Marine debris pollution is becoming an increasingly serious problem, affecting not only navigational safety but also the health of marine ecosystems. Carbon emission causes ocean acidification, which greatly harms mar...
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Marine debris pollution is becoming an increasingly serious problem, affecting not only navigational safety but also the health of marine ecosystems. Carbon emission causes ocean acidification, which greatly harms marine lives. In order to respond to these environmental issues, this paper studies marine debris collection with consideration of carbon cap using logistics network. To the most of our knowledge, this is first work to study marine debris removal from logistics way. We proposed a three-phase marine debris collection framework: (1) identifying initial locations of the debris;(2) utilizing GNOME software to predict the drifting trajectory of the debris;and (3) formulating vessel routing as a mixed integer nonlinear programming with consideration of carbon emission. The model seeks to minimize the total costs including fuel cost, berth cost, unloading cost in the harbor, vessel rent, vessel insurance, and labor cost, with respect to the constraints of carbon cap, vessel capacities, and time windows. After the linearization process, a branch-and-cut (B&C) algorithm with multiple variable fixing techniques and valid inequalities is used to solve the proposed model. The debris dispersion located in Boston vicinity is used as a case study to validate the proposed model and algorithm. The results reveal that the farther away the debris location is from the shore, the higher the collection cost and the more the carbon emission would be. The daily collection cost in the closest location and in the farthest location is $140 lower and $210 higher than that in the initial location. The carbon emission in the farthest location is 21% and 32% higher than that in the initial location and in the closest location. Sensitivity analysis is also carried out for the fuel price and carbon cap to test their impact on total costs These results show that proposed model and algorithm can significantly improve the efficiency of marine debris collection process, reduce carbon emission
Given a connected graph G = ( V, E ), a Safe Set S is a subset of the vertex set V such that the cardinality of each connected component in the subgraph induced by V \ S does not exceed the cardinality of any connecte...
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Given a connected graph G = ( V, E ), a Safe Set S is a subset of the vertex set V such that the cardinality of each connected component in the subgraph induced by V \ S does not exceed the cardinality of any connected component in the subgraph induced by S , whenever there is an edge in G between vertices of the two components. When the vertices of G are weighted, the weight of a component is defined as the sum of the weights of its vertices, and the notion of safe set is extended by considering the weight of connected components in subgraphs induced by S and by V \ S . We propose an integer linear formulation for the Weighted Safe Set Problem that uses only one variable per vertex. The formulation has an exponential number of constraints, which can be generated on-the-fly within a branch-and-cut algorithm. We describe a linear-time separation algorithm for these constraints. In addition, we describe families of cuts based on cliques and on minimum weight cut separators, and discuss separation algorithms. A branch-and-cut algorithm that solves the proposed formulation is computationally compared with two alternative formulations from the literature, and shows faster in solving most of benchmark instances with low edge density.
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