model. F(x), w 0 subject to x X By varying the weights, weighted sums can be used for generating efficient extreme point solutions for design problems, and supported (convex nondominated) points for evaluation problems. In such cases, the pre-selected site set is tied to a restriction on the maximum number of hubs that could be installed. There is, indeed, a stated need for a more refined representation of transportation networks. ( Ambrosino Sciomachen, 2012 ) goin the same direction, adopting a procedure that considers government data on supply and demand of products. 2, on the other hand, when stakes are high, it is important to properly structure the problem and explicitly evaluate multiple criteria. Renewable and Sustainable Energy Reviews. They comprise: i) transport, related to transportation costs, time or distance travelled; ii) hub functionality, regarding the activities carried out on the hub, capacity, skilled labor availability, operating costs, fees, etc.; iii) investment, concerning the required amount of capital for the construction of facilities; iv). In this case, ( krinjar, Rogi Stancovi, 2012 ) point out that the transportation costs between the hubs end up being lower than those of other arcs, resulting from a better use of the infrastructure available.
( Rahimi, Asef-Vaziri Harrison, 2008 ( Ambrosino Sciomachen, 2012 ( Lee, Huang Teng, 2009 ( Dubke Pizzolato, 2011 ) and ( Alumur, Kara Karasan, 2012 ). However, this segmentation makes it difficult to identify the available (or more adequate) approaches to deal with a specific situation, such as logistics hubs; in fact, the applicability of location models is a matter at constant debate. On the other hand, there are several works,.g. When dealing with multiple criteria, the AHP is commonly applied as a first step of decision making, being employed to classify criteria in a scale of importance, such as done by ( Lee, Huang Teng, 2009 ( Tu., 2010 ( Turskis Zavadskas, 2010. Because of these features they might seem, at first glance, more suitable and complete.
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The number of alternatives is either infinite and not countable (when some variables are continuous) or typically very large if countable (when all variables are discrete). Such hubs impact on the efficiency of transportation systems, since they directly affect the flow of goods. Alumur Kara, 2008 farahani., 2013 ) reviewed theliterature on hub location from 2007 onwards. The results would then be used as an input for a more generic network flow model;.e. Although the results obtained with this method are concrete outcomes, its credibility depends intrinsically on the skills of decision makers and their ability and experience in selecting the most appropriate level of preference when comparing decision criteria ( Klapita vecová, 2006 ). But, unlike for multi-criteria, we did not find a preferred set of techniques for solving single-criterion models. Among the methods found, the most adopted ones are fuzzy sets and the analytic hierarchy process (AHP followed by weighted sum, goal programming and technique for order of preference by similarity to ideal solution (topsis). Bragge,.; Korhonen,.; Wallenius,.; Wallenius,. Representations and definitions edit The mcdm problem can be represented in the criterion space or the decision space. Although they have been seen, over time, to be broadly applicable to many network topologies, the models' abstract nature, apparent simplicity, and generality limit their ability to accurately represent important features of logistics systems ( Campbell O'Kelly, 2012 ).