Multi-commodity Multimodal Splittable Logistics Hub Location Problem with Stochastic Demands


Department of Industrial Engineering, Shahed University, Tehran, Iran


This study presents a multimodal hub location problem which has the capability to split commodities by limited-capacity hubs and transportation systems, based on the assumption that demands are stochastic for multi-commodity network flows. In the real world cases, demands are random over the planning horizon and those which are partially fulfilled, are lost. Thus, the present study handles demands using a discrete chance constraint programming to make the model one step closer to the reality. On the other hand, commodity splitting makes it possible for the remaining portion of commodity flow to be transported by another hub or transportation system in such a way that demands are completely fulfilled as much as possible. The problem decides on the optimum location of hubs, allocates spokes to established hubs efficiently, adopts and combines transportation systems and then makes a right decision as to whether transportation infrastructure to be built at points lacking a suitable transportation infrastructure and having the potential for infrastructure establishment. A Mixed Integer Linear Programming (MILP) model is formulated with the aim of cost minimization. Also, the proposed sensitivity analysis shows that, the discrete chance constraint programming is a good approximation of the continuous chance constraint programming when an uncertain parameter follows a normal distribution.  The results indicate the higher accuracy and efficiency of the proposed model comparing with other models presented in the literature.