Borda Count Method

Under the ranking method devised by Jean Charles de Borda (an eighteenth-century French physicist), the DM is asked to rank the p criteria from the most important (ranked first) to the least important (ranked last). The criterion that is ranked first gets p points, the one that is ranked second gets (p - 1) points, and the last place criterion gets 1 point. The sum of all the points for the p criteria is given by 

The criteria weights are then calculated by dividing the points assigned to criterion by the sum S, given by Equation 2.4. 

Let us illustrate the basic definitions (dominated, non-dominated, and ideal soluhons) and the two weighting methods with a numerical example. 

An industrial engineering (IE) department has interviewed five doctoral candidates for a faculty position and has rated them on a scale of 1-10 (with 10 being the best and 1 being the worst) on three key criteria— research, teaching, and service. The criteria values of the candidates are 

Determine the ideal solution to this problem. Is the ideal solution achievable  

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Hint Borda count method is discussed in Chapter 6, Section 6.3.4)... 

The five candidates are then ranked, using their scores, from the highest to the lowest. Thus, Candidate C is ranked first, followed by candidates A, E, D, and B, respectively. Borda count method Assume that the three criteria are ranked as follows ... 

When there are many criteria, it would be difficult for a DM to rank order them precisely. In practice, pairwise comparison of criteria is used to facilitate the criteria ranking required by the Borda count method. Here, the DM is asked to give the relative importance between two criteria Q and Cj, whether Q is preferred to Cj, Cj is preferred to Q or both are equally important. When... 

In this chapter, we discussed several multiple criteria methods for ranking suppliers—linear weighted point (LWP) method, metric, rating, Borda count, pair-wise comparison, and AHP. It was pointed out that for all the ranking methods (except AHP) to work effectively, the criteria values have to... 

Once the survey forms were received electronically, they were analyzed using Rating, Borda Count, and AHP methods (Activity 3 of Figure 7.13). Detailed descriptions of these three Ranking methods are available in Chapter 6, Section 6.3. 

For DM-2, both Borda Count and AHP provide the same rankings. Similar results were obtained for the other DMs also. It was found that cost, quality and delivery were the three most important supplier criteria and Borda Count and AHP methods yielded similar rankings. 

Preemptive GP ranks the objective fimctions with respect to the ordered preferences of the DMs and minimizes the deviations from the target values associated with each objective in the ranked order. Several different techniques can be used to derive preemptive priorities. One convenient way is to use discrete alternative multi-criteria decision-making methods such as rating, Borda count, pairwise comparison, or the analytic hierarchy process (AHP) method (see Ravindran et al. [2010] for an application). These methods also provide a numerical strength-of-preference value that can be used in non-preemptive GP models. The preemptive GP model formulation, assuming that the preference ordering of the objectives is Zy Zy Zy Zy as follows ... 

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