Abstract
In a Green Pickup-and Delivery problem (GPD), green vehicles (e.g., electric or hybrid cars) are used for routing in the problem domain, and these vehicles are particularly constrained with limited fuel capacity, thus shorter traveling range. A refueling infrastructure providing wide-area coverage, meanwhile, has not been fully developed to this end. A recent study reveals that vehicle routing inessence with green constraints only, is at least weakly NP-hard, motivating us to pursue a deeper understanding of the underlying computational challenge associated with this âgreenâ intractability. In this paper we perform complexity analysis on several GPD subproblems (namely, RINGs), that is, theproblems whose task-graphs are under a ring structure. Using measures of width/length of rings, we delineate clearly two complexity boundaries: one between weakly and strongly NP-complete, and the other between tractable and intractable in general. Our results bring new insights for the research anddevelopment (current and active, but with limited success only to this point) of heuristics or algorithmsfor solving GPDs
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