Optimizing of nonlinear logistic problems concerning uncertainty, time dependency and prospect theory

The logistic (transportation) system is a set of complex human, social, economic, and political interactions, and traditionally probability theory has been used for handling the obvious uncertainty. On the basis of recent research possibility theory offers a more useful way of handling the uncertain situations that often arise in logistic (transportation) analysis [1,2,3]. The two classes of uncertainty in transportation are vagueness, which is associated with the lack of clarity of the definition, such as the loss caused by a delivery delay, and ambiguity, which is associated with the lack of clarity in information, e.g., the predicted cost elements are often ambiguous. Considering real road transport, logistic networks, especially in city logistics, the actual circumstances and condition of the transit process are subject to not only the topography of the given network but to timing as well. Referring to the phenomenon of cyclic peak-hours and also to the weekly (monthly, yearly) periodicity of traffic on road, it can be stated that the unit cost of traveling is also a variable, and it can be described as a time series rather than a constant [4]. Obviously the physical distances can be considered as constant values in a given relation, but transit times are subject to external factors [5]. Furthermore the actual costs are rarely constant and predictable, so fuzzy cost coefficient can be applied in order to represent the uncertainty. In modern logistics systems uncertainty and inaccuracy are not tolerated due to th