A Handbook on Multi-Attribute Decision-Making Methods

5The Best–Worst Method (BWM)

5.1 Introduction

As established thus far a decision matrix plays a crucial rule in the multiattribute decision‐making (MADM) process. A decision matrix (D) is described as follows (Yu 1990):

(5.1)

in which a_i = the predetermined, feasible alternative; c_j = the predefined evaluation criterion determined by the decision‐maker; r_(i,j) = the normalized value of the ith alternative with regard to the jth criterion; m = the number of feasible alternatives; and n = the number of criteria. The decision‐maker attempts to choose the set of alternatives that would achieve the decision‐makers main objective or goal that can be portrayed via a set of predetermined criteria. The MADM philosophy prescribes that if the poor performance of an alternative with regard to one of the predefined criterion is compensated by the alternative’s good performance with regard to other criteria, such tradeoff can be accounted for by a compensatory method (Jeffreys 2004; Banihabib et al. 2017). Most compensatory MADM methods would attempt the aggregate the overall performance of each alternative through a weighting mechanism that assigns the proper weight to each of the predefined criteria. Such weighting mechanism is calculated mathematically as follows (Churchman and Ackoff 1954):

(5.2)

in which V_i = the overall performance of the ith alternative; and w_j = the weight assigned ...