Maximum-expectation matching under recourse

IF 6 2区管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

European Journal of Operational Research Pub Date : 2025-02-15 DOI:10.1016/j.ejor.2025.02.012

João Pedro Pedroso , Shiro Ikeda

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Abstract

This paper addresses the problem of maximizing the expected size of a matching in the case of unreliable vertices and/or edges. The assumption is that the solution is built in several steps. In a given step, edges with successfully matched vertices are made permanent; but upon edge or vertex failures, the remaining vertices become eligible for reassignment. This process may be repeated a given number of times, and the objective is to end with the overall maximum number of matched vertices.

An application of this problem is found in kidney exchange programs, going on in several countries, where a vertex is an incompatible patient–donor pair and an edge indicates cross-compatibility between two pairs; the objective is to match these pairs so as to maximize the number of served patients. A new scheme is proposed for matching rearrangement in case of failure, along with a prototype algorithm for computing the optimal expectation for the number of matched edges (or vertices), considering a possibly limited number of rearrangements.

Computational experiments reveal the relevance and limitations of the algorithm, in general terms and for the kidney exchange application.

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追索权下的最大期望匹配

本文解决了在不可靠的顶点和/或边的情况下最大化匹配的期望大小的问题。假设解决方案是通过几个步骤构建的。在给定的步骤中，成功匹配顶点的边被永久保存；但在边或顶点失败时，剩余的顶点可以重新分配。这个过程可以重复给定次数，目标是以匹配顶点的总最大数量结束。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

European Journal of Operational Research 管理科学-运筹学与管理科学

CiteScore

11.90

自引率

9.40%

发文量

786

审稿时长

8.2 months

期刊介绍： The European Journal of Operational Research (EJOR) publishes high quality, original papers that contribute to the methodology of operational research (OR) and to the practice of decision making.