A multi-product vehicle routing scheduling model with time window constraints for cross docking system under uncertainty: A fuzzy possibilistic-stochastic programming

Document Type : Research Paper


1 Young Researchers and Elite Club, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 Department of Mathematics, Islamic Azad University, Qazvin Branch, Qazvin, Iran


Mathematical modeling of supply chain operations has proven to be one of the most complex tasks in the field of operations management and operations research. Despite the abundance of several modeling proposals in the literature; for vast majority of them, no effective universal application is conceived. This issue renders the proposed mathematical models inapplicable due largely to the fact that real-life supply chain problems are set forth in restrained terms or represented less strikingly than they would bear out. This paper is triggered to bridge this gap by proposing a universal mixed integer linear programming (MILP) framework which to large extent simulates many realistic considerations in vehicle routing scheduling problems in cross-docking systems which might have separately been attempted by other researchers. The developed model is pioneer in excogitating the vehicle routing scheduling problem with the following assumptions: a) multiple products are transported between pick-up and delivery nodes, b) delivery time-intervals are imposed on each delivery node, c) multiple types of vehicles operate in the system, d) capacity constraints exists for each vehicle type, and finally e) vehicles arrives simultaneously at cross-docking location. Moreover, to solve the model a hybrid solution methodology is presented by combining fuzzy possibilistic programming and stochastic programming. Finally, in order to demonstrate the accuracy and efficiency of the proposed model, an extensive sensitivity analysis is performed to scrutinize its parameters’ demeanors.