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Top2. State Of The Art
An effective train loading plan can lead to significant and multilateral gains by reducing monetary, time and environmental costs and thus a significant number of researches have driven their attention towards this field (Bontekoning, Macharis, & Trip, 2004). Although, the majority of the studies are relevant to sea port container terminals (Ambrosino & Siri, 2014; Stahlbock & Voß, 2007), nevertheless, a number of studies has started emerging for hinterland terminals also.
The problem of train loading is a subcategory of the problem known in the scientific society as “bin packing”. According to this problem, objects of different volumes (containers) must be packed into a finite number of bins (wagons) in a way that minimizes the number of bins used. Solving techniques based on mathematical models using integer linear programming or metaheuristics are the most well-known approaches to tackle this class of problems. Examples of the constraints taken into account are (narrow view) the maximum weight attached onto wagons, the maximum number of containers per wagon, the number of wagons attached to a train and its total weight as well as (wider view) terminal equipment resources, maximum truck waiting time allowed, etc.
One of the first works concerning the narrow view of the problem is the one of Feo & Gonzáles-Velarde, (1995) who treated the problem of assigning trailers to wagons. Their models and solutions were based on the assumption that no more than two trailers can fit on one wagon. Nearly a decade later, Corry & Kozan, (2006) optimized the train load planning with respect to the service and loading time as well as the restrictions imposed by the safety regulations, which determine the weight distribution along the train. Only one type of container and no weight restrictions for the wagons were taken into account. In a subsequent paper Corry & Kozan, (2008) focused on the minimization of the train length and the total train service time. Neither weight restrictions for the wagons nor for the whole train were considered. An integer linear program was developed but due to its complexity, realistic problem instances were tackled by use of heuristics (local search). A recent work on the subject was this of Aggoun, Rhiat, & Grassien, (2011) that incorporated into the problem the aspects of business constraints, like handling of dangerous commodities and incompatibilities between families of containers.