ENVM7512 Workshop Week 8

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developed by Michaela Plein, Christopher O’Bryan, Scott Spillias and Tracy Rout

Learning objectives of this practical

Practise reducing a consequence table

Understand and be able to perform the steps in a multi-criteria decision analysis

Understand why the multi-attribute utility can be different for different stakeholders and what that means for the decision

First, read the background to the case study on the Rolling Thunder National Wildlife Reserve.

The Rolling Thunder National Wildlife Reserve has acquired several prairie parcels to protect rare orchids. These plants only grow in open grassland, usually requiring direct habitat manipulation (e.g., mowing, grazing) to prevent them from being out-competed by woody species. Several management objectives for these parcels have been developed in addition including maintaining habitat for game birds, especially maintaining vegetation cover during winter. More recently the management decided to expand their conservation objectives to protect rare butterfly and beetle populations, which are also endemic (i.e., only occur in this area) to the prairie. Meanwhile, residential development has increased and is now in proximity to these areas. This leads to new challenges for the management to avoid conflicts with local residents.

Imagine you are the refuge managers and you need to find the best option for managing the prairie grassland vegetation. You need to select a vegetation treatment alternative that performs best across the seven objectives. The following consequence table shows the performance measures for each of the objectives across the different management alternatives.

Exercise 1 – Reducing a consequence table

Reduce the number of alternatives in the table above by finding and eliminating any dominated alternatives. Then delete any irrelevant objectives that result as alternatives are dropped. Make notes of your working.

Exercise 2 – Making a swing weighting table

Open the EXCEL spreadsheet in the learning resources folder for week 8 (“Week 8 – Workshop MCDA Workbook.xlsx”). In tab 1 “Consequence table” you will find the simplified consequence table.

To the right of the simplified consequence table there is a table titled ‘Performance’. Enter the best and worst outcomes under each objective into this table. Remember to note whether the objective is supposed to be minimised or maximised.

Open the “Swing weighting” tab. You should find that the best and worst outcomes under each objective have been copied here, in the ‘Performance’ table. Populate the swing weighting table with the performance measure values for six hypothetical scenarios. In a swing weighting approach, the first scenario is a baseline and includes the worst outcome under each objective. In each of the next scenarios, change one value at a time from the worst outcome to the best outcome. To help you, the value you should change in each scenario is highlighted green.

Exercise 3 – Performing swing weighting

Now you are going to perform a swing weighting by recording your own preferences for each of these 6 scenarios. There are no right or wrong answers here, but there are a few rules to follow.

Rank the 6 hypothetical scenarios according to your preference, where 1 is most desirable and 6 is least desirable (in this case). Enter your ranks into the Rank column of the Scenarios table.

Now assign scores (from 0 to 100) to each hypothetical scenario. Scores are an indication of your relative preference for each scenario. The most desirable scenario should receive 100 and the least desirable scenario should receive 0. Scores should be consistent with your ranks, although you can give two scenarios the same score. Enter your scores into the Score column.

Now in the Swing Weights column, calculate swing weights for each scenario by dividing the score for that scenario by the total score. (You can calculate formulas in Excel by typing ‘=’ and then the formula, selecting cells as you want to include them.). The swing weights across all scenarios should sum to 1.

Go back to the Consequence table tab and check that your swing weights have been transferred to the Swing Weight column of the ‘Normalised management alternative’ table.

Exercise 4 – Normalising the consequence table

To ensure that your final solution is not biased by large values of some of the criteria (e.g., the cost), you need to normalise the values in your consequence table (i.e, make them unitless and of the same scale).

Normalise the value for each objective under each alternative using the formulas below, and enter these into the “normalised consequence table”.

A general formula for normalising values in consequence tables is:

Normalised value =.

More specifically, if the objective is supposed to be minimized the mathematical formula is:

and if the objective is supposed to be maximized the mathematical formula is:

where

Vij = performance of alternative j for objective i,

min[Vi] = minimum value for objective i,

max[Vi] = maximum value for objective i,

Exercise 5 – Calculating Multi-Attribute Utilities (MAUs)

The multi-attribute utility is calculated for each alternative and combines the values under each objective. It can be used to compare participant’s preferences for different alternatives.

Calculate the multi-attribute utility of each alternative using the following formula:

Uj = overall benefit (or utility) of alternative j,

Wi = swing weight given to objective i,

Vij = value for objective i under alternative j.

Enter the multi-attribute utility for each alternative into the table below the Normalised Consequence Table. Again, you can use the formula function in Excel to help do your calculations.

The Rank of each alternative is automatically calculated below the multi-attribute utility. Check how the alternatives are ranked according to your preferences. What does it mean in terms of making a decision for managing the Rolling Thunder prairie parcels?

Once you have your multi-attribute utility for each alternative, click here https://forms.gle/JjSHjcgvpz8paSqx8 and enter them into the form. The demonstrators will compile these so you can view the range of preferences for the different alternatives.