Uncertainty modeling in multi-objective vehicle routing problem under extreme environment

Assumption of fuzziness in the vehicle routing problems under extreme conditions is necessary for modelers, because there are usually insufficient objective input data. In extreme situations, the complexity of the description of vehicles’ movement on routes may cause by two poles: the imprecision of movement time and the uncertainty of the possibility of movement on roads. Traditionally, a fuzzy value has been used to represent the data’s impreciseness; hence, only one pole of expert’s information is taken in the aggregation results. The main objective of this paper is to present an efficient way for fuzzy vehicle routing modeling to minimize the decision-making risks in the optimal planning of routes network and from distribution centers to demand points. To address this, a new two-stage possibilistic bi-criteria vehicle routing problem (VRP) is presented under extreme conditions. In the first stage, the sample of so-called “promising” closed routes are selected based on a “constructive” approach using a simulation algorithm. The expected times of the vehicle movement between demand points are taken as fuzzy triangular numbers. In the second stage, based on Choquet integral’s, a bi-criteria partitioning model for the fuzzy VRP has been constructed. The constraint approach has been defined to obtain the optimal solution of the model. For numerical experiments, a parallel algorithm is created based on D. Knuth’s algorithm of dancing links. An example is presented with the results of our approach for the VRP, where all Pareto-optimal solutions are found from the promising routes.