Multi-commodity rebalancing and transportation planning considering traffic congestion and uncertainties in disaster response

Following the occurrence of disasters, various commodities are distributed to pre-determined relief centers. Owing to the high-level demand uncertainty, initial multi-commodity distribution strategy may be imperfect, resulting in the unexpected cases that some relief centers have surplus commodities while others' needs cannot be fully satisfied. Consequently, it is necessary to rebalance commodities among relief centers to enable their effective use. In this study, commodities rebalancing problem with traffic congestion under uncertainty is considered. Then, this problem is formulated as a bi-objective stochastic mixed-integer nonlinear programming model to minimize the expected total weighted unmet demand proportion and the expected total transportation time. Linearization and epsilon-constraint approaches are devised to solve the established model to obtain the non-dominated solutions. Finally, a case study is implemented to validate the proposed model and solution strategies. Computational results indicate that the proposed method is effective to facilitate the decision-making in the multi-commodity rebalancing problem in disaster response. Furthermore, relief-center weight, stock level, and transportation time play an indispensable role in designing the strategies regarding multi-commodity rebalancing in response to a disaster. Increasingly, this paper expects to not only validate the effectiveness and feasibility of the methodology but underline the importance of incorporation of traffic congestion, uncertainties, fairness principle into the commodity rebalancing problem.