A specialized branch & bound & cut for Single-Allocation Ordered Median Hub Location problems

Robust and fuzzy goal programming optimization approaches for a novel multi-objective hub location-allocation problem: A supply chain overview

“…Recently, elaborative mathematical models based on the above-mentioned pieces of research have been devised. To know more, other research pieces [15][16][17][18] can also be referred to in this regard.…”

“…Constraint (18) assures that the amount of raw material type s to be shipped through hubs k and m and terminated to node j as final commodity r is positive if the connective link between node i and hub k has already been formed. Constraint (19) assures that the amount of raw material s to be shipped through hubs k and m and terminated to node j as final commodity r is positive if the connective link between node j and hub m has already been formed.…”

“…Additionally, to linearize constraint (18), new binary variables vd u f km are defined as equal to the multiplication of v u f k · v u f m , firstly, and then the following constraints are added:…”

Robust optimization approach to capacitated single and multiple allocation hub location problems

“…In this model there is no direct link among non-hub nodes and flow just distributed in the network through the hubs' linking. This is the case, for example in Abdinnour-Helm (1998), Chen (2007, Correia et al (2010b), Costa et al (2007), de Camargo and Miranda (2012, Ebery (2001), Krishnamoorthy (1996, 1999), Ilić et al (2010), Iwasa et al (2009), Kratica et al (2007, Labbé and Yaman (2004), Labbé et al (2005), Pirkul and Schilling (1998), Puerto et al (2011), Puerto et al (2013, Randall (2008), Silva andCunha (2009), Skorin-Kapov andSkorin-Kapov (1994), and Sohn and Park (2000). In the multiple allocation model, several nodes will be selected as a hub and other nodes, namely non-hub nodes (spoke), can connect to more than one hub.…”

A comparative study of formulations and solution methods for the discrete ordered p-median problem

“…Given a vector of weights, this function consists in an ordered weighted average of the allocation costs, namely it sorts these costs in non-decreasing sequence and then it performs the scalar product of this so obtained sorted cost vector and the given vector of weights. This objective function has been widely applied in the field of location analysis and distribution models (Marín et al [10], Kalcsics et al [9] and Puerto et al [17,18]). In addition, it has the potential to yield new models for order statistics embedded within mathematical programming formulations; thus enlarging the applications of optimization tools to the resolution of statistical problems in data analysis.…”