*Intended learning outcomes: Produce an overview on the choice of suitable forecasting technique. Describe consumption distributions and their limits, continuous and discontinuous demand. Explain demand forecasting of variants of a product family. Present safety demand calculation for various planning periods. Disclose the translation of forecast into quasi-deterministic demand. *

## 10.5.1 Comparison of Techniques and Choice of Suitable Forecasting Technique

In Figure 10.5.1.1, the techniques discussed in this section are compared according to a number of criteria.

**Fig. 10.5.1.1** Areas of applicability of forecasting techniques.

When choosing a forecasting technique, it is crucial to find that technique (reasonable in use) that will provide the greatest accuracy of alignment to the demand structure.[note 1008] The following criteria also play a role:

- Adaptability to demand performance
- Possibility of forecast errors
- Aids required
- Expense for data collection and preparation for analysis
- Ascertainability of parameters that describe the performance of the system to be forecast
- The purpose of the forecast and the importance of one material position
- Forecast time frame
- Transparency for the user

## 10.5.2 Consumption Distributions and Their Limits, Continuous and Discontinuous Demand

Thedistribution of forecast errorsis a tabulation of the forecast errors according to the frequency of occurrence of each error value (cf. [APIC16]).

The errors in forecasting are, in many cases, normally distributed, even when the observed data do not come from a normal distribution. Therefore, we now take a closer look into the origin of the observed values.

Aconsumption distribution, such as a statistic for order receipts allocated by time periods, can be understood as an aggregation of multiple individual events during each period. These individual events can be described by: - Thedistribution of the frequency of the eventsthemselves - Adistribution of characteristic values for an event, that is, order quantities A combination of these two distributions results in consumption distribution.

Given the definitions in Figure 10.5.2.1 and a constant process (e.g., for constant demand), the formulas contained in Figure 10.5.2.2 are valid according to [Fers64]. Here, E stands for the *expected value*; VAR stands for the *variance*.[note 1009]

**Fig. 10.5.2.1** Definitions for a consumption distribution.

**Fig. 10.5.2.2** Expected value and variance of the consumption distribution.

In a purely random process, the number of events per period has a Poisson distribution with distribution function P(n) and expected value = variance = λ. Knowing this, we can derive the formulas in Figure 10.5.2.3, where CV corresponds to the *coefficient of variation* for the distribution, that is, the quotient of standard deviation and expected value.

**Fig. 10.5.2.3** Distribution function, expected value, and variance of the consumption distribution under the assumption of a Poisson distribution for the frequency of events.

A few large issues can greatly influence the coefficient of variation for the *order quantity*. The square can very well take on a value of 3. If all issues are equally large, then the value is clearly at its minimum of 0 (e.g., the order quantity for service parts may always equal 1). Even if the measured values of the consumption distribution allowed, based on the rules of statistics, the assumption of a normal distribution as such, a coefficient of variation of CV ≤ 0.4 is a prerequisite for effective procedures in the stochastic materials management. From the formula in Figure 10.5.2.3, it is possible to say how many issues are necessary, so that such a small coefficient of variation results. Specifically, if 1 is assumed as the mean for the coefficient of variation of the distribution of the *order quantity*, then at least 12.5 orders or issues per period are needed, which can be high for a machine manufacturer (λ ≥ (1+1) / 0.16 = 12.5). The value for λ may vary very widely and may be quite small, particularly in the capital goods industry. This type of demand is referred to as *discontinuous* or *lumpy demand**.* It is different from both *regular* demand (regularity as described in Section 10.3.1) and *continuous* (steady) demand. (See the definitions in Section 4.4.2). From above observations, we can establish qualitatively that:

- The
*discontinuous character*of a distribution is the result of a limited number of issues per time unit measured. With this, it is very difficult to calculate a forecast. Large coefficients of variation arise not least due to individual, perhaps rather infrequent, large issues. Wherever possible, large issues should be considered as outliers or as abnormal demand and should be taken out of a stochastic technique by a demand filter[note 1010] and made available to deterministic materials management. This could be achieved by increasing delivery periods for large orders, for example. Figure 10.5.2.4 shows this situation.

**Fig. 10.5.2.4** Discontinuous demand as an effect of rather infrequent, large issues.

- In the case of a stationary process, for example, constant demand, the relative forecast error depends heavily on the number of events, such as the number of orders. Generally, the actual forecast error is larger than that calculated by extrapolation. This is so because changes in the underlying regularities increase error, given that the number of events is small.

Whether demand will appear as continuous or discontinuous also depends upon the choice of the length of the statistical period. Figure 10.5.2.5 shows this effect.

**Fig. 10.5.2.5** Effects of length of statistical period on demand fluctuations.

If the statistical period chosen is too short, this quickly results in discontinuous demand values. These fluctuations are exaggerated and can be leveled by extending the statistical periods. However, the result in materials management may be an increase in levels of goods in stock or work in process, especially if the lead times are shorter than the statistical periods. For practical reasons, a unified length of the statistical period for the entire product range is required. Often, a period of one month is chosen.[note 1011] Even if there is rather discontinuous demand for an individual item, demand for the entire item family may be continuous. In this circumstance, the forecast would be accurate enough for rough-cut planning. If the need for more detailed information should arise, the allocation of the forecast to the various items of the family may be difficult. See also Section 13.2.

## 10.5.3 Demand Forecasting of Variants of a Product Family

Often variants of a product are derived gradually from one basic type, a standard product with options or a product family. Often, a forecast can predict the total demand for a product family. Deriving the demand for components that are the same for all variants is no longer very difficult. Demand forecasting for variants is more difficult. When the number of delivered variants of a product family is large enough, the use of variant items — related to 100 units of the product family, for example — can be recorded in a statistic and used for management.

Theoption percentageOPC is the frequency with which a variant item is used within a product family.

This percentage varies from time period to time period and is therefore a stochastic variable that can be described with expected value and variance. Often, in practice, the dispersion of the option percentage is not taken into consideration; that is, E(PF) is treated as a quasi-deterministic value. This increases the risk of stock failures. To calculate option percentages, sales are subdivided by statistical period. For each period, we determine the actual frequency of use and calculate mean and standard variation from the results of multiple periods. Linking the forecast for the product family with the option percentage for demand for variants is achieved by using the formulas in Figure 10.5.3.1. These formulas are used for every periodic demand.

**Fig. 10.5.3.1** Forecasting demand for variants.

The proportional-factor-weighted demand (expected value and variance) for the product family is the independent demand for a variant. Because of safety demand calculation, the sum of variant demands is greater than the demand for components not dependent upon variants.

For a more in-depth consideration of the formulas in Figure 10.5.3.1, see the footnote.[1]

[1] The following derivation of Prof. Büchel’s formula for multiplicative coupling x of two independent distributions y and z, x= y*z, provides a more in-depth consideration of the matter. See also [Fers64]. Multiplication of a particular value Y of y by z results in a linear transformation of z with the following parameters:

E(Y*z) = Y * E(z) , VAR(Y*z) = Y^{2} * VAR(z) .

The distribution obtained in this way is weighted by f(y) and summed (or, with continuous distributions, integrated) to create a mixed distribution. The zero moments are to be applied for this. The result of the individual linear transformations for the second zero moment — defined as E(u^{2}) = E^{2}(u) + VAR(u) — are as follows:

E((Y*z)^{2}) = E^{2}(Y*z) + VAR(Y*z) = Y^{2} * E^{2}(z) + Y^{2} * VAR(z) = Y^{2} * (E^{2}(z) + VAR(z)) = Y^{2} * E(z^{2}) .

The summation produces the following result:

E(x) = E(y) * E(z) , E(x^{2}) = E(y^{2}) * E(z^{2}), and so the following hold:

VAR(x) = E(x^{2}) – E^{2}(x) = E(y^{2}) * E(z^{2}) – E^{2}(y) * E^{2}(z) = [E^{2}(y) + VAR(y)] * [E^{2}(z) + VAR(z)] – E^{2}(y) * E^{2}(z) = E^{2}(y) * VAR(z) + VAR(y) * E^{2}(z) + VAR(y) * VAR(z).

CV^{2}(x) = VAR(x) / E^{2}(x) = [E^{2}(y) * VAR(z) + VAR(y) * E^{2}(z) + VAR(y) * VAR(z)] / [E^{2}(y) * E^{2}(z)] = CV^{2}(z) + CV^{2}(y) + CV^{2}(y) * CV^{2}(z).

*Note*: The formulas in Figure 10.5.2.2 can be derived analogously. Linear transformations are replaced by the distributions for the sum of multiple issues per period (so-called convolutions), whose parameters are determined as follows:

E(n*z) = n * E(z); VAR(n*z) = n * VAR(z)

A general statement as to the form of the distribution cannot be made; a log-normal distribution (which becomes a normal distribution with small coefficients of variation) represents a useful approximation for practical application. When there are many periods with zero issues (low issue frequency), special consideration of the choice of “risk” may be required.

This is also true for Section. 10.5.2. However, the planning periods, not the statistical periods, are decisive.

## 10.5.4 Safety Demand Calculation for Various Planning Periods

Aplanning periodrepresents the time span between “today” and the point in time of the last demand that was included in a specific planning consideration.

Figure 10.5.4.1 provides a few definitions required for the following discussion.

**Fig. 10.5.4.1** Definitions of variables for safety calculations.

In a forecast calculation, we determine expected value and standard deviation for a particular statistical period, for example, the SP. In materials management, however, it is necessary to have values for various planning periods. If, for example, the planning period is the lead time, then we have to take the total forecast demand during the lead time into consideration. Usually this is up until the receipt of the production or procurement order.[note 1013]

We can infer the formulas shown in Figure 10.5.4.2 on the basis of the models developed in Section 10.5.2; the formulas are also valid for the non-integral proportions of PP:SP.

**Fig. 10.5.4.2** Expected value and standard deviation with continuous demand.

In a nonstationary process, different expected values or standard deviations arise for various time periods in the future. Assuming independent forecast values in individual periods, the expected values and variances of demand can be added during the planning period. For n statistical periods, this produces the formulas shown in Figure 10.5.4.3.

**Fig. 10.5.4.3** Expected value and standard deviation over n statistical periods.

We can also use these formulas for certain periods, usually in the near future, where the demand has been established deterministically, that is, through customer orders, for example. The demand for these periods demonstrates a 0 variance. Similarly, a linear interpolation of the expected value and variance is used to determine intermediate values during a period.

## 10.5.5 Translation of Forecast into Quasi-Deterministic Demand and Administration of the Production or Purchase Schedule

The (stochastic) independent demand to be considered for further planning steps results as the total demand from adding the expected value to the safety demand for the planning period to be covered.

Thesafety demandis the product of the safety factor and the standard deviation during the planning period to be covered.

Figure 10.5.5.1 shows the total demand to be considered as a function of the planning period to be covered. For products manufactured in-house, this total demand belongs to the *production schedule*. For purchased items, the independent demand belongs to the *purchase schedule* for salable products*.*

**Fig. 10.5.5.1** Independent demand as total demand, taken as a function of the planning period to be covered.

If the total demand is subdivided into various partial demands later (for example, the annual demand into 12 monthly demands), a larger share of the safety demand needs to be included in the earlier partial demand. The order point technique discussed in Section 11.3 adds the safety demand de facto to the first partial demand.

Note: As presented in connection with Figure 5.3.2.2, the first step in determining high-cost dependent, but discontinuous or unique demand for an item is to stochastically determine the independent demand belonging to it. After this, the dependent demand is calculated using quasi-deterministic bill-of-materials explosion. In this way, the dependent demand contains the safety demand needed to produce the safety demand for the independent demand.

For *administrating independent demand,* an order-like *object class forecast demand* or *independent demand *is used, with at least the attributes

- Forecast or independent demand ID (similar to an order ID)
- Item ID or item family ID
- Planning date for the demand or its periodicity
- Forecast quantity (an item issue)
- Quantity of the forecast already “consumed” by orders (see Section 12.2.2)

A negative forecast demand is also conceivable. It would express receipt of an item, and serves, e.g., as a substitute for a purchase system that is lacking, or to eliminate an overlap effect on lower structure levels from higher structure levels (see, for example, Section 7.2.1).

There are a number of ways to change or delete a forecast demand:

- By manual administration.
- By periodic recalculation, e.g., according to the principle contained in Figure 10.1.1.1. This is particularly important for demand serving as input to subsequent stochastic materials management.
- With independent demand in the true sense: by successive reduction due to actual demand (e.g., customer orders). If the actual demand reaches the forecast, or if the forecast lapses into the past and is no longer to be considered, the corresponding forecast demand object is automatically deleted. See also Section 12.2.2.

## Course sections and their intended learning outcomes

##### Course 10 – Demand Planning and Demand Forecasting

Intended learning outcomes: Produce an overview of forecasting techniques. Explain history-oriented techniques for constant demand in detail. Identify history-oriented techniques with trend-shaped behavior. Describe three future-oriented techniques. Disclose how to use forecasts in planning.

##### 10.1 Overview of Demand Planning and Forecasting Techniques

Intended learning outcomes: Produce an overview on the problem of demand planning. Present the subdivision of forecasting techniques. Disclose principles of forecasting techniques with extrapolation of time series and the definition of variables.

##### 10.2 Historically Oriented Techniques for Constant Demand

Intended learning outcomes: Describe the moving average forecast. Explain the first-order exponential smoothing forecast. Differentiate between the moving average forecast and the first-order exponential smoothing forecast.

##### 10.3 Historically Oriented Techniques with Trend-Shaped Behavior

Intended learning outcomes: Explain the regression analysis forecast and the second-order exponential smoothing forecast. Describe the Trigg and Leach adaptive smoothing technique. Produce an overview on seasonality.

##### 10.4 Future-Oriented Techniques

Intended learning outcomes: Explain the trend extrapolation forecast and the Delphi method. Describe scenario forecasts.

##### 10.5 Using Forecasts in Planning

Intended learning outcomes: Produce an overview on the choice of suitable forecasting technique. Describe consumption distributions and their limits, continuous and discontinuous demand. Explain demand forecasting of variants of a product family. Present safety demand calculation for various planning periods. Disclose the translation of forecast into quasi-deterministic demand.

##### 10.6 Summary

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##### 10.7 Keywords

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##### 10.8 Scenarios and Exercises

Intended learning outcomes: Choose an appropriate forecasting technique. Calculate an example for the moving average forecasting technique and for the first-order exponential smoothing technique. Differentiate between the moving average forecast and the first-order exponential smoothing forecast.

##### 10.9 References

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##### Case [Course 10]

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