Exact solution algorithms for the maximum flow problem with additional conflict constraints

Şuvak, Zeynep; Altınel, İ. Kuban; Aras, Necatı

doi:10.1016/j.ejor.2020.04.001

Cited by 15 publications

(1 citation statement)

References 33 publications

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“…In the scientific literature, incompatibility constraints have been largely studied under different names as negative disjunctive , conflicts or exclusionary side constraints . Examples of their applications arise in the context of horizontal collaboration among carriers and shippers where transportation lanes cannot include incompatible goods as food and chemicals (see Colombi et al., 2017), in transportation problems where pairs of suppliers are incompatible when serving the same customer (Goossens and Spieksma, 2009), knapsack problems (Bettinelli et al., 2017), and max‐flow problems (Şuvak et al., 2020). The introduction of services incompatibility in the healthcare domain has a high practical relevance.…”

Section: Introductionmentioning

confidence: 99%

Hybridizing adaptive large neighborhood search with kernel search: a new solution approach for the nurse routing problem with incompatible services and minimum demand

Gobbi

Manerba

Mansini

et al. 2022

Int Trans Operational Res

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The average age of the population has grown steadily in recent decades along with the number of people suffering from chronic diseases and asking for treatments. Hospital care is expensive and often unsafe, especially for older individuals. This is particularly true during pandemics as the recent SARS-CoV-2. Hospitalization at home has become a valuable alternative to face efficiently a huge increase in treatment requests while guaranteeing a high quality of service and lower risk to fragile patients. This new model of care requires the redefinition of health services organization and the optimization of scarce resources (e.g., available nurses). In this paper, we study a Nurse Routing Problem that tries to find a good balance between hospital costs reduction and the well-being of patients, also considering realistic operational restrictions like maximum working times for the nurses and possible incompatibilities between services jointly provided to the same patient. We first propose a Mixed Integer Linear Programming formulation for the problem and use some valid inequalities to strengthen it. A simple branch-and-cut algorithm is proposed and validated to derive ground benchmarks. In addition, to efficiently solve the problem, we develop an Adaptive Large Neighborhood Search hybridized with a Kernel Search and validate its performance over a large set of different realistic working scenarios. Computational tests show how our matheuristic approach manages to find good solutions in a reasonable amount of time even in the most difficult settings. Finally, some interesting managerial insights are discussed through an economic analysis of the operating context.

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Section: Introductionmentioning

confidence: 99%

Hybridizing adaptive large neighborhood search with kernel search: a new solution approach for the nurse routing problem with incompatible services and minimum demand

Gobbi

Manerba

Mansini

et al. 2022

Int Trans Operational Res

View full text Add to dashboard Cite

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Minimum cost flow problem with conflicts

2021

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The minimum cost flow problem with conflicts is a recent extension of the ordinary minimum cost flow problem. It includes flow compatibility restrictions in addition to flow balance equalities and capacity constraints: at most one of the conflicting arcs can have positive flow. In this work we study this extension of the minimum cost flow problem, which can be faced in many real‐world applications. We give mixed‐integer programming formulations of the problem after briefly analyzing its complexity and propose two exact solution algorithms. One of them is a branch‐and‐bound procedure with combinatorial branching rules based on conflicts in an optimal solution of the relaxations. The other one is a Russian Doll Search method exploring the maximal stable sets of the conflict graph, which is obtained from the original network with the purpose of representing the conflict relations among arcs. Also, a set of preprocessing procedures is introduced with the aim of reducing the size of the problem. We can say that the new algorithms are very efficient according to the results of extensive computational experiments realized on a large set of test problems.

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Maximum weight perfect matching problem with additional disjunctive conflict constraints

2022

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We focus on an extension of the maximum weight perfect matching problem with additional disjunctive conflict constraints in conjunction with the degree and binary restrictions. Given a simple graph with a nonnegative weight associated with each edge and a set of conflicting edges, the perfect matching problem with conflict constraints consists of finding a maximum weight perfect matching without any conflicting edge pair. Unlike the well‐known ordinary maximum weight perfect matching problem this one is strongly 𝒩𝒫‐hard. We propose two branch‐and‐bound algorithms for the exact solution of the problem. The first one is based on an equivalent maximum weight stable set formulation with an additional cardinality restriction obtained on the graph representing conflict relations and uses the information coming from its maximal stable sets. The second one is essentially a recursive depth first search scheme that benefits from simple upper bounds incorporated with a fast infeasibility detection procedure to prune the branch‐and‐bound tree. According to the extensive computational tests it is possible to say that they are both very efficient.

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Exact solution algorithms for the maximum flow problem with additional conflict constraints

Cited by 15 publications

References 33 publications

Hybridizing adaptive large neighborhood search with kernel search: a new solution approach for the nurse routing problem with incompatible services and minimum demand

Hybridizing adaptive large neighborhood search with kernel search: a new solution approach for the nurse routing problem with incompatible services and minimum demand

Minimum cost flow problem with conflicts

Maximum weight perfect matching problem with additional disjunctive conflict constraints

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