Disservice representation using the Gini coefficient in semi-desirable facility location problems

We consider various bi-objective models for the semi desirable facility location problem. In these problems, the disservice caused by the facility is traditionally measured by distance-related objective functions. In this paper, we modify the objective function representing the disservice using the Lorenz curve and the Gini coefficient. Both of these concepts are widely used in the economics literature to measure the discrepancy in wealth distribution within a population. The use of the Gini coefficient enables the measurement of how the disservice caused by the facility varies across different Pareto optimal solutions. We use a bi-objective particle swarm optimizer (bi-PSO) to compare how the change in the objective function representing the disservice affects the recommended location of the facility. Results suggest that some solutions identified as "Pareto optimal" by traditional formulations are dominated by other solutions when the Gini coefficient is used. Additionally, the use of the Gini coefficient causes a change in the "optimal" location of a semi desirable facility in some instances.