Construction of the AHP Framework

In this section, practical formulation - a mathematical model for the climate change response decision problem under conditions of three overarching conflicting objectives (environmental, social and economic) using the analytical hierarchy process (AHP) - is presented. For example, trading off environmental impacts against economic impacts is a challenge for all climate change response strategies for both businesses and governments (Raymond & Brown, 2011). Multi-objective analysis was used in this case to choose among, prioritise and generate the most feasible menu of acceptable strategic choices based on a multiplicity of criteria under each objective (Steuer & Na, 2003). The solution derived was a set of points on a surface, in up to

three dimensions that all fit a predetermined definition of an optimum, commonly referred to as Pareto Optimality (Pareto, 1906).

The Analytical Hierarchy Process (AHP) is a process that helps pick up one of the options of a list of choices. Each choice has a few parameters attached to it and weights can be assigned for each parameter. AHP picks the best choice from the list of choices. One of the greatest strengths of this multi-criteria decision aid method is that it takes into account many different parameters for many alternatives in both qualitative and quantitative forms, and gives the result that best matches the parameters.

The following section gives a step-by-step brief of how to apply this method to mathematically solve a corporate climate change challenge. The challenges are brought about by the need to trade-off among a diverse set of conflicting alternatives, with the understanding that, while it is imperative for a business to respond to climate change (an environmental perspective), for- profit businesses still have to do so within the confines of economic sustainability.

Steps in the AHP methodology 2.8.1 Construction of the Hierarchy

The first step in an AHP problem is to decompose the decision problem (climate change response) into its constituent parts in a hierarchical format (Hwang & Syamsuddin, 2010), progressing from the top layer which is the general, to the lower more specific sub-objective. Thus the progression is from the ultimate objectives, sub-objectives and sub-sub-objectives, down to the discrete bottom level alternatives. Each set of alternatives can be further divided into an appropriate level of detail, bearing in mind that the more depth in the relevance tree, the less discrete the alternative becomes. At the top, the overarching objective is a climate change response strategy.

2.8.2 Pairwise Comparison by Decision Makers

The next step is to assign a relative weight for each objective. A set of questionnaires is formed based on the original Saaty Rating Scale on linguistic variables (Table 2-2).

Table 2-2 Saaty Linguistic Variables Intensity of

Importance Definition Explanation

1 Equally important Two factors contribute equally to the objective

3 Somewhat more important Experience and judgment slightly favour one over the other

5 Much more important Experience and judgment strongly favours one over the other

7 Very much more importance Experience and judgment very strongly favours one over the other. Its importance is demonstrated in practice

9 Absolutely more important The evidence favouring one over the other is of the highest possible validity

2,4,6,8 Intermediate values When compromise is needed

Source: Saaty (1980)

Using the linguistic variable measurements to demonstrate the effect of each objective on the strategy, decision makers are presented with a series of pairwise comparison questions of the format: How important is criteria E relative to criteria F? The options are based on the five linguistic variables ―equally important‖, ―somewhat more important‖, ―much more important‖, ―very much more important‖, or ―absolutely more important‖. Alternatively the decision makers could subjectively assign their own personal weights between 0 and 100.

Each sub-objective has a local (often called immediate) and a global priority. The sum of all the criteria beneath a given parent criterion in each tier of the model must equal one. Its global priority shows its relative importance within the overall model.

2.8.3 Aggregating the Weights

Because the perception of each decision maker varies depending on knowledge, experience and objective interests, a geometric mean was used to deal with the N numbers of decision makers to integrate their judgment values. This had the effect of shortening the gap effects between very low and very high values, therefore controlling for biases. The geometric means for each leaf of the hierarchy for the lower numbers were calculated as follows:

Gu = (gl1 * gl2 * gl3 *…. Gln)1/n (1)

And the weight for the lower fuzzy numbers was:

Similarly we obtain wu and wm for upper and medium numbers.

Three weights were obtained for each leaf for lower, medium and upper. These three values describe the pessimistic, normal and optimistic modes (Syamusuddin & Hwang, 2009) for further deliberation and choice by all decision makers. Scores were then synthesised through the model, yielding a composite score for each choice at every tier, as well as an overall score as shown below:

Wfl =( ∑ )/n (3)

Wfm = (∑ (4)

Wfu = (∑ (5)

Problem structuring is one of the key issues that executives confronted by the climate change challenge battle with. AHP allows environmental, economic and social objectives to be coped with simultaneously, whilst also allowing for a careful structuring of the climate change risks and opportunities before committing to a strategic path of action. The framework proposed in this section allowed for the evaluation of both qualitative and quantitative factors, thereby combining sophistication and realism to solve a practical challenge faced by businesses.