Allowing for decision variable dependent preferences

So far, the assumption was made that the scaling of preferences is not affected by any variations in the decision variables. This assumption has to be removed whenever a preference is dependent on the value of a decision variable. For instance, the preference for maintaining an airbase from the part of the surrounding municipalities will be dependent on the number of flight movements per year. This relationship is non-linear (Fig. 14.2). Beyond a certain threshold of flight movements per year, the preference will drop sharply. This threshold is in the order of three flight movements per hour. Allowing day flights only, this means about 13 400 flight movements per year. When twice this number of flight movements is allowed, the preference for maintaining the airbase will flatten out at a fairly low level. In the LP model, we assume a linear relationship as determined by these two threshold points.

A sensitivity analysis on the scaling of the preference value for nature (associated with Valkenburg as a military airbase) shows that this preference value must be kept above 2.82 (which corresponds to one flight per 11.8 minutes) to ensure that Alternative 2 of Table 13.5 - maintaining the military airbase at Valkenburg - remains the best option. Figure 14.2 was used for the relationship between the occupancy and the average flying cost per flight movement.

The LP program optimises the economics, expressed in the number of flight movements, under a constraint for the preference value for nature. Conversely, it maximises the overall preference value, while setting a constraint for the cost per flight movement. By doing this repeatedly for various constraint values, the average flying cost per flight movement, the preference value for nature and the overall preference are found as a function of the occupancy of the airbase (Fig. 14.3).

The curves represent the Pareto set of solutions of the LP model. They can be used in negotiations among stakeholders. For instance, surrounding villages could agree on a tax charge to them to keep the occupancy of the airbase at a somewhat lower level than according to the economic constraint (average flying cost per flight movement) required by the government. A justifiable value for that constraint is the average cost per flight movement corresponding with an occupancy for which maintaining the airbase just remains the best option.

Flight movements per year (x1000)

Figure 14.2 Preference for maintaining the airbase depends on its occupancy

Flight movements per year (x1000)

Figure 14.2 Preference for maintaining the airbase depends on its occupancy

Time between flights (minutes)

lO CO OJ

1 1

1 1 1

1

T"

1

Is

1 1 1

1 1 1

2000 I

500 8

I Average cost per flight movement

II Preference value of nature

III Overall preference

Flight movements per year

Figure 14.3 Average flying cost per flight movement, preference value for nature and overall preference as a function of airbase occupancy

From Table 13.5, we can derive that this turning point is at an overall preference value of 4.62. The corresponding occupancy and average cost per flight movement are, according to Figure 14.3,22 300 flight movements per year and an average cost per flight movement of € 1807. The associated average time between flights is 11.8 minutes.

If the surrounding villages would wish to bring this time between flights to, say, 15 minutes, they would have to pay taxes to cover the difference in average cost per flight movement of € 2 027 and € 1807 (times the reduced number of flight movements of 17520 per year). The corresponding tax for the 86000 inhabitants of the surrounding villages would be around € 40 per inhabitant per year.

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