Location of cross-docking centers and vehicle routing scheduling under uncertainty: A fuzzy possibilistic–stochastic programming model

The location of multiple cross-docking centers (CDCs) and vehicle routing scheduling are two crucial choices to be made in strategic/tactical and operational decision levels for logistics companies. The choices lead to more realistic problem under uncertainty by covering the decision levels in cross-docking distribution networks. This paper introduces two novel deterministic mixed-integer linear programming (MILP) models that are integrated for the location of CDCs and the scheduling of vehicle routing problem with multiple CDCs. Moreover, this paper proposes a hybrid fuzzy possibilistic–stochastic programming solution approach in attempting to incorporate two kinds of uncertainties into mathematical programming models. The proposed solving approach can explicitly tackle uncertainties and complexities by transforming the mathematical model with uncertain information into a deterministic model. m′m′ imprecise constraints are converted into 2Rm′2Rm′ precise inclusive constraints that agree with R  αα-cut levels, along with the concept of feasibility degree in the objective functions based on expected interval and expected value of fuzzy numbers. Finally, several test problems are generated to appraise the applicability and suitability of the proposed new two-phase MILP model that is solved by the developed hybrid solution approach involving a variety of uncertainties and complexities.