A Probabilistic Mathematical Programming Model for Transportation Network Optimization under Dynamic Multiple Barriers Uncertainty

This study presents a scenario-based bi-objective mathematical programming model for facility location and customer allocation under the uncertainty of multiple dynamic barriers (such as traffic or road closures). The model, by considering multiple scenarios with different occurrence probabilities, models the effects of dynamic barriers on transportation costs and carbon emissions. The proposed model simultaneously pursues two objectives: minimizing transportation costs and reducing carbon emissions. Multiple dynamic barriers are modeled through various scenarios, and their effects on rectilinear distance and carbon emissions are taken into account through defined coefficients. In addition, the model considers operational constraints such as facility capacity, workload balance, maximum allowable distance, and maximum allowable carbon emissions to ensure its practical applicability in logistics planning. The model is solved using the weighting method and LINGO optimization software, and sensitivity analysis has been performed on the objective weights, the number of active multiple dynamic barriers, the percentage increase in distance and carbon emissions, and the minimum demand for activating a facility. The results show that the model is capable of determining optimal locations for facilities and customer allocations by considering the impact of each dynamic barrier on distance and carbon emissions, while creating a suitable balance between economic and environmental objectives. Finally, suggestions for future research, including considering stochastic demand and using metaheuristic algorithms, are presented.