Case background A Hydrogen energy company has 3 choices for its plant location. The board needs to make pairwise comparison judgments and priority (p164), with some support of a predefined scale of priorities (or weights) in the decision-making process. Please follow the steps and fill in the figures and questions where needed.

Step 1: List the hierarchy of the location decision

Step 2: Use the foundation scale Intensity of importance on an absolute scale Definition Explanation 1 Equal importance Two activities contribute equally to the objective 3 Moderate importance of one over another Experience and judgement favor one activity over another 5 Very strong importance Experience and judgement strongly favor one activity over another 7 Very strong importance An activity is strongly favoured and its dominance demonstrated in practice 9 Extreme importance The evidence favouring one activity over another is of the highest possible order of affirmation 2, 4, 6, 8 Intermediate values between the two adjacent judgments When compromise is needed

Step 3: compare the relative importance of the 3 attributes: water accessibility, land cost, and transport. Assume that 1. Water accessibility is extremely more important than land cost with a scale of 8. 2. Water accessibility is very strongly more important than transport with a scale of 6 3. Transport is strongly more important than land cost with a scale of 4 Please express the figures in form of a matrix below: Normalizing this matrix by dividing the score by the total of each column: Factor The weight of each attribute is obtained by averaging each row: Water accessibility: Land cost: Transport:

Step 4: evaluate each system against each attribute. Let us start with water accessibility. The evaluation below shows the importance of each system in terms of water accessibility: 1. Large scale is moderately to strongly better than medium scale with a score of 3 2. Large scale is extremely better than small scale with a score of 7 3. Medium scale is strongly better than small with a score of 5 Please express the figures in the form of a matrix below Now we use the same calculations for the attributes by normalizing each column by dividing the score by the total of each column as shown below In terms of water accessibility, the score for each system is obtained by averaging each row: Water accessibility Large scale: Medium scale: Small scale: A similar process can be repeated for the other two attributes: land cost and transport. Let us continue with land cost. The evaluation below shows the importance of each system in terms of land cost: 1. Large scale is moderately to strongly better than medium scale with a score of 2 2. Large scale is extremely better than small scale with a score of 3 3. Medium scale is strongly better than small with a score of 4 Please express the figures in the form of a matrix below Now we use the same calculations for the attributes by normalizing each column by dividing the score by the total of each column as shown below In terms of land cost, the score for each system is obtained by averaging each row: Large scale: Medium scale: Small scale: Let us finish with transport. The evaluation below shows the importance of each system in terms of transport 1. Small scale is moderately to strongly better than medium scale with a score of 2 2. Small scale is extremely better than large scale with a score of 3 3. Medium scale is strongly better than large with a score of 4 Please express the figures in the form of a matrix below Now we use the same calculations for the attributes by normalizing each column by dividing the score by the total of each column as shown below: In terms of transport, the score for each system is obtained by averaging each row: Large scale: Medium scale: Small scale:

Step 5: The results of the evaluation of each system against each attribute are shown below. Please evaluate each system against accessibility, land cost and transport.

Step 6: Finding consistence ratio, if the consistence ration is over 0.1, please change the scale of defined in Step 3 and Step 4 (highlighted with yellow) As shown above the weight for accessibility, land cost, and transport are: The aggregate score for each system is shown below: Large scale: Medium scale: Small scale: