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Optimization of the Vehicle Soft-Routing Model: Effect of the Route Third Dimension on the Transportation Costs and Travelled Route Shape

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  • Milad Askary

    (Iran University of Science and Technology)

  • Ahmad Makui

    (Iran University of Science and Technology)

  • Mohammad Reza Mohammad Aliha

    (Iran University of Science and Technology)

Abstract

This study initially surveys one of the most popular operations research models known as vehicle routing problem (VRP) and expresses its weakness confronting the real-world situations. For this, the purpose of the present article expands the dimensions of the problem under study from two dimensions to three dimensions. The third dimension is considered the route slope because of its role in increasing the transportation cost. To solve this problem, a new mixed integer programming as vehicle soft routing problem (VSRP) proposes optimizing this class of problems in a three-dimensional cartesian coordinate system. To compare VSRP vs VRP, several numerical cases are examined. Computational results show that using the VSRP will decrease the total cost under all numerical cases. In addition, the graphically projected routes show that selected routes sequencing in VSRP have lower slope than the routes selected by VRP models. For example, in one of the numerical cases, we are faced with a 5.2% decrease in cost and a 286% improvement in lowering the route slope based on defined index.

Suggested Citation

  • Milad Askary & Ahmad Makui & Mohammad Reza Mohammad Aliha, 2025. "Optimization of the Vehicle Soft-Routing Model: Effect of the Route Third Dimension on the Transportation Costs and Travelled Route Shape," SN Operations Research Forum, Springer, vol. 6(4), pages 1-20, December.
    • Handle: RePEc:spr:snopef:v:6:y:2025:i:4:d:10.1007_s43069-025-00551-9
    DOI: 10.1007/s43069-025-00551-9
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