The ANP ‘BOCR’ method

A decision has several favourable and unfavourable concerns to consider, in which some of these are sure things, while others are less certain. Hence, the favourable sure things are called ‘Benefits’ while the unfavourable ones are termed ‘Costs’. The uncertain concerns of a decision are the positive ‘Opportunities’ that the decision might create and the negative ‘Risks’ that it can entail (Saaty, 2010). The four concerns utilises a separate structure for the decision and are referred to collectively as BOCR (i.e. using the initials of the positive ones before the initials of the negative ones).

The general theory of the ANP model, which consists of a goal, and four separate BOCR models (subnets) will be used later for modelling the selection problem. The benefits model shows which alternative would be most beneficial, i.e. yield the most benefits, and the opportunities model shows which alternative has the greatest potential for benefits, i.e. offers the most opportunities, where as the costs model (costs may include monetary, human, and intangible costs) shows which alternative would be most costly and finally, the risks model shows which alternative has the highest potential risks, i.e. pose the most risk for each alternative. Opportunities and risks are considered as ‘hidden’ benefits and costs, respectively (Saaty, 2001). Each BOCR model should have some control criteria (subcriteria) in it to be evaluated with. BOCR is then performed as an analysis to weigh these categories. They are the criteria which one can use to represent the different kinds of

influences that can be perceived. They will later need to be combined into an overall influence using the usual AHP/ANP calculations. The analysis will derive four rankings of the alternatives, one for each of the BOCR merits. Two formulas can be used for synthesis; one multiplicative and one additive subtractive.

The ANP ‘BOCR’ approach consists of the following steps (Saaty, 2001):

1. Define a decision making problem and present it as in the case of the AHP, in the

form of a general goal to be achieved;

2. Decompose the problem into a network with four sub-networks, namely: Benefits

(B), Opportunities (O), Costs (C) and Risks (R). BOCR should jointly contribute to the achievement of the main ultimate goal defined in step (1);

3. Build individual BOCR hierarchical structures. For each structure, define control

elements (criteria and subcriteria);

4. Pairwise compare the elements in each level with respect to the same upper level

element (compare criteria to the control goal of BOCR, subcriteria to criteria), and the interdependence among the elements. More specifically, for Benefits and Opportunities: Ask what gives the most benefits or presents the greatest opportunity to influence the criterion (subcriterion); for Costs and Risks: Ask what incurs the most cost or faces the greatest risk.

5. Calculate priorities in each subnetwork. Calculate global priorities by multiplying

the priority of the subcriteria by the priority of the respective criterion and divide by 4 (B, O, C and R). It is recommended for further analysis to select only those subcriteria that have global priorities above 3% in case of a large number of subcriteria (i.e. >20) or 5% in case of a small number of subcriteria (i.e. <15);

6. Produce a general network consisting of clusters and elements that contribute to all

control criteria;

7. For the most significant subcriteria (i.e. global priorities > 3%), create subnets.

Each subnet should consist of the Alternatives’ cluster and clusters with other elements such as influencing factors, stakeholders of decision making process, their objectives and point of view, etc. Define their influences and feedbacks. Note that each subnet must include the Alternatives cluster which are the same in any subnet, while other elements may differ;

8. Pairwise compare the elements within and among the clusters (always considering

the upper criterion and BOCR within which the comparison takes place). Pairwise compare the clusters in respect to how much they influence a particular control criterion;

9. Calculate the priorities of alternatives for each B, O, C, R network. Using the priorities obtained in step (5), form an unweighted supermatrix (ideal values), a weighted supermatrix and a limit supermatrix for each subnetwork by ANP. The priorities of the alternatives under each merit are calculated by normalising the alternative-to-goal column of the limit supermatrix of the merit;

10. Calculate overall priorities of alternatives by synthesising priorities of each alternative under each merit from step (9) with corresponding normalised weights b, o, c, and r from step (5). There are two ways commonly used to combine the scores of each alternative under B, O, C, and R:

i. Multiplicative (Pi = BiOi / CiRi)

ii. Additive-negative (Pi = bBi + oOi = c(1/Ci)Normalised + r(1/Ri)Normalised

The additive formula requires determining of the importance of each subnetwork: B, O, C, R based on the so called strategic criteria as explained in steps (11-13); 11. Determine the priorities of the strategic criteria. Build another hierarchy consisting

of elements that are more general to allow analysis of the problem from more general perspective. Likewise, in the AHP, the nine-point scale should be used to obtain pairwise comparison results of the importance of strategic criteria toward achieving the overall objective. Calculate the priorities of the strategic criteria and examine the consistency property of the matrix;

12. Using a five-step scale (very high, high, medium, low, very low) indicate the importance of B, O, C, and R with respect to each strategic criterion. Ready values can be adopted which have been calculated as follows (Saaty, 2008): very high – 0.42, high – 0.26, medium – 0.16, low – 0.10, and very low – 0.06;

13. Determine the priorities of the B, O, C, R. Calculate the priority of a merit by multiplying the score of a merit on each strategic criterion from step (4) with the priority of the respective strategic criterion from step (3) and summing up the calculated values for the merit. Normalise the calculated values of the four merits, and obtain the priorities of the B, O, C, R, that is b, o, c and r, respectively;

14. Synthesise the whole model by applying the above explained formulae (additive- negative and multiplicative). The alternative with the highest values is the best one that contributes most to the achievement of the main goal; and