This paper has addressed the new model for the hub location-allocation problem that can evaluate the impact of cost and time of tardiness in delivering goods to the destination, find the optimal number of hubs and vehicles with different capacities, and congestion in hubs. In addition, this study investigates the problem from two perspectives: scheduled time and real-time. Also, it compares the problem in circumstances with tardiness and solves the problem with two objective functions by minimizing the total costs, handling time, and delay time caused by congestion in the hubs. Moreover, the uncertainty of transportation costs and hub establishment are considered. For this purpose, the Monte-Carlo simulation is used. Due to the models being non-convex and non-derivative, they are NP-hard. So, the models are solved with the particle swarm optimization (PSO) algorithm. The models are tested on Australian Post (AP) data for single and multiple allocations. Also, we presented a model that can illustrate the effect of tardiness on the results and service time. The results show multiple allocation than single ones needs the smaller hubs and cheaper vehicles for transportation due to access the nodes to several hubs.

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