Best Worst Method | A multi-criteria decision-making method

Best-Worst Method (BWM) is a multi-criteria decision-making (MCDM) method developed by Jafar Rezaei (Delft University of Technology) in 2015.

What is a multi-criteria decision-making (MCDM) problem?

An MCDM problem is a problem where a number of alternatives (options) need to be evaluated with respect to a number of criteria (attributes) in order to (i) select the best alternative, or (ii) rank all the alternatives, or (iii) sort the alternatives into a number of classes.

An MCDM method is a method to find a solution for (one or more parts of) an MCDM problem, where the main phases are:

Formulate the problem (identify the goal(s); alternatives; and criteria),
Evaluate the alternatives with respect to the criteria,
Find the importance of the criteria,
Synthesis the data collected in the previous phases to find a solution,
Check the reliability and validity of the outcome.

These phases are executed with a close interaction between the decision-maker(s)(DMs) and the analyst.

BWM is an MCDM method which can be used in several phases of solving an MCDM problem. More specifically it can be used to evaluate the alternatives with respect to the criteria (specially in the cases where objective metrics are not available to evaluate the alternatives). It can also be used to find the importance (weight) of the criteria which are used in finding a solution to satisfy the main goal(s) of the problem.

BWM has been used to solve many real-world MCDM problems in the areas such as business and economics, health, IT, engineering, education, and agriculture. In principle, wherever the aim is to rank and select an alternative from among a set of alternatives, this method can be used. It can be used by one decision-maker or a group of decision-makers.

How does BWM work?

See the page Slides and Papers, and BWM Solvers.

Why BWM?

BWM is a pairwise comparison-based method that offers a structured way to make the comparisons. This structure brings several major benefits [1]:

By identifying the best and the worst criteria (or the alternatives) before conducting the pairwise comparisons among the criteria (or the alternatives), the DM already has a clear understanding of the range of evaluation which could lead to more reliable pairwise comparisons. This, in turn, implies more consistent pairwise comparisons, which has been shown in the original BWM study.

The use of two pairwise comparisons vectors formed based on two opposite references (best and worst) in a single optimization model could mitigate possible anchoring bias that the DM might have during the process of conducting pairwise comparisons. This so-called consider-the-opposite-strategy has been shown to be an effective strategy is mitigating the anchoring bias.

In pairwise comparison-based methods we either have methods for which we use a single vector (e.g. Swing and SMART family) or a full matrix (e.g. AHP). Although using one vector for the input data makes the method very data(and time)-efficient, the main weakness of methods based on only one vector is that the consistency of the provided pairwise comparisons cannot be checked. On the other hand, although using a full matrix provides the possibility of checking the consistency of the provided pairwise comparisons, methods which are based on full pairwise comparison matrix are not data(and time)-efficient. Asking too many questions from the DM, which occurs in the case of full matrix, might even contribute to the confusion and inconsistency of the DM. BWM stands in the middle. That is to say, it is the most data(and time)-efficient method which could, at the same time, provide the possibility of checking the consistency of the provided pairwise comparisons. As the two vectors are formed with considering two specific reference criteria (or alternatives), BWM should not be seen as a case of incomplete pairwise comparison matrix.

BWM (its original non-linear model), in the not-fully-consistent cases with more than three criteria (or alternatives) might bring about multiple optimal solutions. This is a reflection of the inconsistency which exists in the provided data. Having multiple optimal solutions (compared to a unique solution) brings more flexibility to the cases where there are multiple DMs involved. This means that in the context of group decision-making, having multiple optimal solutions (for all or some DMs) could result in a higher chance (compared to the case that each DM has a unique solution) for a compromise solution to coincide (or at least be very close) to one of the optimal solutions. Although having multiple optimal weights is advantageous in some cases, especially in group decision-making problems, where debating plays a central role, in other cases, having a unique solution is preferred. The linear BWM model provides a unique solution.

[1] Rezaei, J. (2020). A Concentration Ratio for Non-Linear Best Worst Method. International Journal of Information Technology & Decision Making, 19(3), pp. 891-907. [free to download here]