Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2012.06655

A multi-period and bi-objective approach for locating ambulances: a case study in Belo Horizonte, Brazil

Charles Paulino de Oliveira·Elisangela Martins de Sá·Flávio Vinícius Cruzeiro Martins
View original source ↗Read source document ↗Export metadata ↓

Abstract

This work aims to apply the Facility Location Problem in the Emergency Medical Service (EMS) of Belo Horizonte, Brazil. The objective is to improve two previous optimization models from literature to handle base locations and ambulances allocation/relocation problems. The proposed multi-period models introduce the concept of relocation to the local EMS, which allows ambulances to move among bases in different periods to raise the system coverage. This paper also proposes a bi-objective approach aiming to minimize the number of bases and maximize the coverage of demands, which is solved using the epsilon-constraint method. Results show that coverage levels increase by up to 31% for the deterministic approach and up to 24% for the probabilistic approach. Ambulances' relocation optimization might improve coverage levels by up to 21% for the deterministic approach and up to 15% for the probabilistic approach when change scenarios from static to multi-period. Also, since the multi-period model solutions result in installing a larger number of bases, the bi-objective approach is a powerful tool for the decision-maker. Bi-objective results suggest modest increments in the objective function when the stations' number exceeds 28 for the deterministic approach. The probabilistic approach increments in the objective function start to narrow above 30 installed stations.

Explore related subjects

math.OC

Keep this discovery

BibTeXRIS

Charles Paulino de Oliveira, Elisangela Martins de Sá, Flávio Vinícius Cruzeiro Martins. 2020-12-11. A multi-period and bi-objective approach for locating ambulances: a case study in Belo Horizonte, Brazil. https://arxiv.org/abs/2012.06655

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Deterministic and Random Bipartite Matching on General Networks: Convex Flow Reformulation, Asymptotic Properties, and Fast Algorithms

Minimum-distance bipartite matching on general networks has numerous applications various fields. This paper first focuses on deterministic problems and presents an exact edgewise-separable convex-flow reformulation. By introducing a smooth monotone rearrangement approximation of the edge-wise imbalance profiles, the convex-flow reformulation's can be solved efficiently. If we further conduct a first-order resistance-based approximation of the convex program, a one-step Laplacian-based estimator can be analytically derived in closed forms. The paper also studies random problems where supply and demand points are randomly distributed. We show that the expected optimal matching distance scales with the square root of the number of points if the supply/demand point distributions are identical, or linearly otherwise. In the former case, the optimal flow is proven to be centered, symmetric, and sub-Gaussian. In the latter case, the limiting resistance network characterizes how supply-demand imbalance is redistributed and motivates a fast algorithm that approximate the optimal flow based on the limiting resistance. Numerical experiments show that the proposed estimators closely approximate the exact matching cost while substantially reducing computation time. The proven theoretical properties of the random matching solution are numerically verified by large-scale Monte Carlo simulations.

math.OC↗
arXiv2026

Conformal-DRO: Distributionally Robust Optimization with Conformalized Ambiguity Set

Data-driven distributionally robust optimization (DRO) typically treats the conditional outcome law as fixed and uses ambiguity sets to capture estimation error. This paper studies latent distributional heterogeneity, where each instance has an unobserved law but contributes only one observation, so uncertainty persists even if the mixture law is known. We propose Conformal-DRO, which uses nested conformal regions to construct an ambiguity set for the future latent law. Under exchangeability, the set covers this law with probability at least $1-\alpha$ in finite samples, without estimating underlying latent laws or their mixing mechanism. The conformal path induces a data-driven transport geometry, while $\alpha$ determines the radius. The worst-case problem reduces to a finite linear program over conformal shells and admits sparse adversarial solutions. The resulting robust value provides a finite-sample certificate for the selected decision's expected cost.

math.OC↗
arXiv2026

The best approximation tuple: an extension of the Cheney-Goldstein algorithm and results to the multiple sets case

In this paper we extend the algorithm and several results published in the celebrated 1959 paper of Cheney and Goldstein about the best approximation pair (BAP) problem in two separate directions. One is the consideration of more than two sets. The other is the ability to handle each set as an intersections of a finite family of sets. We call the resulting problem the "Best Approximation Tuple (BAT) problem". The fundamental observation that leads to this generalizations is to recognize and handle one set (the "pivot set") as different from the remaining sets (the "satellite sets") instead of seeking cycles as the minimizers of a target functional. This enable us to overcome a certain theoretical obstacle related to cycles and minimizers of general functionals. We prove the convergence of the algorithm to the unique solution of the problem in the Euclidean case with strictly convex and compact satellite sets. Because of the lack of Fej\'er monotonicity, our convergence analysis is not standard, and is based on almost unknown properties of orthogonal projections regarding equality and inequality in the definition of nonexpansiveness.

math.OC↗