Heuristic methods for the sectoring arc routing problem

Delimitation of service areas in reverse logistics networks with multiple depots

“…That is, for instance, the case of districting, where a large region is partitioned into smaller sub-regions (districts), to facilitate the organization of the 'operations' that have to be performed within the region (Muyldermans et al, 2003). Districting problems arise in many real-world applications, such as political districting (Bozkaya et al, 2003), sales territories (Zoltners and Sinha, 1983), or waste collection (Moura˜o et al, 2009).…”

The mixed capacitated arc routing problem with non-overlapping routes

“…These values represent the minimum between at most eight shortest deadheading travel times, as we are dealing with mixed graphs. In fact, if both a, b ∈ E R , eight distances are considered to compute D ab (see Mourão et al (2009)), resulting in a symmetric distance matrix D. Note that, "nicer" solutions are obtained with a smaller AT D value. We can observe that routing distances tend to increase when the shape of the service zones deviates from "nice" compact shapes such as circles or squares.…”

“…We may find measures based on maximum travel times (Mourão et al, 2009;Gonzalez-Ramírez et al, 2011); on maximum Euclidean distances (Ríos-Mercado and Fernández, 2009;Assis et al, 2014); on the sum of the Euclidean distances (Kim et al, 2006;Mourgaya and Vanderbeck, 2007;Salazar-Aguilar et al, 2012); on the averages and standard deviations of distances, or travel times between customers, or to a reference point in a zone (Poot et al, 2002;Tang and Miller-Hooks, 2006;Mourão et al, 2009); on the perimeters of the zones (Lei et al, 2012); or even perimeters and areas of the zones (Lin and Kao, 2008). Jarrah and Bard (2012) define clusters of clients in the plane in such a way that the ratio of the difference between the maximum and the minimum x coordinate and the difference of the maximum and the minimum y coordinate lies within a given interval.…”

“…In the first approach, the partitioning and the routing problems are sequentially solved, using multi phase methods (Teixeira et al, 2004;Mourão et al, 2009). In the second, the partitioning and the routing are solved together as a whole problem (Kim et al, 2006;Mourão et al, 2009;Ramos and Oliveira, 2011). In the last one, only the partitioning problem is solved.…”

“…This is the case of household waste collection (see e.g. Ghiani et al (2005); Mourão and Amado (2005); Belenguer et al (2006); Bautista et al (2008); Mourão et al (2009) ;Gouveia et al (2010)), or road network maintenance (see e.g. Amaya et al (2007)).…”