The p-Median Problem

Daskin, Mark S.; Maass, Kayse Lee

doi:10.1007/978-3-319-13111-5_2

Cited by 122 publications

(63 citation statements)

References 29 publications

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“…The penalties are a constant that increases the distance and objective function when that tree is selected. The model complexity in this study is characteristic of a NP-hard to reach an optimum solution (Daskin and Maass, 2015).…”

Section: Discussionmentioning

confidence: 99%

Optimal selective logging regime and log landing location models: a case study in the Amazon forest

et al. 2018

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Reduced-impact logging is a well known practice applied in most sustainable forest management plans in the Amazon. Nevertheless, there are still ways to improve the operational planning process. Therefore, the aim of this study was to create an integer linear programming (ILP) to fill in the knowledge gaps in the decision support system of reduced impact logging explorations. The minimization of harvest tree distance to wood log landing was assessed. Forest structure aspects, income and wood production were set in the model, as well as the adjacency constraints. Data are from a dense ombrophylous forest in the western Brazilian Amazon. We applied the phytosociological analysis and BDq method to define the selective logging criteria. Then, ILP models were formulated to allow the application of the constraints. Finally, 32 scenarios (unbalanced forest, UF, and balanced forest, BF) were generated and compared with real executed plans (RE). Robust results were achieved and the expected finding of each scenario was met. The feasibility to integrate ILP models in uneven-aged forest management projects was endorsed. Consequently, the UF and BF scenarios tested were efficient and concise, introducing new advances for forest management plans in the Amazon. The proposed models have a high potential to improve the selective logging activities in the Amazon forest.KEYWORDS: forest planning, reduced-impact logging, integer linear programming, sustainable forest management, Liocourt quocient Regime de corte seletivo ótimo em modelos de locação de pátios de estocagem de madeira: um estudo de caso na floresta amazônica RESUMO A exploração de impacto reduzido é uma prática bem conhecida e aplicada na maioria dos planos de manejo florestal sustentável na Amazônia. Todavia, ainda há a possibilidade de melhoria do processo de planejamento da operação. Diante da falta de métodos auxiliares à tomada de decisão, o objetivo do trabalho foi desenvolver modelos de programação linear inteira (PLI) para suprir esta demanda. Considerou-se a minimização da distância entre as árvores exploradas e os pátios de estocagem de madeira. Aspectos estruturais, econômicos e produtivos foram incorporados ao modelo, bem como restrições de adjacência. Os dados derivam de uma floresta ombrófila densa na Amazônia Ocidental. Previamente, utilizou-se uma análise fitossociológica e o método BDq como critério de remoção. Posteriormente, modelos de PLI foram formulados para exemplificar as aplicações. Finalmente, 32 cenários (para floresta desbalaceada, UF, e floresta balanceada, BF) foram gerados e comparados com o plano executado no campo (RE). Resultados robustos foram obtidos e atenderam às expectativas de cada cenário. A viabilidade da integração dos modelos de PLI em projetos de manejo de florestas ineqüiâneas foi testado. Os cenários UF e BF testados foram eficientes e concisos, confirmando seu potencial para aumentar a eficiência de planos de exploração madeireira e manejo florestal na Amazônia.

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Section: Discussionmentioning

confidence: 99%

Optimal selective logging regime and log landing location models: a case study in the Amazon forest

et al. 2018

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“…Vast literature exists on solving and approximating P-MED, going back at least as early as the work of ReVelle and Swain (1970) . Daskin and Maass (2015) have provided a recent overview of solution methods, construction and improvement algorithms and metaheuristics for P-MED. Among these, they provide a mixedinteger linear program.…”

Section: Related Literaturementioning

confidence: 99%

The median routing problem for simultaneous planning of emergency response and non-emergency jobs

Huizing

Schäfer

Mei

et al. 2020

European Journal of Operational Research

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a b s t r a c tThis paper studies a setting in emergency logistics where emergency responders must also perform a set of known, non-emergency jobs in the network when there are no active emergencies going on. These jobs typically have a preventive function, and allow the responders to use their idle time much more productively than in the current standard. When an emergency occurs, the nearest responder must abandon whatever job he or she is doing and go to the emergency. This leads to the optimisation problem of timetabling jobs and moving responders over a discrete network such that the expected emergency response time remains minimal. Our model, the Median Routing Problem, addresses this complex problem by minimising the expected response time to the next emergency and allowing for re-solving after this. We describe a mixed-integer linear program and a number of increasingly refined heuristics for this problem. We created a large set of benchmark instances, both from real-life case study data and from a generator. On the real-life case study instances, the best performing heuristic finds on average a solution only 3.4% away from optimal in a few seconds. We propose an explanation for the success of this heuristic, with the most pivotal conclusion being the importance of solving the underlying p -Medians Problem.

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“…Step 4 consists of defining the optimization model itself, which is the classic model of p-medians studied widely in various applications with numerous variations [53,59,[72][73][74][75][76][77][78][79][80][81]. Thus, the model proposed in this paper is now presented in detail explaining all its variables and constraints:…”

Section: Optimization Model For the Allocation Of Storage Yardsmentioning

confidence: 99%

Allocation of Storage Yards in Management Plans in the Amazon by Means of Mathematical Programming

Silva

Figueiredo

et al. 2018

Forests

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Abstract:The present study aimed to optimize the location of wood storage yards in forest management for the production of wood in the Brazilian Amazon. The area of forest management studied was 638.17 ha, with 1478 trees selected for harvest with a diameter at breast height of at least 50 cm in accordance with Brazilian legislation. Taking the topography into account-permanent preservation areas, restricted areas, and remaining trees-and using GIS tools, 7896 sites were identified that could be used as wood storage yards. By using mathematical programming techniques, more specifically binary integer linear programming, and based on the classical p-median model, optimal locations for the opening of yards were defined. Four scenarios were proposed combining distance and volume constraints. The scenarios evaluated promoted reductions in infrastructure investment compared with traditional planning. The results showed reductions in the number of forest roads (-6.33%) and trails to extract logs (-15.49%) when compared to traditional planning. The best performing scenario was that with the maximum volume restriction. It was concluded that the application of mathematical programming was able to promote significant gains in the harvest planning of native forests of the Amazon with the potential to reduce environmental damage.

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The p-Median Problem

Cited by 122 publications

References 29 publications

Optimal selective logging regime and log landing location models: a case study in the Amazon forest

Optimal selective logging regime and log landing location models: a case study in the Amazon forest

The median routing problem for simultaneous planning of emergency response and non-emergency jobs

Allocation of Storage Yards in Management Plans in the Amazon by Means of Mathematical Programming

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