Freight transportation function in supply chain optimization models: A critical review of recent trends

•Critical Review of freight transportation functions in supply chain models.•We identified one paradigm, two trends and an anomaly in transportation modeling.•We identified a lack of correspondence between transportation modeling and costs.•We propose a graphical framework to handle anomalies in transportation modeling.

Supply chain mathematical programming models mainly used for computer-aided decision-making processes, have been widely used to date as an advanced support to the experts’ opinions. Transportation operations are often a central aspect of such models. We developed a detailed review of the freight transportation function included in supply chain models, and some transportation aspects were identified and analyzed in recent articles (2009–2013). We identified one paradigm, two trends and an anomaly regarding transportation modeling. The main anomaly-related observation refers to the absence of correspondence between the modeling of transportation operations and the transportation cost function considered in the models. This gap has not been so far considered in the literature and we propose a framework to guide, in a more systemic way, the transportation considerations into optimization models. In addition, some concerns regarding trade-off analysis, private/outsourced fleet considerations, the role of time and distance in transportation cost analysis, among others, were also included. These issues are expected to be significant for supply chain analysts whose decisions emerge from modeling and computer-aided tools.