The Location-allocating Hub Problem with Direct Transportation Capability Considering Congestion and Tardiness Time in Hubs

Objective: This paper seeks to find the optimal number of hubs and their location to keep the preparation time and congestion in the hubs and costs at a minimum. Also, this study considers the tardiness time for the conditions that the customer's need is not answered in the specified time, which can help to make the problem conditions more realistic. Therefore, in this study, the scheduled time and the real-time system are considered. This paper considers the tardiness and congestion time for hub optimization problems with single, multiple, and multiple direct transport allocations. The decision variables in this model determine the number of hubs, the capacity of the hubs, and their location. Congestion and tardiness also affect service time, especially if the capacity and cost of hubs are limited. Methods: This paper uses a mathematical model to solve the hub problem of optimizing the allocation – location of single, multiple, and multiple with direct transportation. GAMS software is used to find the optimal number of hubs and locations as two objective functions are optimized. The first objective function includes transportation costs, hub setup, and tardiness costs, and the second one consists of the handling time in the hubs and the congestion inside the hubs. The sensitive analysis is investigated for the service time based on the congestion and tardiness time. Results: This model is tested on AP (Australian Post) data for single, multiple, and multiple with direct shipping allocation models. This study also solves the exact model for 100 nodes allocated to all three models. The hubs' capacity, congestion, and tardiness determine the number of hubs. In this paper, hubs are considered small, medium, and large. Congestion levels are also considered changeable. In addition, a comparison is made between single and multiple allocations concerning cost and capacity limitation to investigate service time. The findings indicate that a hub with limited cost and capacity needs more service time. The lexicography method is also used to convert objective functions into one function. Conclusion: The more the number of hubs increases, the total costs, including the transportation and hub establishment costs will also increase. Therefore, considering the transportation costs and the establishment of the hub, it can be said that single and multiple allocations can be used in some situations. However, multiple allocations with direct transport have the lowest transpo