. The approach brings precision to the job of managing return-rate/availability results at every stage in distribution and is capable of improving the consistency of performance. Not least, population retail class targets, cognisant of actual average return-rate and availability standards across the retail network, enable the calculation of area targets which recognise precisely the nature of the composition of local retail populations.