How to build performance formula with BSC Designer
Intro
While working under creating and setting key performance indicators of business performance specialists might face such problem as sophisticated non linear function to be used (especially for financial perspective). As it is written in the paragraph called “Optimization direction” of the article “How to manage indicators and performance values with BSC Designer”, by default settings program offers two optimization directions: minimization and maximization, both linear. But using special mathematical formula builder the range of formulas that could be created and used for any indicator is actually wide.
Certainly BSC Designer does not aim to be huge mathematical tool and calculate sophisticated formulas with tens of variables but it steel has a powerful function aimed to build any mathematical formula to calculate performance within each of indicators. There are just three variables in use but it could be operated by any combination of over eight mathematical functions! Let’s find out what does any of those variables and functions mean and how to create formulas using those builder.
Formula builder
To show builder interface run BSC Designer and select any indicator in the project’s tree. Then look at the bottom panel, find “Optimization” field and click on the little button (with an image of sum) right near to it. A new dialog window will appear – this actually is a mathematical formula builder. Let’s look at every element that could be used in this builder.
Variables
There are just three variables in BSC Designer which could be used in mathematical formulas:
- Minimal Value / Min value = mn (builder syntax). This variable is set by the user for each indicator and shows the smallest value it could be equal. By default a new indicator has a minimal value of “0” but it also could be set as a negative number (for example mn = -493). Measure unit for this variable is real number but smaller then maximal value;
- Maximal Value/ Max value = mx (builder syntax). This variable is also set by the user for each indicator and shows the biggest value it could be equal. By default any new indicator in BSC Designer has a maximal value of “100” but it could be changed into any integral or fractional number both positive and negative (for example mx = 73834.04). Measure unit for this variable is real number but bigger then minimal value;
- Current Value / Score Value = Score (builder syntax). This variable could be set by the user, might be imported from other *.bsc project (using feature called imported indicator; read more in the article Cascading process in company with BSC Designer) or might be imported from any database (using feature called SQL indicators; read more about this feature in the article SQL indicators with BSC Designer) for each indicator and shows current value and indicator equals for the certain date. By default a new indicator in BSC Designer has a current value of “50” but it could be changed by the user or imported from other project or database. Score might equal integral or fractional number both positive and negative (for example Score = 203.7). Measure unit for this variable is real number but it should fit into interval between minimal value (mn) and maximal value (mx).
Operators
Formulas builder in BSC Designer support common mathematical operators. Anyway sometimes it could be hard to say with symbol from “Qwerty” keyboard means some mathematical operator so it is described in the list of operators below:
- “+” – Addition. The mathematical process of combining quantities. For example: 3 + 5 = 8;
- “-” – Subtraction. The inverse of addition, the process of removing one number from another. For example: 8 -5 = 3;
- “*” / “(a)(b)” / “ab” – Multiplication. The operation of scaling one number by another. For example: 2 * 2 = 4;
- “/” – Division. The inverse of multiplication, the process of dividing one number (dividend) by another (divisor).The divisor could not equal 0. For example: 4 / 2 = 2.
Functions
The button named “Function” located under “Formula” field offers several common mathematical functions that operates with the real numbers and variables in different combinations. The list of those functions with little descriptions for each of them is presented below:
- Sin (a) – The sine trigonometry function. For example: Sin (30) = 0.5;
- Cos (a) – The cosine trigonometry function. For example: Cos (0) = 1;
- Tan (a) - The tangent trigonometry function. Also could be operated as (Sin (a)) / (Cos (a)). For example: Tan (0) = 0;
- Power (a, b) – Exponentiation with the base of “a” and the exponent of “b”. For example: power (2, 4) = 16;
- Exp (a) – Exponentiation with the base of “e” (a constant number, approximately equals 2.7182818) and the exponent of “a”. For example: Exp (2) = 7.389056 (approximately);
- Sqrt (a) – Exponentiation with the base of “a” and the exponent of “0.5”. Also called a square root. For example: Sqrt (16) = 4;
- Min (a, b) – The function selects the smallest among two numbers. For example: Min (3, 5) = 3;
- Max (a, b) – The function selects the biggest among two numbers. For example: Max (3, 5) = 5;
- Pi – is not actually a function but a number. Pi is a known constant which is approximately equal to 3.14159.
Default formula
This is the main field of the whole builder. Information might be input here manually or with help of buttons above. By default it contains linear formula of maximization ((Score – mn) / (mx – mn)) or minimization ((mx – Score) / (mx – mn)). But some elements could be added as well as the whole formula could be changed. The finished formula might contain any combinations of available functions, numbers and variables that could ever be executed in math. Several examples are listed below (images of the optimization graph and the functions under it).
Default maximization formula = ((Score – mn) / (mx – mn))
Formula = (sin(Score/mx*2.5) – mn) / (mx – mn)
Formula = tan( ((Score) – sqrt(mn)) / (mx – mn) )
Formula = min((exp(Score)*exp(mx)),Power( sqrt(score),Pi)*0.9)
Conditions
There are also special conditions available for the variable called “Score”. Main function (on top) is working for any interval of “Score” except for those that are noticed below it. So if the function of optimization should change if current value riches some line (for example if it becomes more then 45) it might be easily programmed with BSC Designer’s formula builder. Click on “Add Condition” button, input new function that should be executed after current value is more then 45, select “>” operator and “45” in number field.
Setting up the condition
The performance graph for this function (after score riches 45 and more the graph begins to fluctuate)
Conclusion
That is how to use the powerful feature of Balanced Scorecard Designer called mathematical formula builder. Knowing meaning of each of the operators, functions and variables it becomes quite clear how to create even sophisticated formulas to calculate some special indicators’ performance. It also needs to be noticed that after the formula and conditions are set it will be no need to open this builder - the program will calculate everything automatically.
It needs to be noticed that the examples in this article are random and sure could be used for serious projects. It is up to company’s specialists what formulas and conditions are needed to be used for every indicator. Practically most of the indicators are calculated using default linear functions of maximization or minimization score. But if some more specific formula is needed to be used our client might open this article and BSC Designer’s formula builder to create it. If it happens that our builder does not support some mathematical operators you need or you still cannot create a proper formula ask our support team (the support form could be found on this page) to help you to find the solution.
