In the context of data analysis, the term Artificial Intelligence (AI) describes that a general rule about the connection between data or the effect of data on each other is automatically derived from a large amount of data.

To put it bluntly, one tries to use standard algorithms and methods (such as neural networks, multidimensional optimization, etc.) to gain core information from data about whose connection or effect almost nothing is known.

**NLPP application:** NLPP uses algorithms that can definitely be assigned to the class of AI processes. A big advantage of our algorithms is that they are all mathematically proven and it is therefore clear why they work. Furthermore, it can be proven that the algorithms deliver optimal results without the need for thousands of training data.

A benchmark is a standard of comparison, i.e. a value against which another value is compared.

When it comes to prices, it is often of interest to know how the price in focus (purchase price, sales price, offer price, etc.) compares to other prices. You would like to make a statement like "My price is good/normal/bad compared to all other prices" and also be able to state the deviation from the benchmark, preferably in the form of a monetary amount.

You can calculate benchmarks in many different ways. The type of calculation alone already has a major influence on the result. Here's an example: Let's assume our prices that we want to calculate a benchmark for are: "1, 2, 3, 4 and 1000".

Depending on how we calculate the benchmark, very different numbers come out:

1. Normal average (arithmetic average) = sum of all numbers divided by the number = (1+2+3+4+1000) / 5 = 202

2. Median = the middle element = the value in the third position = 3

Intuitively, the median "fits" better than the average in our example. The problem, however, is that intuition fails with many numbers. It is therefore very important to understand how a benchmark is calculated and what influences the result in one direction or another.

The average is generally not a good calculation method for price benchmarks. Since all values - including the outliers - are included in the calculation, there is a considerable risk of obtaining a benchmark value that is too high. The result: In the case of purchase prices, the benchmark falsely gives the buyer a good feeling ("we procured the parts at good prices"), and in the case of sales prices it leads to non-competitive prices ("we are a little below average with our offer") .

**NLPP application:** NLPP uses a "distortion-free" calculation method that delivers optimal benchmark values. Furthermore, NLPP provides not only one benchmark value, but three: "Best Practice", "Market" and "Worst Practice". We also call these "Green Line", "Blue Line" and "Red Line" benchmarks. This type of benchmark calculation allows us to specify a target price range. And this range is considerably more realistic than just a single benchmark value.

A "Best in Class" benchmark tries to deliver a benchmark for a subset of the data (e.g. all products with a price between 10 EUR and 20 EUR) which represents the best price. This procedure is mostly used when it is unclear how an overall benchmark could be calculated.

The problem with "Best in Class" benchmarks is that one can ask the question why the subset for the calculation was chosen in this way and not otherwise? What happens to the "Best in Class" benchmark if you define the subset differently?

**NLPP application:** Our solution does not use a "best in class" benchmark, but calculates several benchmarks (Green, Blue and Red Line) for the entire product portfolio.

Target price calculated using a performance pricing model, which corresponds to the best price-performance ratio to be expected on the market.

When calculating best practice benchmarks, it is important that all data are included in the calculation. Calculating the best practice benchmark only on the basis of the "best 20% prices" is mathematically nonsensical, since you cannot calculate a benchmark for one subgroup and then apply it to another subgroup.

Here's an example: We calculate the average size of a professional basketball team ("best practice" benchmark) and compare this value with an elementary school team. The result is of course devastating, but also mathematically nonsensical.

**NLPP application:** From the NLPP input data, the software calculates the Green Line, i.e. the "Best Practice" benchmark line, which serves as a benchmark. It separates the top products – here: the preferred 25% of products with the best price-performance ratio – from the rest of the products.

The "least squares method" (LSM for "Least Square Method") is a standard estimation method to minimize the deviations of the predicted values from the actual values in the context of a regression analysis (search for a regression formula). "The sum of all deviations between the actual value and the predicted value squared" is used.

Squaring the values ensures that positive values are always obtained (example: -2^2 = 4). This is necessary because there are both upward (i.e. positive) and downward (i.e. negative) deviations from the actual value. If only the deviations were added, the positive and negative values would cancel each other out.

The "least squares method" is the simplest estimation method for a regression analysis.

**NLPP application:** Since the "least squares method" is not suitable for all situations, NLPP also supports two other estimation methods. Practical experience shows that the "least squares method" only delivers an optimal result in very few cases. Most of the time, the other NLPP estimation methods are superior.

The term cost analysis summarizes procedures and methods that analyze how the costs (and thus later also the prices) of a product are made up. The aim is to understand which areas (material, production costs, overhead costs, profit, etc.) account for what proportion of the total costs or the sales price and whether this proportion is understandable and justified.

For this purpose, a workshop is often held at the supplier's in order to get an on-site picture of the processes and to be able to depict the organizational structure of the supplier in the calculation used.

**NLPP Application:** NLPP rates products based on value for money. It doesn't matter how the costs of a product are distributed. It's all about finding out whether or not you, the buyer, are getting value for the price you paid.

Reference variable (parameter, product feature, product property) whose change also changes the price of a product. For example, the performance of a car is a price driver, because the general rule is: the higher the performance, the more expensive the car.

If costs are used instead of the price, then the reference values used are referred to as cost drivers. This makes a clear distinction between price and costs.

See also: value drivers / performance drivers / price drivers

**NLPP application: **The performance drivers used are usually also price drivers, because the better the performance of a product, the higher the price.

Simple form of performance pricing, which can only depict linear relationships between product properties and the price. Linear means that every change in a product property by one unit changes the price by a fixed amount.

Example: 1 kg of apples = 1 EUR, 2 kg of apples = 2 EUR, 3 kg... where the product property is the weight (in kg) and the constant change is 1 EUR per 1 kg.

Problems arise when the constant price change is larger than the product price, because then negative prices are predicted. Example: constant price change = 5 EUR and product price = 2 EUR. Now, if the product property is reduced by one unit, the price is reduced by 5 EUR. This leads to: EUR 2 + EUR -5 = EUR -3 - Negative product prices certainly do not make sense.

NLPP application: As the name NLPP suggests, NLPP also supports non-linear performance pricing procedures in addition to the LPP procedures. These have the advantage that the problem of negative target prices shown above cannot occur.

Describes how the result formula is structured. In a linear regression, this always has the following structure:

(Factor-1 * Parameter-1) + (Factor-2 * Parameter-2) + ...

One or more multiplications are always added. It does not matter whether the parameters used are squared again or transformed in some other way. The basic structure is and remains linear.

**NLPP application: **Three linear regression methods are supported. Tests have shown that in around 30% of all cases, linear models deliver the best result, i.e. the best target price formula.

NLPP application: Three linear regression methods are supported. Tests have shown that in around 30% of all cases, linear models deliver the best result, i.e. the best target price formula.

NLPP application: NLPP is an MCA/MCDA procedure, as several criteria (value drivers) are used to evaluate the price-performance ratio of products. Compared to classic MCDA methods, NLPP is even more stringent, since the parameters do not have to be weighted manually.

The term MLPP is misleading or is used in an ambiguous and incorrect way.

Multi/... Linear Performance Pricing (MLPP) simply means that multiple parameters (multi) can be used in an LPP analysis. See also the term multiple regression. However, almost all meaningful performance pricing analyzes always require more than just one parameter. Therefore, the term MLPP should perhaps sound better than LPP.

From time to time one also comes across the term "multivariate analysis systems" - however, this is a method that plays no part in performance pricing. In multivariate regression analysis, not only one dependent variable (in the case of performance pricing this would be the price) but several dependent variables (i.e. a vector) are determined.

**NLPP application: **All regression methods available in NLPP are multidimensional, i.e. they correspond to a multiple or multidimensional regression.

Regression analysis can be performed with one or more parameters. For example, the formula "price = 1.5 * weight" is the result of a one-dimensional regression analysis. As soon as more than one parameter is used, one speaks of a multidimensional or "multiple regression".

In practice, solutions that can only take one parameter into account are not practical because the results are too imprecise.

NLPP application: All regression methods available in NLPP are multidimensional, i.e. they correspond to a multiple regression.

Describes how the result formula is constructed. In the case of a non-linear regression, this has a considerably more complex structure than in the case of a linear regression. Mathematical operators such as ln(x), e(x) or sin(x) are also used - very flexibly depending on the application - which increases the quality and significance of the data analysis.

**NLPP application:** Three different non-linear regression methods are supported. Tests have shown that non-linear methods deliver better results than linear methods in about 70% of all cases.

The most powerful form of performance pricing, which depicts both linear and non-linear relationships between product properties and the price. Non-linear means that each change of a product property by one unit can change the price by different amounts.

Since various mathematical operators and functions are used in the target price formula, it can map the structure of the input data much more flexibly and therefore deliver much better results.

Problems such as negative target prices, which can arise when using purely linear methods, do not exist with non-linear methods. These always deliver positive target prices.

**NLPP application:** NLPP is the only application on the market that currently supports three different non-linear methods and thus delivers significantly better results in the form of precise and realistic target prices than solutions that only involve linear methods.

Method based on regression analysis used in purchasing, development and sales to evaluate different products or services in terms of price and performance.

A performance pricing analysis requires properties, quantities and prices of products as input data. This data is then used to calculate how the properties affect the price.

There are many different ways in which a performance pricing calculation can be carried out. A distinction is made as to whether the target price formula uses a linear or non-linear structure. Furthermore, the procedures differ in the type of methods used to find out how product properties affect the price.

The simplest type of performance pricing is the "LPP-LSM" method. LPP stands for "Linear Performance Pricing" and LSM for the "Least Square Method".

The LPP-LSM method has not proven itself in practice because the relationships between product features and price cannot be correctly mapped with this simple method. For example, it can happen that LPP-LSM results predict negative target prices for products.

**NLPP application**: NLPP implements a total of 6 different performance pricing methods and automatically uses the method that delivers the best target price formulas.

The term predictive costing refers to various procedures and methods with the help of which one would like to make a prediction about prices/costs. The aim is to use as little known information as possible to predict the future price or future costs as best as possible.

**NLPP application:** The target price formula calculated by NLPP enables simple, fast and highly precise predictive costing: The user simply enters the parameter values of the part for which a target price or target costs are to be estimated.

The term price analysis describes procedures and methods to find out whether a price is appropriate and fair in relation to the service delivered or the value delivered. However, price analysis is not just a simple comparison of prices from different offers. The spectrum of methods is large and includes, for example: classic benchmarking with other companies, calculation of average prices, analysis of the competition or analysis of customer benefits.

Price analysis is all about finding out whether or not you, the buyer, are getting reasonable value for the price you paid.

**NLPP Application: **NLPP rates products based on value for money. For this purpose, NLPP calculates how strongly important product properties influence the price. With this knowledge, it is then possible to calculate the fair price of a product and compare it with the current price.

Many analysis methods provide a target price. However, it is clear that it is impossible to calculate an exact target price. Rather, price ranges are of interest. Such a price range indicates which maximum and minimum prices can be expected. This type of specification is considerably more practical and also more realistic. On the one hand, it is easier to estimate where the current price is compared to the price range, and on the other hand, the price changes to be expected can be estimated more easily.

**NLPP application: **Three target prices are always calculated for each part number. These form a target price range, which indicates the most likely target price to be expected, as well as a price upper limit (worst practice) and a price lower limit (best practice). Furthermore, three benchmark lines are displayed graphically, so that a quick assessment of the current situation is possible at a glance.

Price inconsistency occurs when the actual prices for a group of parts (e.g. all parts from a supplier) do not have a logical pricing structure compared to the calculated target prices. Parts that should have a low price according to the NLPP target price calculation are currently much more expensive, parts that should have a higher price according to the target price calculation are currently cheaper.

A price inconsistency indicates that the supplier's pricing does not follow a comprehensible structure but is highly influenced by chance.

**NLPP application:** With NLPP and the three benchmark lines "Worst Practive", "Market" and "Best Practice" price inconsistencies can be determined and evaluated very quickly.

Collective term for all types of NLPP formulas such as target price formula, target cost formula, etc. that are calculated on the basis of the data used.

NLPP application: Since the NLPP method is universal, the meaning of the calculated formula is defined by the input data used by the user and is not specified by the software.

If component "price information" uses HK cost, then you get a target "HK cost" formula. When you use sales prices, you get a target "sales prices" formula.

R2, also called the coefficient of determination, is a mathematical number that is often used incorrectly to determine the quality of a linear regression model. The wrong rule "the higher R2, the better the result" is used. Our experience shows: R2 is certainly one of the most frequently misused key figures in mathematics. R2 says nothing about whether a price driver has a high or low

Influence R2 cannot make any statement on multicollinearity (=whether two or more price drivers correlate or have a dependency).

R2 gets bigger the more price drivers you use, regardless of whether or not the model can really explain the data better. With the help of "corrected coefficients of determination" one tries to get this under control - which unfortunately does not work, since the basic problem of R2 is not addressed.

Interestingly, there is very little correct and in-depth information in the literature showing that R2 is totally inadequate to assess the quality of a regression analysis. However, there is a very good summary by Clay Ford (Statistical Research Consultant, University of Virginia) based on a lecture by Cosma Shalizi (Associate Professor, Statistics Department, Carnegie Mellon University). This clearly shows why R2 is nonsensical (see: http://data.library.virginia.edu/is-r-squared-useless/ )

What nonsensical correlations and conclusions can be drawn with a focus on R2 can be found at http://www.tylervigen.com/spurious- see correlations very nicely.

**NLPP application: **With NLPP we have solved all the problems of R2 and use working and significantly better methods to evaluate the quality of the result. The advantage of our approach is that you always get the best possible target price formula for the data you analyze with NLPP.

Regression analyzes are statistical analysis methods that aim to model relationships between a dependent variable and one or more independent variables. In the context of performance pricing, the dependent variable is price and the independent variable(s) are product characteristics. The result of a regression analysis is a regression model, which consists of a formula that uses the independent variables to calculate the dependent variable.

Example: price = 0.234 * length + 1.687 * quantity + 7.432 * weight

There are many different regression analyses/regression procedures (see "Linear Regression" or "Non-Linear Regression"), as not every regression procedure is suitable for every situation. The result can only be trusted if a regression method appropriate to the situation is used.

**NLPP application:** NLPP uses regression analysis to calculate how strong the influence of product properties is on the price. Six different regression methods are used to calculate the best possible target price formula. This is necessary because it is impossible for a single regression procedure to provide correct results in all situations.

The term shadow calculation includes all processes and methods to estimate the "ideal price" of a component. For this purpose, an ideal-typical production and its cost structure are shown. The aim is to understand as well as possible which areas (material, production costs, overhead costs, profit, etc.) account for what proportion of the total costs in order to have a better basis for negotiating with the suppliers on this basis and with the knowledge of the ideal component price.

NLPP application: NLPP evaluates products based on the price-performance ratio based on user data. Apart from a few details about part properties, the purchase quantity and the current price, no further information is required. Expert know-how to recreate a production is not necessary when using NLPP. By using market data, the target price calculated by NLPP can be implemented very precisely and realistically.

All types of procedures and methods used to estimate an "ideal price" or the "ideal cost" of a component. There are various approaches that differ in terms of the required training time, implementation time, focus (one item number, entire parts portfolios, etc.).

**NLPP application:** NLPP uses the idea of "performance pricing" to calculate a precise target price. The idea is based on the rule that a better product usually costs more. In contrast to most methods, the basis for evaluation is the performance - i.e. the value of a product for the customer - and not the required use of resources by the manufacturer (the classic calculation of the manufacturing costs is such).

Reference variable (parameter, product feature, product property) that changes the value of a product positively/negatively.

**NLPP application: **NLPP can be used to find out how changing a value driver affects the price of the product. If this connection is clear, each product can be evaluated according to price/performance. NLPP thus shows whether a reasonable value or a reasonable service is provided for the price paid.

Target price calculated by a performance pricing model, which corresponds to the most expensive expected price-performance ratio on the market. Under no circumstances should more be paid for a product than the determined worst practice target price.

When calculating worst practice benchmarks, it is important that all data are included in the calculation. Calculating the worst practice benchmark based only on the "worst 20% prices" is mathematically nonsensical, since you cannot calculate a benchmark for one parts group and then apply it to another parts group.

Here's an example: We calculate the average size of a professional basketball team (benchmark) and compare this value with an elementary school team. The result is of course devastating, but also mathematically nonsensical.

**NLPP application:** Benchmark line calculated from the NLPP input data, which serves as a benchmark. It distinguishes the most expensive products - here: the 25% of products with the worst price-performance ratio - from the rest of the products.

Price of a product (part, assembly, unit, component, machine, etc.) which was estimated using a method such as performance pricing and serves as the basis for estimating a "good price".

If a reliable target price can be estimated easily, quickly and precisely, this is of great benefit to companies, as it is clear in every phase of the product life cycle whether the current price is too high.

**NLPP application:** NLPP calculates three target prices per product based on very precise target price formulas. The key here are the three precise NLPP target price formulas for best practice, market benchmark and worst practice.

Contractually fixed individual prices offer price certainty for the current procurement portfolio. Target price formulas go one step further: they also set the price range for new/future parts.

This pays off above all if the product portfolio to be procured could change significantly within the contract period. Frequently affected are product groups with a high variance in part numbers, e.g. B. screws or labels.

With target price contracting, buyers include this effective protection against such future price surprises in their contracts.

**NLPP application:** NLPP calculates very precise target price formulas for a product family, which can then be used in contracts.

In addition to the mathematically optimal result, the user can also calculate simple target price formulas and specify which parameters should be included in the target price formula. NLPP thus offers the greatest flexibility for switching from prices per item number to target price contracting.

A formula that calculates a target price based on some information about a product.

The classic manufacturing cost calculation (HK calculation) also represents a target price formula - albeit one that includes many parameters and that cannot be "just like that" written down on a piece of paper.

Target price formulas use most product properties such as dimensions, weight, materials, etc. as parameters. These parameters are easy to collect and therefore a target price formula is easy to apply.

The challenge is to calculate a target price formula that is as accurate as possible from the given data. This requires complex mathematical processes. The basic idea of these methods is regression analysis.

**NLPP application:** Basically, NLPP provides three target price formulas, each of which corresponds to a price benchmark and - viewed together - result in a price range. The advantage is that a much more realistic assessment of the current price is possible with the help of a range of target prices. NLPP guarantees that the best possible target price formula is found automatically from the data used.