When you combine individual performance indicators to one key performance indicator, you can give each one a different weight. Now the question is how to derive the weights. For this a mathematical method is available called AHP. AHP stands for Analytic Hierarchy Process and the method derives ratio scales from paired comparisons. It also allows for some small inconsistency in judgment. As an input you can use actual measurements like price, weights and so on or subjective opinions like satisfaction feelings or preferences. And as an output you will get ratio scales and a consistency index. The method is based on the solution of an eigenvalue problem. The ratio scales result from eigenvectors and the consistency index from the eigenvalue. The process is done in several steps. First you have to define your objective. Then you structure the elements in groups of criteria, sub-criterea and alternatives. In each group you make a pairwise comparison of elements and calculate the weighting and consistency ratio. Then you can evaluate the alternatives according to the weighting and get a ranking. Let us take an example your objective is to buy a gadget like a smartphone or MP3 player. The criteria are the color of the model, the memory and the delivery time. As colors, pink, blue, green, black and red are available, the memory space range from 8 megabyte to 64 megabyte and delivery time is immediate five days or four weeks. Our models are available as shown here. Two models with a price of 120 and two models with a price of 150. These are your alternatives. Now in the first step you structure the elements in groups of criteria, sub-criterea and alternatives. The objective is to buy the gadget and your criteria are color, memory and delivery. To each criteria you have the sub-criterea, the colors, the memory space and the delivery times. You then have to compare all elements pairwise with respect to the objective. So in the first step you have to compare the criteria, color, memory and delivery. You start to compare color with memory and you are using a scale ranging from 9 to 1 over 9. One means both criteria have same importance they are equal. 9 means criteria color is 9 times more important than memory. One over 9 means memory is 9 times more important than color. So let's make the comparison. You compare color with memory and in your opinion memory is 3 times more important than color. So on the scale you will have 1 over 3. Then you compare color with delivery. You say delivery is 2 times more important than color. Then you get as a result 1 over 2. Memory and delivery are equal important in your opinion so you put in a 1. For 3 criteria you have 3 comparison. In the next step you arrange your comparisons in a matrix as shown in this slide. From this matrix you compute the normalized principle eigenvector. This can be done in an Excel calculation. An Excel sheet is available from the author. As a result you get the following waiting. Color 17% Memory 43% and delivery 40%. So the most important criteria is memory followed by delivery followed by color. Now you make the same pairwise comparison for the sub criteria in this case the different colors. For example you compare the pink color with blue color. You think pink is 2 times nicer than blue so you put in a 2. Pink compared to green in your opinion is pink 3 times better than green and so on. In total because you have 5 criteria you need to do 10 comparison. Again you arrange the result of the comparison in a matrix and compute the normalized principle eigenvector of the matrix. As a result you will get the percentages as shown here and now you wait the sub criteria according to the weights of the main criteria. The complete result will look like this and the next step is now to evaluate the alternatives. We have available model 1. The color is pink and pink has a weight of 2.2%. The memory space of model 1 is 32 megabyte. 32 megabyte has a weightage of 19%. The delivery time is immediate. Immediate has a result of 18%. So counting together you will get the first result of the benefit for model 1 with 39%. You do the same for all other models and then you will see that model 3 has the highest ranking. Probably you noticed that we didn't put in the price of the models as one of the criteria. The reason is very simple. If you separate the benefits from the cost we can do a cost benefit analysis. You can draw a diagram showing the benefits as a function of the relative cost of the models. So you put in the models according to the benefits resulting from the analysis over the relative costs. As it is shown here for model 1.2.4. Now let's assume you have only the selection of model 1 or 3. As you can see in the diagram, model 3 has similar benefits compared to model 1 but higher cost. Probably you would go for model 1 with immediate delivery and lower price. If only model 2 and model 4 would be available, then you can see that model 4 has significant higher benefits than model 2. Probably you would go for model 4 accepting the longer delivery and higher price. The method shown can be applied in many different fields. You can use AHP to evaluate product features to make a selection from strategic alternatives to select a set of key performance indicators or to make consolidated decisions with multiple inputs from different stakeholders.