Sales forecasting: accurate calculation or fortune-telling? Sales forecast: effective steps to create it
The definition of “forecasting sales volumes” is usually understood as possible ways and results of further development of the organization, as well as carrying out a possible assessment of a number of indicators in order to identify the profitability or unprofitability of the enterprise.
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As a rule, forecasting is carried out for several time periods, both the near future and subsequent stages of the company’s existence. Next, it is proposed to consider all the key features of forecasting the economic activity of an organization, indicating the sequence of stages and actions necessary to implement this process.
How to correctly forecast sales
Here are some important tips, the implementation of which determines whether an organization can conduct high-quality and practical sales forecasting:
- Forecast sales for each month separately and for the year as a whole. The forecast can also be drawn up for several years in advance for long-term planning of the enterprise and its subsequent development.
- Using the results of previous periods to determine sales figures. This allows you to make an objective forecast based on specific data on the organization’s activities. When analyzing a company's performance, one should also take into account the possibility of seasonal fluctuations in sales volumes. Read also Formulas for calculating sales volume >>
- If a company is engaged, for example, in the tourism business, therefore, depending on the season, performance indicators will also differ. In this case, it is necessary to prepare a separate forecast for the quarter, depending on previous periods.
- Mandatory adjustments to forecasting economic activity due to new circumstances. During the operation of a company, various changes may occur, both in the market itself and within the organization. These changes may be related to the development and expansion of the company, the opening of new branches and representative offices. The development of the customer base is also taken into account, an increase in which will significantly affect subsequent profits, which, in particular, must be reflected in the forecast.
- Checking the compliance of data with market pricing policies. This comparison must be carried out regularly, for which a mandatory market research is first carried out for changes and adjustments in prices for goods or services provided.
- The use of an automated system through which it is possible to forecast both individual areas of activity and the entire company as a whole. At the same time, the use of specialized software components allows you to fully implement all the necessary measures to obtain the most accurate and realistic forecast.
Methods for forecasting sales volumes
Currently, when drawing up a forecast of sales volumes, it is customary to be guided by various methods that, one way or another, make it possible to obtain an accurate and complete set of data.
All methods can be divided into three main groups:
- method of using the obtained expert assessments
- method of analysis and subsequent forecasting of time intervals
- group of cause-and-effect conclusions and decisions.
First group methods involves conducting a preliminary market analysis. In particular, an analysis is carried out of the current state of the market, relations on it, possible development prospects and much more. It is important to use this group of methods in cases where it is impossible to predict the subsequent development of an organization based on certain data, in particular, on available numerical indicators. However, although the method is quite relevant, it still does not allow making an accurate forecast and needs to make appropriate adjustments.
Second group methods involves the creation of two models independent of each other, which in turn consist of components such as the forecast of randomness and determination. When calculating the value of determination, problems will not arise if the direction of activity has been chosen and comprehended. Complexity can only arise if the randomness component is determined. This is again due to the impossibility of accurately determining the likelihood of random factors influencing the work of an organization. Based on a comparison of the two components, it is possible to derive general trends for the further development of the organization.
Third group methods allows you to obtain data based on the behavior of one of the indicators of the organization’s economic activity. By using this method, you can create a unique model of the object’s behavior in the future. The only problem to be solved when carrying out such an analysis is the search and analysis of various groups of factors that in one way or another influence the further work of the company. In this case, the solution cannot be discovered by simple statistical means and must certainly be worked out.
Any of the forecasting methods is practical and relevant, allows you to get an accurate specific result and therefore will be an excellent choice when drawing up an activity plan for any organization.
An example of forecasting the economic activity of an organization
As an example, I would like to give a sequence of certain actions aimed at obtaining in the future an accurate and structured forecast of the activities of a particular organization.
The process looks like this:
- Formulation and detailing of problems in the operation of the enterprise.
- Collection and systematization of information necessary for analysis, subsequent selection of the optimal forecasting method.
- Application of the chosen method in practice and obtaining data.
- Conducting a comparative analysis of planned and actual results.
Using the Class365 automated system for sales forecasting
As a rule, in order to ensure the most realistic and accurate forecasting, it is customary to use various automated software systems, for example, CRM systems.
Working in the Class365 online program will not require much time and effort, but it will certainly allow you to obtain a detailed structured sales forecast and develop an optimal scheme for the further development of the organization’s economic activities.
By working with the automated Class365 system, you save yourself from the routine work of collecting data and creating reports. Select the required period and the system will automatically generate a report based on your request, without making a single mistake. Based on such reliable information, you can easily make a realistic sales forecast for the coming period.
The program allows you to automate all the main processes of your business: financial and trade accounting, work with a warehouse, online store, interaction with clients.
The online program does not require a long implementation period or costs, and can be accessed from anywhere with Internet access. You will not need to train your employees, as they will be able to master the program on their own in no more than 15 minutes! In short, you have nothing to lose, getting a powerful tool for managing and developing your business!
Get started with the online program right now absolutely free and appreciate all the benefits of an automated approach to sales forecasting!
on the topic
FORECASTING METHODS
SALES VOLUME
Completed by a group student 5120-1 IV- th course
faculty economic
Maleeva Svetlana Viktorovna
Accepted Scientific supervisor assistant professor
departments
economic cybernetics
Maksishko Natalya Konstantinovna
/F.I.O., academic degree and title/
Registration number_________
Date of_________
Signature _________
Course work: 31 pages, 5 tables, 3 figures, 10 sources.
The object of the study is methods for forecasting sales volumes.
The purpose of this work is to present in a systematic form methods for forecasting sales volumes, most often used in economic practice. The main attention in the work is paid to the applied significance of the methods under consideration, to the economic interpretation and interpretation of the results obtained, and not to the explanation of the mathematical and statistical apparatus, which is covered in detail in the specialized literature.
The research method is descriptive, comparative.
In the course of this work, the main methods of forecasting sales volumes, their classification, stages of implementation and analysis were considered.
FORECAST, TREND, CYCLIC FLUCTUATIONS, SEASONAL FLUCTUATIONS, CORRELATION AND REGRESSION ANALYSIS, LEADING INDICATORS.
INTRODUCTION........................................................ ........................................................ ......... 3
1 CLASSIFICATION OF SALES FORECASTING METHODS........ 3
2 METHODS OF EXPERT ASSESSMENTS.................................................................... ............... 3
3 TIME SERIES ANALYSIS.................................................... ....................... 3
4 SEASONAL VARIATIONS.................................................... ............................... 3
5 CYCLIC OSCILLATIONS.................................................... ...................... 3
6 CASUAL FORECASTING METHODS.................................................... 3
CONCLUSIONS................................................. ........................................................ ............ 3
LIST OF SOURCES USED............................................... 3
The enterprise management process is the continuous development of management decisions and their application in practice. The success of the business largely depends on the effectiveness of developing these solutions. And before starting any business, you need to determine the purpose of your actions. During the production process, enterprise managers very often have to deal with critical problems, and the final financial result of the enterprise will depend on how optimal the decision is made.
The need for a solution arises only in the presence of a problem, which in general is characterized by two states - given (desired) and actual (predicted), and it is forecasting that will be the starting point in the process of making a management decision. The discrepancy between these states predetermines the need to develop a management decision and monitor its implementation.
The purpose of this work- present in a systematic way sales forecasting methods, most often used in economic practice. The main attention in the work is paid to the applied significance of the considered methods, on the economic interpretation and interpretation of the results obtained, and not on the explanation of the mathematical and statistical apparatus, which is covered in detail in the specialized literature.
For forecasting to be most effective, goals must be specific and measurable. That is, for each goal there must be criteria that would allow assessing the degree to which the goal has been achieved. Without these criteria, it is not possible to implement one of the main management functions - control. Based on this, we can conclude that a goal, the degree of achievement of which can be quantitatively measured, will always be better than a goal formulated only verbally.
Forecasting is a kind of ability to foresee, analyze a situation and its expected course and changes in the future. Since every decision is a projection into the future, and the future contains an element of uncertainty, it is important to correctly determine the degree of risks associated with the implementation of the decisions made.
In the easiest way forecasting market situation is extrapolation, i.e. extending past trends to the future. The existing objective trends in changes in economic indicators to a certain extent predetermine their value in the future. In addition, many market processes have some inertia. This is especially true in the short term forecasting. At the same time, the forecast for a long-term period should take into account as much as possible the likelihood of changes in the conditions in which the market will operate.
Methods for forecasting sales volume can be divided into three main groups:
Methods of expert assessments;
Methods for analysis and forecasting of time series;
Casual (cause-and-effect) methods.
Expert assessment methods are based on a subjective assessment of the current moment and development prospects. It is advisable to use these methods for opportunistic assessments, especially in cases where it is impossible to obtain direct information about any phenomenon or process.
The second and third groups of methods are based on the analysis of quantitative indicators, but they differ significantly from each other.
Methods for analysis and forecasting of time series are associated with the study of indicators isolated from each other, each of which consists of two elements: a forecast of a deterministic component and a forecast of a random component. Developing the first forecast does not present any great difficulties if the main development trend is determined and its further extrapolation is possible. Predicting a random component is more difficult, since its occurrence can only be estimated with a certain probability.
At the core casual methods there is an attempt to find the factors that determine the behavior of the predicted indicator. The search for these factors actually leads to economic-mathematical modeling - the construction of a behavior model of an economic object that takes into account the development of interrelated phenomena and processes. It should be noted that the use of multifactor forecasting requires solving the complex problem of selecting factors, which cannot be solved purely statistically, but is associated with the need for an in-depth study of the economic content of the phenomenon or process under consideration. And here it is important to emphasize the primacy of economic analysis over purely statistical methods of studying the process.
Each of the considered groups of methods has certain advantages and disadvantages. Their use is more effective in short-term forecasting, since they to a certain extent simplify real processes and do not go beyond the concepts of today. The simultaneous use of quantitative and qualitative forecasting methods should be ensured.
Let us take a closer look at the essence of some methods for forecasting sales volume, the possibilities of their use in marketing analysis, as well as the necessary initial data and time restrictions.
Expert-assisted sales forecasts can be obtained in one of three forms:
1) point forecast;
2) interval forecast;
3) forecasting the probability distribution.
Point forecast of sales volume – this is a forecast of a specific figure. It is the simplest of all forecasts because it contains the least amount of information. As a rule, it is assumed in advance that a point forecast may be erroneous, but the methodology does not provide for the calculation of the forecast error or the probability of an accurate forecast. Therefore, in practice, two other forecasting methods are more often used: interval and probabilistic.
Interval sales volume forecast provides for the establishment of boundaries within which the predicted value of the indicator will be located with a given level of significance. An example is a statement like: “In the coming year, sales volume will be from 11 to 12.4 million UAH.”
Probability distribution forecast is associated with determining the probability of the actual value of an indicator falling into one of several groups at established intervals. An example would be a forecast like:
Although when making a forecast, there is a certain probability that actual sales will not fall within the specified interval, but forecasters believe that it is so small that it can be ignored when planning.
The intervals that take into account low, medium and high sales levels are sometimes called pessimistic, most likely and optimistic. Of course, a probability distribution can be represented by a large number of groups, but the three specified interval groups are most often used.
Sales forecasting: accurate calculation or fortune-telling? When we were building a system at the development company Urban Group, the commercial director, Dmitry Usmanov, asked the question whether we would sign up for a specific figure. We named the number, date and time.
Three weeks later at 12.15 we were sitting in a cafe and watching the admission schedule. At 12.00 the arrivals for the last day are posted. The forecast accuracy was 99.7%.
The most common question our clients ask us is: “How can you calculate future sales so accurately?”
It's all about the coffee) No, not the one by which you can find out the fate of your business, but the one we drink while we solve the problem of forecasting for each specific enterprise.
Do not confuse sales forecasts based on detailed calculations with unscientific fortune telling. Let's look at how to create the most accurate sales forecast and what problems it solves.
Why do you need a sales forecast?
1. Setting goals
. The figure obtained from the annual forecast is what the company should achieve for the next year, the plan that needs to be fulfilled. This is part of the business plan for the enterprise and a real, clearly calculated goal for the sales department, which can be used as a starting point when calculating bonuses. Very often the goal is set out of desires, and not out of real possibilities.
Therefore, before setting a goal, you must first make a forecast and then set the goal. If the goal is higher than the forecast, then you need to understand through what changes the goal will be achieved.
2. Formation of the necessary base of labor and production resources. Based on the forecast number of customers and sales volume. Task: plan purchases and determine the company's future needs for equipment and personnel.
3. Inventory management . At each moment of time, production will have at its disposal a warehouse balance sufficient to complete tasks at a certain stage. There is no shortage or excess of materials in the warehouse - only rational spending of funds!
4. Increased business mobility . On the forecast chart (or in the table), you can see in advance the moments of a possible decline in sales volume (for example, due to the seasonality of the product) and take measures to correct the situation before the end of the period. In addition, the chances of instantly tracking an unplanned decline in sales, promptly identifying the reasons for the decline in performance, and correcting the situation in a timely manner increase.
5. Cost control and optimization . Forecasting will show what overall costs the company will incur for the production and sale of products. This means that you can develop a budget and determine in advance which costs are subject to reduction in the event of failure to meet the forecast for an increase in sales volume.
The cornerstone of inventory management and a huge headache for the manager. How to do this in practice?
The purpose of these notes is not to present the theory of forecasting - there are many books. The goal is to concisely and, as far as possible, without deep and rigorous mathematics, to give an overview of various methods and practices of application specifically in the field of inventory management. I tried not to “get into the weeds”, to consider only the most frequently encountered situations. The notes were written by a practitioner and for practitioners, so you should not look for any sophisticated techniques here, only the most general ones are described. So to speak, mainstream in its purest form.
However, as elsewhere on this site, participation is welcome in every possible way - add, correct, criticize...
Forecasting. Formulation of the problem
Any forecast is always wrong. The whole question is how wrong it is.
So we have sales data at our disposal. Let it look like this:
In mathematical language this is called a time series:
A time series has two critical properties
the values must be ordered. Swap any two values and get another series
it is implied that the values in the series are the result of measurements at equal fixed intervals of time; Forecasting the behavior of a series means obtaining a “continuation” of the series at the same intervals for a given forecast horizon
This implies a requirement for the accuracy of the initial data - if we want to get a weekly forecast, the initial accuracy must be no worse than weekly shipments.
It also follows that if we “extract” monthly sales data from the accounting system, they cannot be used directly, since the amount of time during which shipments were made is different in each month and this introduces an additional error, since sales volume is approximately proportional to this time .
However, this is not such a difficult problem - let's just bring these data to the daily average.
In order to make any assumptions regarding the further course of the process, we must, as already said, reduce the degree of our ignorance. We assume that our process has some internal patterns of flow that are completely objective in the current environment. In general terms this can be represented as
Y(t) - the value of our series (for example, sales volume) at time t
f(t) is a certain function that describes the internal logic of the process. In what follows we will call it a predictive model.
e(t) - noise, error associated with the randomness of the process. Or, what is the same thing, related to our ignorance, inability to take into account other factors in the model f(t).
Now our task is to find a model such that the error value is noticeably smaller than the observed value. If we find such a model, we can assume that the process in the future will proceed approximately in accordance with this model. Moreover, the more accurately the model describes the process in the past, the more confidence we have that it will work in the future.
Therefore, the process is usually iterative. Based on a simple look at the graph, the forecaster selects a simple model and selects its parameters so that the value
was in some sense the minimum possible. This quantity is usually called “residuals”, since this is what remains after subtracting the model from the actual data, what the model could not describe. To assess how well the model describes the process, it is necessary to calculate a certain integral characteristic of the error value. Most often, to calculate this integral error value, the average absolute or root-mean-square value of the residuals over all t is used. If the error is large enough, they try to “improve” the model, i.e. choose a more complex type of model, take into account more factors. We, as practitioners, should strictly observe at least two rules in this process:
Naive forecasting methods
Naive methods
Simple average
In the simple case of measured values fluctuating around a certain level, the obvious course of action is to estimate the average and assume that actual sales will continue to fluctuate around that value.
Moving average
In reality, as a rule, the picture “floats” at least a little. The company is growing, turnover is increasing. One modification of the average model that takes this phenomenon into account is to discard the oldest data and use only the last k points to calculate the average. The method is called the “moving average”.
Weighted moving average
The next step in modifying the model is the assumption that later values of the series more adequately reflect the situation. Each value is then assigned a weight, which increases the more recent the value is added.
For convenience, you can immediately select the coefficients so that their sum is one, then you won’t have to divide. We will say that such coefficients are normalized to unity.
The forecasting results for 5 periods ahead using these three algorithms are shown in the table
Simple exponential smoothing
In English-language literature, the abbreviation SES is often found - Simple Exponential Smoothing
One of the variations of the averaging method is exponential smoothing method. It differs in that a number of coefficients are chosen in a very specific way - their value falls according to an exponential law. Let us dwell here in a little more detail, since the method has become widespread due to its simplicity and ease of calculation.
Let us make a forecast at time t+1 (for the next period). Let's denote it as
Here we take the forecast of the last period as the basis for the forecast, and add an amendment related to the error of this forecast. The weight of this adjustment will determine how “sharply” our model will respond to changes. It's obvious that
It is believed that for a slowly changing series it is better to take a value of 0.1, and for a rapidly changing series it is better to select around 0.3-0.5.
If we rewrite this formula in another form, it turns out
We have obtained the so-called recurrence relation - when the subsequent term is expressed through the previous one. Now we express the forecast of the last period in the same way through the value of the series before last, and so on. As a result, it is possible to obtain a forecast formula
As an illustration, we will demonstrate smoothing at different values of the smoothing constant
Obviously, if turnover grows more or less monotonically, with this approach we will systematically receive underestimated forecast figures. And vice versa.
And finally, the smoothing technique using spreadsheets. For the first forecast value, we will take the actual value, and then use the recursion formula:
Components of a predictive model
Obviously, if turnover grows more or less monotonically, with such an “averaging” approach we will systematically receive underestimated forecast figures. And vice versa.
In order to more adequately model a trend, the concept of “trend” is introduced into the model, i.e. some smooth curve that more or less adequately reflects the “systematic” behavior of the series.
Trend
In Fig. shows the same series assuming approximately linear growth
This trend is called linear, based on the shape of the curve. This is the most commonly used type; polynomial, exponential, and logarithmic trends are less common. Having chosen the type of curve, specific parameters are usually selected using the least squares method.
Strictly speaking, this component of the time series is called trend-cyclical, that is, it includes oscillations with a relatively long period, for our purposes - about ten years. This cyclical component is characteristic of the global economy or the intensity of solar activity. Since we are not solving such global problems here, our horizons are smaller, we will leave the cyclical component out of the equation and continue to talk about the trend everywhere.
Seasonality
However, in practice it is not enough for us to model behavior in such a way that we imply the monotonic nature of the series. The fact is that examination of specific sales data often leads us to the conclusion that there is another pattern - periodic repetition of behavior, a certain pattern. For example, when looking at ice cream sales, it is obvious that in winter they are generally below average. This behavior is completely understandable from a common sense point of view, so the question arises: could this information be used to reduce our ignorance, to reduce uncertainty?
This is how the concept of “seasonality” arises in forecasting - any change in a value that repeats at strictly defined intervals. For example, a surge in sales of Christmas decorations in the last 2 weeks of the year can be considered seasonal. As a rule, the increase in supermarket sales on Friday and Saturday in comparison with other days can be considered as seasonality with a weekly frequency. Although this component of the model is called “seasonality,” it is not necessarily associated specifically with the season in the everyday sense (spring, summer). Any periodicity can be called seasonality. From the point of view of a series, seasonality is characterized primarily by a period or lag of seasonality - the number through which repetition occurs. For example, if we have a series of monthly sales, we might assume the period is 12.
There are models with additive and multiplicative seasonality. In the first case, a seasonal adjustment is added to the original model (in February we sell 350 units less than average)
in the second, we multiply by the seasonality factor (in February we sell 15% less than the average)
Note that, as mentioned at the beginning, the very presence of seasonality should be explainable from the point of view of common sense. Seasonality is a consequence and manifestation product properties(peculiarities of its consumption in a given point of the globe). If we can accurately identify and measure this property of this particular product, we can be sure that such fluctuations will continue in the future. Moreover, the same product may well have different seasonality characteristics (profiles) depending on the place where it is consumed. If we cannot explain such behavior in terms of common sense, we have no reason to expect the pattern to repeat in the future. In this case, we must look for other factors external to the product and consider their presence in the future.
The important thing is that when choosing a trend, we must choose a simple analytical function (that is, one that can be expressed by a simple formula), while seasonality is usually expressed by a tabular function. The most common case is annual seasonality with 12 periods according to the number of months - this is a table of 11 multiplicative factors representing an adjustment relative to one reference month. Or 12 coefficients relative to the monthly average, but it is very important that the same 11 remain independent, since the 12th is uniquely determined from the requirement
The situation when M is present in the model statistically independent (!) parameters, in forecasting is called a model with M degrees of freedom. So if you come across special software in which, as a rule, you need to set the number of degrees of freedom as input parameters, this is where it comes from. For example, a model with a linear trend and a period of 12 months will have 13 degrees of freedom - 11 from seasonality and 2 from trend.
We will consider how to live with these components of the series in the following parts.
Classic seasonal decomposition
Decomposition of a series of sales.
So, we can often observe the behavior of a series of sales, in which there are components of trend and seasonality. We intend to improve the quality of the forecast given this knowledge. But in order to use this information, we need quantitative characteristics. Then we will be able to exclude trend and seasonality from the actual data and thereby significantly reduce the amount of noise, and therefore the uncertainty of the future.
The procedure for isolating non-random components of a model from actual data is called decomposition.
The first thing we will do with our data is seasonal decomposition, i.e. determination of numerical values of seasonal coefficients. To be specific, let’s take the most common case: sales data is grouped monthly (since a forecast with an accuracy of up to a month is required), a linear trend and multiplicative seasonality with a lag of 12 are assumed.
Smoothing a series
Smoothing is a process in which the original series is replaced by another, smoother, but based on the original one. The purpose of such a process is to assess general trends, trends in a broad sense. There are many methods (as well as goals) of smoothing, the most common
consolidation of time intervals. It is clear that a sales series aggregated monthly behaves more smoothly than a series based on daily sales
moving average. We already looked at this method when we talked about naive forecasting methods
analytical alignment. In this case, the original series is replaced by some smooth analytical function. The type and parameters are selected expertly to minimize errors. Again, we already discussed this when we talked about trends
Next we will use smoothing using the moving average method. The idea is that we replace a set of several points with one according to the “center of mass” principle - the value is equal to the average of these points, and the center of mass is located, as you might guess, in the center of the segment formed by the extreme points. So we set a certain “average” level for these points.
As an illustration, our original series, smoothed at 5 and 12 points:
As you might guess, if averaging occurs over an even number of points, the center of mass falls into the gap between the points:
What am I leading to?
In order to carry out seasonal decomposition, the classical approach suggests first smoothing a series with a window that exactly coincides with the seasonality lag. In our case, lag = 12, so if we smooth over 12 points, it appears that the disturbances associated with seasonality are leveled out and we get an overall average level. Then we will begin to compare actual sales with smoothed values - for the additive model we will subtract the smoothed series from the fact, and for the multiplicative model we will divide. As a result, we get a set of coefficients, several for each month (depending on the length of the series). If the smoothing is successful, these coefficients will not have too much spread, so averaging for each month will not be such a foolish idea.
Two points that are important to note.
- Averaging of coefficients can be done either by calculating the standard average or the median. The latter option is highly recommended by many authors, since the median does not react as strongly to random outliers. But in our training task we will use the simple average.
- We will have a seasonality lag of 12, even. Therefore, we will have to do one more smoothing - replace two adjacent points of the first smoothed series with the average, then we will get to a specific month
The picture shows the result of re-smoothing:
Now we divide the fact into a smooth series:
Unfortunately, I only had data for 36 months, and when smoothing at 12 points, one year is correspondingly lost. Therefore, at this stage I received seasonality coefficients of only 2 for each month. But there is nothing to do, it is better than nothing. We will average these pairs of coefficients:
Now we remember that the sum of the multiplicative seasonality coefficients should be = 12, since the meaning of the coefficient is the ratio of monthly sales to the monthly average. This is exactly what the last column does:
Now we've done it classic seasonal decomposition, that is, we obtained the values of 12 multiplicative coefficients. Now it's time to tackle our linear trend. To assess the trend, we will eliminate seasonal fluctuations from actual sales by dividing the fact by the value obtained for a given month.
Now let’s plot data with seasonality eliminated on a graph, draw a linear trend and, for fun, make a forecast for 12 periods ahead as the product of the trend value at a point by the corresponding seasonality coefficient
As can be seen from the picture, the data cleared of seasonality does not fit into a linear relationship very well - the deviations are too large. Perhaps if you remove outliers from the original data, everything will become much better.
To more accurately determine seasonality using classical decomposition, it is highly desirable to have at least 4-5 complete cycles of data, since one cycle is not involved in calculating the coefficients.
What to do if, for technical reasons, there is no such data? We need to find a method that will not discard any information and will use all available information to assess seasonality and trend. Let's try to consider this method in the next part.
Exponential smoothing taking into account trend and seasonality. Holt-Winters method
Returning to exponential smoothing...
In one of the previous parts we already looked at the simple exponential smoothing. Let us briefly recall the main idea. We assumed that the forecast for point t is determined by some average level of previous values. Moreover, the method by which the forecast value is calculated is determined by the recurrence relation
In this form, the method gives digestible results, if the series of sales is quite stationary - there is no pronounced trend or seasonal fluctuations. But in practice, such a case is happiness. Therefore, we will consider a modification of this method that allows us to work with trend and seasonal models.
The method was called Holt-Winters after the names of its developers: Holt proposed the accounting method trend, Winters added seasonality.
In order to not only understand the arithmetic, but also to “feel” how it works, let’s turn our heads a little and think about what changes if we introduce a trend. If for simple exponential smoothing the forecast estimate for the p-th period was done as
where Lt is the “general level” averaged according to the well-known rule, then if there is a trend, an amendment appears
,
that is, a trend estimate is added to the overall level. Moreover, we will average both the general level and the trend independently using the exponential smoothing method. What is meant by trend averaging? We assume that in our process there is a local trend that determines a systematic increment at one step - between points t and t-1, for example. And if for linear regression a trend line is drawn over the entire set of points, we believe that more recent points should contribute more because the market environment is constantly changing and more recent data is more valuable for the forecast. As a result, Holt proposed using two recurrence relations - one smoothes general row level, the other smooths out trend component.
The smoothing technique is such that the initial values of the level and trend are first selected, and then a pass is made through the entire series, calculating new values using formulas at each step. From general considerations, it is clear that the initial values should somehow be determined based on the values of the series at the very beginning, but there are no clear criteria here; there is an element of voluntarism. Two approaches are most often used in choosing “reference points”:
The initial level is equal to the first value of the series, the initial trend is zero.
We take the first few points (5 pieces), draw a regression line (ax+b). We set the initial level as b, the initial trend as a.
By and large, this issue is not fundamental. As we remember, the contribution of early points is negligible, since the coefficients decrease very quickly (exponentially), so that with a sufficient length of the initial data series, we will most likely receive almost identical forecasts. The difference, however, may become apparent when estimating the model error.
This figure shows the results of smoothing with two choices of initial values. It is clearly seen here that the big error in the second option is due to the fact that the initial trend value (taken from 5 points) turned out to be clearly overestimated, since we did not take into account the growth associated with seasonality.
Therefore (following Mr. Winters) we will complicate the model and make a forecast taking into account seasonality:
In this case, as before, we assume multiplicative seasonality. Then our system of smoothing equations receives one more component:
where s is the seasonality lag.
And again, we note that the choice of initial values, as well as the values of smoothing constants, is a matter of the will and opinion of the expert.
For truly important forecasts, however, it can be proposed to compile a matrix of all combinations of constants and, by brute force, select those that give the smallest error. We will talk about methods for assessing the error of models a little later. In the meantime, let's start smoothing our series by Holt-Winters method. In this case, we will determine the initial values using the following algorithm:
The initial values have now been determined.
The results of all this mess:
Conclusion
Surprisingly, such a simple method gives very good results in practice, quite comparable to much more “mathematical” ones - for example, with linear regression. And at the same time, the implementation of exponential smoothing in an information system is an order of magnitude simpler.
Forecasting rare sales. Croston method
Forecasting rare sales.
The essence of the problem.
All known forecasting mathematics, which textbook authors are happy to describe, is based on the assumption that sales are in some sense “even.” It is with this picture that concepts such as trend or seasonality arise.
What if sales look like this?
Each column here represents sales for the period; there are no sales between them, although the product is present.
What kind of “trends” can we talk about here when about half of the periods have zero sales? And this is not the most clinical case yet!
It is already clear from the graphs themselves that we need to come up with some other prediction algorithms. I would also like to note that this task is not a far-fetched task and is not some kind of rare one. Almost all aftermarket niches deal with exactly this case - auto parts, pharmacies, provision of service centers,...
Problem formulation.
We will solve a purely applied problem. I have data on sales of an outlet accurate to days. Let the supply system response time be exactly one week. The minimum task is to predict the sales speed. The maximum task is to determine the amount of safety stock based on a service level of 95%.
Croston's method.
Analyzing the physical nature of the process, Croston (J.D.) suggested that
- all sales are statistically independent
- whether a sale occurred or not is subject to the Bernoulli distribution
(with probability p the event occurs, with probability 1-p it does not) - if a sale event occurs, the purchase size is distributed normally
This means that the resulting distribution looks like this:
As you can see, this picture is very different from Gauss’s “bell”. Moreover, the top of the depicted hill corresponds to the purchase of 25 units, whereas if we “head-on” calculate the average for a series of sales, we get 18 units, and the calculation of the standard deviation gives 16. The corresponding “normal” curve is drawn here in green.
Croston proposed estimating two independent quantities - the period between purchases and the actual size of the purchase. Let's look at the test data, I just happen to have data on real sales on hand:
Now let's divide the original row into two rows according to the following principles.
| original | period | size |
| 0 | ||
| 0 | ||
| 0 | ||
| 0 | ||
| 0 | ||
| 0 | ||
| 0 | ||
| 0 | ||
| 0 | ||
| 0 | ||
| 4 | 11 | 4 |
| 0 | ||
| 0 | ||
| 4 | 3 | 4 |
| 5 | 1 | 5 |
| ... | ... | ... |
Now we apply simple exponential smoothing to each of the resulting series and obtain the expected values of the interval between purchases and the purchase value. And dividing the second by the first, we get the expected intensity of demand per unit of time.
So, I have test data on daily sales. Selecting the series and smoothing with a small value of the constant gave me
- expected period between purchases 5.5 days
- expected purchase size 3.7 units
therefore, the weekly sales forecast will be 3.7/5.5*7=4.7 units.
Actually, that's all the Croston method gives us - a point estimate of the forecast. Unfortunately, this is not enough to calculate the required safety stock.
Croston's method. Algorithm refinement.
Disadvantage of the Croston method.
The problem with all classical methods is that they model behavior using a normal distribution. And here lies the systematic error, since the normal distribution assumes that a random variable can vary from minus infinity to plus infinity. But this is a minor problem for fairly regular demand, when the coefficient of variation is small, and therefore the probability of negative values appearing is so insignificant that we can easily turn a blind eye to it.
Another thing is forecasting rare events when the expectation of the purchase size is of little importance, and the standard deviation may well be at least of the same order:
To avoid such an obvious error, it was proposed to use the lognormal distribution, as it more “logically” describes the picture of the world:
If anyone is confused by all sorts of scary words, don’t worry, the principle is very simple. The original series is taken, the natural logarithm of each value is taken, and the resulting series is assumed to already behave as normally distributed with all the standard mathematics described above.
Croston method and safety stock. Demand distribution function.
I sat here and thought... Well, okay, I got the characteristics of the demand flow:
expected period between purchases 5.5 days
expected purchase size 3.7 units
expected demand intensity 3.7/5.5 units per day...
even if I got the standard deviation of daily demand for non-zero sales - 2.7. What about safety stock?
As is known, safety stock must ensure the availability of goods when sales deviate from the average with a certain probability. We have already discussed service level metrics, let’s first talk about the level of the first kind. The strict formulation of the problem sounds like this:
Our supply chain has a response time. The total demand for a product during this time is a random value that has its own distribution function. The condition “probability of non-zeroing of the stock” can be written as
In the case of rare sales, the distribution function can be written as follows:
q - probability of a zero outcome
p=1-q - probability of a non-zero outcome
f(x) - density of purchase size distribution
Please note that in my previous study, I measured all these parameters for the daily sales series. Therefore, if my reaction time is also one day, then this formula can be successfully applied right away. For example:
assume that f(x) is normal.
suppose that in the region x<=0 вероятности, описываемые функцией очень низкие, т.е.
then the integral in our formula is looked for using the Laplace table.
in our example p = 1/5.5, so
the search algorithm becomes obvious - having set SL, we increase k until F exceeds the specified level.
By the way, what's in the last column? That's right, the second type of service level corresponding to a given stock. And here, as I already said, there is some methodological incident. Let's imagine that sales occur approximately once every... well, let's say 50 days. And let’s also imagine that we hold zero stock. What level of service will there be? It seems like zero - no stock, no maintenance. The stock control system will give us the same figure, since there is a constant out of stock. But from the point of view of banal erudition, in 49 cases out of 50, sales exactly correspond to demand. That is does not lead to loss of profit and customer loyalty, and for nothing else service level and not intended. This somewhat degenerate case (I sense an argument is about to begin) is simply an illustration of why even a very small supply with infrequent demand produces high levels of service.
But these are all flowers. What if my supplier has changed, and now the response time is a week, for example? Well, this is where things get really fun. For those who don’t like “multi-formulas,” I recommend that you don’t read further, but wait for the article about the Willemain method.
Our task now is to analyze the amount of sales during the system response period, understand its distribution, and then pull it out from there dependence of the level of service on the amount of stock.
So, we know the demand distribution function for one day and all its parameters:
As before, the result of one day is statistically independent from any other.
Let a random event be something that happened in n days smooth m facts of non-zero sales. According to Bernoulli's law (okay, I'm sitting here and copying from a textbook!) the probability of such an event
where is the number of combinations from n to m, and p and q are again the same probabilities.
Then the probability that the amount sold in n days resulting in exactly m sales facts will not exceed the value z, will be
where is the distribution of the amount sold, that is, the convolution of m identical distributions.
Well, since the desired result (total sales do not exceed z) can be obtained for any m, it remains to sum up the corresponding probabilities:
(the first term corresponds to the probability of a zero outcome for all n trials).
Anything further, I’m too lazy to tinker with all this; those who wish can independently construct a table similar to the one above applied to the normal probability density. To do this, you just need to remember that the convolution of m normal distributions with parameters (a,s 2) gives the same normal distribution with parameters (ma,ms 2).
Forecasting rare sales. Willemain method.
What's wrong with Croston's method?
The fact is that, firstly, it implies the normality of the distribution of the purchase size. Secondly, for adequate results this distribution should have low variance. Third, although it is not so fatal, the use of exponential smoothing to find distribution characteristics implicitly implies that the process is nonstationary.
Well, God bless him. The most important thing for us is that actual sales do not look even close to normal. It was this thought that prompted Thomas R. Willemain and the company to create a more universal method. And the need for such a method was dictated by what? That's right, the need to forecast the need for spare parts, especially automotive parts.
Willemain method.
The essence of the approach is to use the bootstrapping procedure. This word was born from the old saying “pull oneself over a fence by one’s bootstraps,” which almost literally corresponds to our “pull oneself out by your own hair.” The computer term boot, by the way, also comes from here. And the meaning of this word is that a certain the entity contains the necessary resources to transfer itself to another state, and if necessary, such a procedure can be launched. This is exactly the process that happens to the computer when we press a certain button.
When applied to our narrow problem, the bootstrapping procedure means the calculation of internal patterns present in the data, and is performed as follows.
According to the conditions of our task, the system response time is 7 days. We DO NOT know and DO NOT TRY to guess the type and parameters of the distribution curve.
Instead, we randomly “pluck” days from the entire series 7 times, sum up the sales of these days and record the result.
We repeat these steps, each time recording the amount of sales for 7 days.
It is advisable to carry out the experiment quite a few times to get the most adequate picture. 10 - 100 thousand times will be very good. It is very important here that the days are selected at random evenly throughout the entire analyzed range.
As a result, we should get “as if” all possible sales outcomes for exactly seven days, taking into account the frequency of occurrence of identical results.
Next, we divide the entire range of the resulting amounts into segments in accordance with the accuracy that we need to determine the reserve. And we build a frequency histogram, which will show the real distribution of purchase probabilities. In my case I got the following:
Since I sell piece goods, i.e. The purchase size is always an integer, so I didn’t break it into segments, I left it as is. The height of the bar corresponds to the share of total sales.
As you can see, the right, “non-zero” part of the distribution does not resemble a normal distribution (compare with the green dotted line).
Now, based on this distribution, it is easy to calculate service levels corresponding to different stock sizes (SL1, SL2). So, having set the target level of service, we immediately get the required supply.
But that's not all. If you introduce financial indicators into consideration - cost, forecast price, cost of maintaining inventory, you can easily calculate the profitability corresponding to each size of inventory and each level of service. It is shown in my last column, and the corresponding graphs are here:
That is, here we find out the most effective inventory and level of service from the point of view of making a profit.
Finally (once again) I would like to ask: “why do we base the level of service on ABC analysis?" It would seem that in our case optimal level of service of the first kind is 91%, regardless of which group the product is in. This great mystery is...
Let me remind you that one of the assumptions on which we were based is sales independence one day from another. This is a very good assumption for retail. For example, expected bread sales today do not depend in any way on yesterday's sales. This picture is generally typical where there is a fairly large customer base. Therefore, randomly selected three days can give such a result
such
and even like this
It's a completely different matter when we have relatively few customers, especially if they buy infrequently and in large quantities. in this case, the probability of an event similar to the third option is practically zero. To put it in simple terms, if I had large shipments yesterday, most likely today there will be a lull. And the option looks absolutely fantastic when demand is high for several days in a row.
This means that the independence of sales of neighboring days in this case may turn out to be bullshit, and it is much more logical to assume the opposite - they are closely related. Well, you won't scare us with that. All we have to do is we won’t hold out the days by chance, we'll take the days going by contract:
Everything is even more interesting. Since our series are relatively short, we don’t even need to bother with random sampling - it’s enough to run a sliding window over the series, the size of the reaction time, and the finished histogram is in our pocket.
But there is also a drawback. The point is that we get far fewer observations. For a window of 7 days per year, you can get 365-7 observations, whereas with a random sample, 7 out of 365 is the number of combinations of 365! / 7! / (365-7)! Too lazy to count, but it's much more than that.
And a small number of observations means unreliable estimates, so save up data - they are never superfluous!
A mistake many businessmen make is selling blindly. They do not make any sales forecasts, assessing only the results of the reporting period. This pattern resembles a roller coaster: first a peak, then a long lull.
Why shouldn't you do this?
- If you don't make a sales forecast, your staff will drop. There is no guideline for what to strive for.
- Any figure is assessed on the principle of “at least something”.
- There is no spirit of competition, there are no leaders to follow.
To achieve goals, you must first set them. To increase revenue, you need to make a forecast. The main thing is that the desired growth is realistic. Practice shows that forecast figures are achieved when the planned indicators differ from the actual capabilities of your sellers by no more than 30-35%.
Please note the following methods for making a forecast:
1. Plus 10% of what is achieved
This method is familiar to those who have studied the Soviet economy and its forecasting methods. The main point of this method is to predict indicators that are 10-15% higher than what was achieved during the previous reporting period.
This method works well when your company has already built a sales system and each manager has minimum acceptable performance indicators.
However, with this method, it is important to establish the real capabilities of your salespeople. So that the forecast has a challenge, and does not contain indicators of the lower bar of what is acceptable.
2. Compare with the best
This is a popular motivator for achieving your goals. The main point of the method is to show that if someone could meet the expectations of the sales forecast, then others can too.
However, as a guide to numbers in a forecast, this method is not always effective. At a minimum, because in any sales department there are “locomotives” and “candidates for dismissal.” Therefore, in order for the forecast to be more realistic and justified, you need to focus on something in between the results of these two categories.
3. We look at competitors
It is logical to make a forecast based on your own achievements, but periodically you need to compare yourself with your competitors in order to achieve a leading position.
This is a great way to forecast sales if you have access to competitive information. To their strategy, business processes, purchasing prices, discounts, and much more that is not written about in commercial proposals and is not discussed on the website.
You can get this information in different ways. Including carrying out guerrilla methods of work. For example, call a competitor under the guise of a buyer and see how his chain of work with the client is structured.
4. Encourage your desires
One method of creating a sales forecast is that you start from your actual desires. Even if this does not correspond to common sense. But you set certain numbers for your goal and select methods for its implementation.
5. Focus on your sales funnel
This method can be used for forecasting if you have measurements of the results of all stages of sales. Those. you know all the numbers that affect sales in your business.
To get all the necessary indicators, analyze the work of your department. To make a forecast, figures for a period of 2-3 months are needed.
What information should you analyze:
- how much time is spent on average on one cold call,
- how much time is spent on average collecting information about a potential client,
- how many calls do you need to make to get through the chain to the person, the solution,
- how many meetings can one manager realistically hold per day,
- what percentage of meetings end with an order,
- number of repeat sales,
- average check.
With these numbers in hand, you can make a realistic forecast.
How to decompose a plan
You need to decide on the goals you set in your forecasts. Next, it is important to decompose them into tasks for each employee.
Therefore, when drawing up a sales forecast, break down the overall vision into specific areas that need to be worked on to achieve results.
The following plans need to be made:
- For new clients;
- For new products;
- By increasing the share of current clients;
- From various channels;
- By customer churn;
- For non-repayment of receivables (if there is such a problem).
Break down each figure in the plan into the following areas:
- By region;
- By department;
- By employees;
- By month/day;
- Based on intermediate performance indicators, taking into account indicators in the funnel (current and new client base).
The more accurately and in detail you break down the numbers in each plan, the more likely the forecast will be realized.
Decomposition example
Let's give an example of decomposition of the sales forecast to the level of daily indicators for each employee. But before you do this, make sure the business structure is working optimally. It is necessary to conduct a small audit in 4 areas.
Clients. It is necessary to segment the current customer base in order to identify the main target groups and focus on working with the most profitable ones.
Channels. Analyze the conversion of each of them taking into account the average cost per lead and stop investing in what does not bring results.
Employees. Only the best personnel should remain in the department. Screening will happen automatically if you implement 2 principles:
- the principle of “compound salary”, in which the bonus part for fulfilling the sales forecast is at least 50%;
- the principle of “large thresholds”, which regulates the payment of bonuses: did not fulfill up to 80% of the plan - did not receive a bonus, 80-100% - plus 1 salary, exceeded the plan - plus 2 salaries.
Products. Get rid of illiquid and low-margin products. This will prevent resource wastage.
Based on the optimally configured system, proceed to decomposition, following the plan below.
1. Determine your projected profit figure. Look at the profits of previous periods. Eliminate one-time transactions. Consider marketing influences and seasonality.
2. Knowing your marginality, calculate revenue using the share of profit.
3. Divide the revenue by the average bill and get the approximate number of transactions that need to be concluded to achieve the target profit.
4. Using the conversion rate from application to buyer, calculate the number of leads.
5. Based on the intermediate conversion in the funnel, calculate the total number of actions that need to be completed as part of the business process. We are talking about calls, meetings, presentations, follow-up calls, commercial proposals sent, and invoices issued.
6. Once you have quantitative indicators for each stage, divide them by the number of working days of the forecast period (most often it is customary to talk about a month).
This way, you will find out what and how much each salesperson should do so that in the end the entire department closes the plan by the end of the month. Monitor the implementation of these indicators on a daily basis.
