Balancing Service Efficiency and Spatial Equality in Public Facility Location Problems

Core Concepts

This article proposes four new location problems that balance the trade-off between service efficiency (total travel distance) and spatial equality (total spatial envy) in public service systems.

Abstract

The article deals with the location problem for balancing service efficiency and spatial equality in public service systems. It is assumed that some people may feel envy if they have to travel longer distances to access services compared to others. The strength of the envy can be measured by comparing one's travel distance to a service facility with a threshold distance.
The authors propose four extended p-median problems:

Minimum Envy Location Problem (MELP): Minimizes the total spatial envy function.
Minimum Distance and Envy Location Problem (MDELP): Minimizes a weighted sum of total travel distance and total spatial envy.
Capacitated MELP (CMELP): Capacitated version of MELP.
Capacitated MDELP (CMDELP): Capacitated version of MDELP.

The models are formulated as mixed integer linear programming problems and have several analytical properties related to the trade-off between service efficiency and spatial equality. The performance of the proposed models is extensively tested on three sets of benchmark instances, including randomly generated and real-world geographical data. The results show that the equality measures, such as standard deviation, mean absolute deviation, and Gini coefficient of travel distances, can be substantially improved by minimizing the travel cost and the spatial envy, while only slightly increasing the mean travel distance.

Stats

The mean travel distance can be increased by up to 3.69% to achieve a 13.92% reduction in the standard deviation of travel distances.
The mean travel distance can be increased by up to 4.42% to achieve a 13.57% reduction in the standard deviation of travel distances.

Quotes

"Delivering quality services in an efficient and equitable manner is critical to general public."
"The strength of the envy can be measured by comparing one's travel distance to service facility with a threshold distance."
"The total travel distance, as an efficient indicator, and the total spatial envy, as an equality indicator, are simultaneously minimized by the weighted objective function."

Key Insights Distilled From

Extended p-median problems for balancing service efficiency and equality

by Yunfeng Kong... at arxiv.org 04-26-2024

https://arxiv.org/pdf/2312.14408.pdf

Deeper Inquiries

How can the proposed models be extended to consider other equity measures beyond spatial envy, such as social or economic equity

To extend the proposed models to consider other equity measures beyond spatial envy, such as social or economic equity, the objective function can be modified to incorporate these additional measures. For social equity, factors like demographic diversity, income levels, or access to essential services can be included in the model. Economic equity considerations may involve factors like job opportunities, economic development, or income distribution. By adjusting the objective function to account for these diverse equity measures, the model can provide a more comprehensive evaluation of service equality.

What are the implications of the model parameters (threshold distance and weight factor) on the trade-off between efficiency and equity, and how can these parameters be determined in practice

The model parameters, specifically the threshold distance and weight factor, play a crucial role in determining the trade-off between efficiency and equity in public service planning. The threshold distance (𝑑∗) sets the limit beyond which individuals may experience envy, impacting the spatial distribution of facilities. The weight factor (𝛽) determines the balance between the total travel distance and the total spatial envy, influencing the emphasis on efficiency versus equality. In practice, these parameters can be determined through a combination of data analysis, stakeholder consultation, and sensitivity analysis. By analyzing historical data, conducting surveys, and considering stakeholder preferences, appropriate values for 𝑑∗ and 𝛽 can be identified to achieve the desired balance between efficiency and equity.

How can the proposed models be integrated with other facility location considerations, such as facility capacity, budget constraints, or environmental impact, to develop more comprehensive public service planning frameworks

Integrating the proposed models with other facility location considerations, such as facility capacity, budget constraints, or environmental impact, can lead to more comprehensive public service planning frameworks. Facility capacity constraints can be incorporated by adding constraints on the maximum number of customers each facility can serve. Budget constraints can be addressed by including cost considerations in the objective function, ensuring that the optimal solution is financially feasible. Environmental impact considerations can be integrated by evaluating the ecological footprint of facility locations and minimizing negative environmental effects. By combining these factors with the proposed models, public service planning frameworks can be developed that optimize efficiency, equity, capacity, budget, and environmental sustainability simultaneously.