Combined preference modelling with LPoptimisation for airbase Valkenburg

The essence of the LP model is an assignment model with additional constraints. Within this assignment model, four functions - military airbase, VIP airport, residential area, and nature area - are assigned to seven locations, according to the preferences for a location in the light of six criteria - security, nature, housing, infrastructure, economics, and water management.

First, the preference measurement model described in Section 5.2 was used as the basis for the LP model, to find the overall order of the preferences of the alternatives from the viewpoint of the stakeholders.

subject to:

E Bi

=

i=1

ViBi

G

Ft

=

Fma

>

rvip

>

com

>

Ft

>

Ft

5000 1000 0

30000

C fixed + cmaFma + cvipFvipccomFcom

Fvip + Fcom

5000 1000 0

30000

C fixed + cmaFma + cvipFvipccomFcom where:

P = overall preference of the alternative yielding the highest preference;

pij = preference for alternative i according criterion j;

i = index i refers to the alternatives (i = 1,2,3,..., m);

j, k = indices j, k refer to the criteria (j, k = 1,2,3,..., n);

m = total number of alternatives;

n = total number of criteria;

Tjk = ratio of the trade-offs between criteria j and k;

Wj = weight factor Wj of criterion Cj, determined by the ratios Tjk between the trade-offs;

Bi = Binary variable indicating if alternative i is chosen

Ft = total number of flight movements per year;

Fma = number of military flight movements per year;

Fvip = number of VIP flight movements per year;

Fcom = number of commercial flight movements per year;

Ct = total costs of flight movements;

Cfixed = fixed costs for the military airbase;

cma = operational cost per military flight movement;

cvip = operational cost per VIPflight movement;

ccom = operational cost per commercial flight movement.

Parameters used in all calculations:

Pi/j = preference input values according to Table 13.2;

Tjk = trade-off ratio input values according Table 13.4.

With these parameters, the weight factors Wj (j = 1,2,..., 11) were calculated with the method described in Section 5.2. The result is given in Table 14.1. In the LP optimisations, the following cost parameters were used:

The Pareto-set of optimum solutions is then obtained by systematically:

• Varying the constraint for the average cost per flight movement while optimising the preference value for nature, and

Table 14.1 Weight factors

Constraints

C1

C2

C3

C4

C5

C6

Functions

NP MA

NP VA

NP RA

HN RA

SC NL

SC VIP

Weight factors

0.128

0.128

0.128

0.103

0.154

0.154

Constraints

C7

C8

C9

C10

C11

Functions

WT RA

IS RA

EC MA

EC VA

EC RA

Weight factors

0.051

0.077

0.026

0.026

0.026

NP: Nature preservation; HN: Housing need; SC: Security; WT: Water; IS: Infrastructure; EC: Economics; MA: Military Airbase; VA: VIPs Airport; RA: Residential area; NA: Nature area; NL: National.

• Varying the constraint for the preference value for nature while optimising the average cost per flight movement.

A linear relationship is assumed for the nature preference value as a function of the airbase occupancy (Fig. 14.3).

This relationship is incorporated in the model by adding the following constraints:

where:

P2/1 = preference for nature in alternative 2; pmin = minimum preference for nature in alternative 2; Si = slope of the line defining the relationship between the number of flight movements and the preference value for nature;

bi = intercept of the line defining the relationship between the number of flight movements and the preference value for nature.

The results are summarised in Figure 14.3 which provides the necessary information for sound political decision making on the destiny of the airbase.

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