A comparison of formulations and solution methods for the minimum-envy location problem. Additional results

We consider a discrete facility location problem with a new form of equity criterion. The model discussed in the paper analyzes the case where demand points only have strict preference order on the sites where the plants can be located. The goal is to find the location of the facilities minimizing the total envy felt by the entire set of demand points. We define this new total envy criterion and provide several integer linear programming formulations that reflect and model this approach. Extensive computational tests are reported, showing the potentials and limits of each formulation on several types of instances

Intra-facility equity in discrete and continuous p-facility location problems

We consider facility location problems with a new form of equity criterion. Demand points have preference order on the sites where the plants can be located. The goal is to find the location of the facilities minimizing the envy felt by the demand points with respect to the rest of the demand points allocated to the same plant. After defining this new envy criterion and the general framework based on it, we provide formulations that model this approach in both the discrete and the continuous framework. The problems are illustrated with examples and the computational tests reported show the potential and limits of each formulation on several types of instances. Although this article is mainly focused on the introduction, modeling and formulation of this new concept of envy, some improvements for all the formulations presented are developed, obtaining in some cases better solution times.Project TED2021-130875B-I00, supported by MCIN/AEI/ 10.13039/ 501100011033 and the European Union ‘‘NextGenerationEU/PRTR’’Research project PID2022- 137818OB-I00 (Ministerio de Ciencia e Innovación, Spain)Agencia Estatal de Investigación (AEI), Spain: PID2020-114594GB-C2; Regional Government of Andalusia, Spain P18-FR-1422 and B-FQM-322-UGR20 (ERDFIMAG-Maria de Maeztu, Spain grant CEX2020-001105-M/AEI/10.13039/ 501100011033Funding for open access charge: Universidad de Granada / CBU

IMPROVING QUALITY OF SERVICE IN EMS SYSTEMS BY REDUCING DISPARITIES BETWEEN SERVICE ZONES

Emergency medical service (EMS) systems respond to emergency or urgent calls so as to provide immediate care, such as pre-hospital care and/or transportation, to hospitals. Care must be provided in a timely manner; in fact quality of service is usually directly associated with response time. To reduce the response time, the number and location of vehicles within the service area are important variables. However with limited capacity, increasing the number of vehicles is often an infeasible alternative. Therefore, a critical design goal is to decide at which facilities stations should be located in order to serve as much demand as possible in a reasonable time, and at the same time maintain equitable service between customers. This study aims to focus on locating ambulances which respond to 911 calls in EMS systems. The goals are to find the optimal base station location for vehicles so that the number of calls or customers served is maximized while disparity between those customers is minimized, to consider the survival rate of patients directly in the model, and develop appropriate meta-heuristics for solving problems which cannot be solved optimally

Balancing the arrival times of users in a two-stage location problem

There has been a number of facility location problems dealing with the introduction of the equity issue in the travel distances distribution. In this paper we analyze a new aspect of equity concerning the distribution of the arrival times of customers. Given a depot and a set of demand points generating flow which also represent potential locations, we consider a discrete two-stage location problem whose aim is to locate a given number of facilities and to allocate the demand points to a facility. We assume as objective the maximization of the minimum difference between two consecutive arrival times of flows to the depot through the patronized facility. This particular equity measure is introduced in order to reduce risks of congestion in the dynamic of flow arrivals at the common destination. The problem is described through two Integer Programming formulations. Computational results for solution methods based on both formulations are then shown and analyzed

Fairness in maximal covering location problems

Acknowledgments The authors thank the anonymous reviewers and the guest editors of this issue for their detailed comments on this paper, which provided significant insights for improving the previous versions of this manuscript. This research has been partially supported by Spanish Ministerio de Ciencia e Innovación, AEI/FEDER grant number PID2020-114594GB C21, AEI grant number RED2022-134149-T (Thematic Network: Location Science and Related Problems), Junta de Andalucía projects P18- FR-1422/2369 and projects FEDERUS-1256951, B-FQM-322-UGR20, CEI-3-FQM331 and NetmeetData (Fundación BBVA 2019). The first author was also partially supported by the IMAG-Maria de Maeztu grant CEX2020-001105-M /AEI /10.13039/501100011033 and UENextGenerationEU (ayudas de movilidad para la recualificación del profesorado universitario. The second author was also partially supported by the Research Program for Young Talented Researchers of the University of Málaga under Project B1-2022_37, Spanish Ministry of Education and Science grant number PEJ2018-002962-A, and the PhD Program in Mathematics at the Universidad de Granada.This paper provides a mathematical optimization framework to incorporate fairness measures from the facilities’ perspective to discrete and continuous maximal covering location problems. The main ingredients to construct a function measuring fairness in this problem are the use of (1) ordered weighted averaging operators, a popular family of aggregation criteria for solving multiobjective combinatorial optimization problems; and (2) -fairness operators which allow generalizing most of the equity measures. A general mathematical optimization model is derived which captures the notion of fairness in maximal covering location problems. The models are first formulated as mixed integer non-linear optimization problems for both the discrete and the continuous location spaces. Suitable mixed integer second order cone optimization reformulations are derived using geometric properties of the problem. Finally, the paper concludes with the results obtained from an extensive battery of computational experiments on real datasets. The obtained results support the convenience of the proposed approach.Spanish Ministerio de Ciencia e InnovaciónAEI/FEDER grant number PID2020-114594GB C21AEI grant number RED2022-134149-T (Thematic Network: Location Science and Related Problems)Junta de Andalucía projects P18- FR-1422/2369FEDERUS-1256951B-FQM-322-UGR20CEI-3-FQM331NetmeetData (Fundación BBVA 2019)IMAG-Maria de Maeztu grant CEX2020-001105-M /AEI /10.13039/501100011033UE NextGenerationEUResearch Program for Young Talented Researchers of the University of Málaga under Project B1-2022_37Spanish Ministry of Education and Science grant number PEJ2018-002962-

Fair Robust Assignment Using Redundancy

We study the consideration of fairness in redundant assignment for multi-agent task allocation. It has recently been shown that redundant assignment of agents to tasks provides robustness to uncertainty in task performance. However, the question of how to fairly assign these redundant resources across tasks remains unaddressed. In this paper, we present a novel problem formulation for fair redundant task allocation, in which we cast it as the optimization of worst-case task costs. Solving this problem optimally is NP-hard. Therefore, we exploit properties of supermodularity to propose a polynomial-time, near-optimal solution. Our algorithm provides a solution set that is α times larger than the optimal set size in order to guarantee a solution cost at least as good as the optimal target cost. We derive the sub- optimality bound on this cardinality relaxation, α. Additionally, we demonstrate that our algorithm performs near-optimally without the cardinality relaxation. We show the algorithm in simulations of redundant assignments of robots to goal nodes on transport networks with uncertain travel times. Empirically, our algorithm outperforms benchmarks, scales to large problems, and provides improvements in both fairness and average utility.We gratefully acknowledge the support from ARL Grant DCIST CRA W911NF-17-2-0181, NSF Grant CNS-1521617, ARO Grant W911NF-13-1- 0350, ONR Grants N00014-20-1-2822 and ONR grant N00014-20-S-B001, and Qualcomm Research. The first author acknowledges support from the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1845298

Fair Robust Assignment Using Redundancy

We study the consideration of fairness in redundant assignment for multi-agent task allocation. It has recently been shown that redundant assignment of agents to tasks provides robustness to uncertainty in task performance. However, the question of how to fairly assign these redundant resources across tasks remains unaddressed. In this paper, we present a novel problem formulation for fair redundant task allocation, in which we cast it as the optimization of worst-case task costs. Solving this problem optimally is NP-hard. Therefore, we exploit properties of supermodularity to propose a polynomial-time, near-optimal solution. Our algorithm provides a solution set that is α times larger than the optimal set size in order to guarantee a solution cost at least as good as the optimal target cost. We derive the sub- optimality bound on this cardinality relaxation, α. Additionally, we demonstrate that our algorithm performs near-optimally without the cardinality relaxation. We show the algorithm in simulations of redundant assignments of robots to goal nodes on transport networks with uncertain travel times. Empirically, our algorithm outperforms benchmarks, scales to large problems, and provides improvements in both fairness and average utility.We gratefully acknowledge the support from ARL Grant DCIST CRA W911NF-17-2-0181, NSF Grant CNS-1521617, ARO Grant W911NF-13-1- 0350, ONR Grants N00014-20-1-2822 and ONR grant N00014-20-S-B001, and Qualcomm Research. The first author acknowledges support from the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1845298