Operations Research and cost-effective spatial conservation planning: data, models, tools and future directions

Biodiversity conservation questions human practices towards biodiversity and, therefore, largely conflicts with ordinary societal aspirations. Decisions on the location of protected areas, one of the most convincing conservation tools, reflect such a competitive endeavor. Operations Research (OR) brings a set of analytical models and tools capable of resolving the conflicting interests between ecology and economy. Recent technological advances have boosted the size and variety of data available to planners, thus challenging conventional approaches bounded on optimized solutions. New models and methods are requested to use such a massive amount of data in integrative schemes addressing a large variety of concerns. Here, we provide an overview on the past, present and future challenges that characterize spatial conservation models supported by OR. By enlarging the spatial, temporal, taxonomic and societal horizons of biodiversity conservation planners navigate around multiple bio-socioeconomic equilibria and are able to decide on cost-effective strategies to improve biodiversity persistence

Warehouse Storing and Collecting of Parts

This report deals with reducing the high costs resulting from the wear and tear of the fork-lifts used to store or collect items in a warehouse. Two problems were identified and addressed separately. One concerns the way items should be stored or collected at storage locations on the shelves of one corridor. The other problem seeks for an efficient way to define which fork-lift should operate on each corridor, and the order by which the fork-lifts should visit the corridors. We give to both problems formulations that fit in the framework of combinatorial optimization

Spatial adaptive responses of highly threatened European mammal species under climate change

Current species’ range displacements are mostly triggered by climate change but European landscapes are largely dominated by human activities. In this study we identify the most promising spatial adaptive trajectories (SATs) for the thirty most threatened non volant mammal species in Europe up to 2080 (under three climate and land change scenarios) and where/when SATs of each species synchronically converge. We found large contrasts on the persistence of species in SATs, with some species largely reliant on the functionality of areas where many SATs converge. Overall, SATs and convergence centers are not adequately covered by existing conservation areas and coincide with crop and arable lands, compromising species persistence. It is important to invest in the protection of SATs and convergence centers through a mix of conventional instruments and new collaborative forms with the socio-economy. Anticipative plans at long-term coupled with risk analysis offer decision–makers templates to prevent negative surprises

A computational comparison of compact MILP formulations for the zero forcing number

Consider a graph where some of its vertices are colored. A colored vertex with a single uncolored neighbor forces that neighbor to become colored. A zero forcing set is a set of colored vertices that forces all vertices to become colored. The zero forcing number is the size of a minimum forcing set. Finding the minimum forcing set of a graph is NP-hard. We give a new compact mixed integer linear programming formulation (MILP) for this problem, and analyse this formulation and establish relation to an existing compact formulation and to two variants. In order to solve large size instances we propose a sequential search algorithm which can also be used as a heuristic to derive upper bounds for the zero forcing number. A computational study using Xpress (a MILP solver) is conducted to test the performances of the discussed compact formulations and the sequential search algorithm. We report results on cubic, Watts-Strogatz and randomly generated graphs with 10, 20 and 30 vertices.publishe

A tool for data analysis

Funding Information: The first and third authors were financially supported by the Fundação para a Ciência e a Tecnologia, Portugal (Portuguese Foundation for Science and Technology) through the projects UIDB/MAT/00297/2020 , UIDP/MAT/00297/2020 (Centro de Matemática e Aplicações), and PTDC/CCI-BIO/4180/2020 . The second author was financially supported by the Forest Research Center, a research unit funded by Fundação para a Ciência e a Tecnologia (FCT), Portugal , through the project ( UIDB/00239/2020 ). Publisher Copyright: © 2023 The Author(s)Consider a graph with vertex set V and non-negative weights on the edges. For every subset of vertices S, define ϕ(S) to be the sum of the weights of edges with one vertex in S and the other in V∖S, minus the sum of the weights of the edges with both vertices in S. We consider the problem of finding S⊆V for which ϕ(S) is maximized. We call this combinatorial optimization problem the max-out min-in problem (MOMIP). In this paper we (i) present a linear 0/1 formulation and a quadratic unconstrained binary optimization formulation for MOMIP; (ii) prove that the problem is NP-hard; (iii) report results of computational experiments on simulated data to compare the performances of the two models; (iv) illustrate the applicability of MOMIP for two different topics in the context of data analysis, namely in the selection of variables in exploratory data analysis and in the identification of clusters in the context of cluster analysis; and (v) introduce a generalization of MOMIP that includes, as particular cases, the well-known weighted maximum cut problem and a novel problem related to independent dominant sets in graphs.publishersversionpublishe

Scheduling aircraft’s engines repair process: a mathematical model

In this talk, we discuss a scheduling problem that originated at TAP - Maintenance & Engineering - the maintenance, repair and overhaul organization of Portugal’s leading airline. In the repair process of aircrafts’ engines, the operations to be scheduled may be executed on a certain workstation by any processor of a given set, and the objective is to minimize the total weighted tardiness. A mixed integer linear programming formulation, based on the flexible job shop scheduling, is presented here, along with computational experiment on a real instance, provided by TAP-ME, from a regular working week. The model was also tested using benchmarking instances available in literature

A decomposition approach for the p-median problem on disconnected graphs

The p-median problem seeks for the location of p facilities on the vertices (customers) of a graph to minimize the sum of transportation costs for satisfying the demands of the customers from the facilities. In many real applications of the p-median problem the underlying graph is disconnected. That is the case of p-median problem defined over split administrative regions or regions geographically apart (e.g. archipelagos), and the case of problems coming from industry such as the optimal diversity management problem. In such cases the problem can be decomposed into smaller p-median problems which are solved in each component k for different feasible values of pk, and the global solution is obtained by finding the best combination of pk medians. This approach has the advantage that it permits to solve larger instances since only the sizes of the connected components are important and not the size of the whole graph. However, since the optimal number of facilities to select from each component is not known, it is necessary to solve p-median problems for every feasible number of facilities on each component. In this paper we give a decomposition algorithm that uses a procedure to reduce the number of subproblems to solve. Computational tests on real instances of the optimal diversity management problem and on simulated instances are reported showing that the reduction of subproblems is significant, and that optimal solutions were found within reasonable time

Definition of the productivity regions

Eucalyptus productivity is strongly related with climate and soil types of the area where it is planted. To accurately assess the potential productivity of that species in Portugal, plantations were monitored at different management units compartments (MUC) at several locations all over Portugal. Certain indices of productivity of the Eucalyptus at each MUC were recorded, as well as the type of climate and soil characteristics of the region. Both climate and soil, factors that affects Eucalyptus grow, were classified in in ten classes 1, 2, . . . , 10 of expected growing productivity for the Euca- lyptus. Thus, every MUC belongs to a unique pair (c, s), with 1 \leq c \leq 10 and 1 \leq s \leq 10 indicating the type of climate and the type of soil of the region where MUC is located, respectively, and it is expected that to have high (low) productivity indices when c and s are both close to 10 (1). The aim of this work is to identify regions that have similar productivity levels based on the classifications of soil and climate types and to check if the available data provided by RAIZ show that those factors affect the productivity indices. During the 5-days ESGI this team worked on the datasets provided by RAIZ, presented an update for the existing MAI productivity chart and developed new clusters for the Density, Yeld and Consumption productivity indices. The definition of some quality measures for the clusters, allowed to compare the different approaches and also point out some fragilities on the datasets. Indeed, a review of classification regarding climate and/or soil characteristics is suggested, as well as the need of a bigger sample for the Density, Yeld and Consumption productivity indices in order to get more reliable outputs