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ISSN 1895-2038, e-ISSN:1734-459X

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Creative Commons licence CC BY-NC (Attribution-NonCommercial) Logforum. 2021. 17(2), article 6, 243-251; DOI: https://doi.org/10.17270/J.LOG.2021.572

MIXED-INTEGER PROGRAMMING FORMULATIONS FOR THE TRUCK SCHEDULING PROBLEM WITH FIXED OUTBOUND DEPARTURES

Pascal Wolff1, Jiazhen Huo1, Hans-Christian Pfohl2

1Tongji University, Shanghai, China
2
Technical University of Darmstadt, Darmstadt, Germany

Abstract:

Background: Truck scheduling at cross-docking terminals has received much academic attention over the last three decades. A vast number of mixed-integer programming models have been proposed to assign trucks to dock-doors and time slots. Surprisingly, only a few models assume fixed outbound truck departures that are often applied in the less-than-truckload or small parcel and express delivery industry. To the best of our knowledge, none of these papers explore whether a discrete-time or continuous-time model formulation has a better computational performance. This paper attempts to close this research gap and tries to shed light on which type of formulation is advantageous. Therefore, a variant of the truck scheduling problem with fixed outbound departures is considered. This problem's objective is to find a feasible truck schedule that minimizes the number of delayed freight units.

Methods: We propose two model formulations for the described variant of the truck scheduling problem with fixed outbound departures. Specifically, the problem is formulated as a discrete-time and a continuous-time mixed-integer programming model.

Results: A computational experiment is conducted in order to assess the computational performance of the presented model formulations. We compare the discrete-time and continuous-time formulation in terms of both the solution quality and computational time.

Conclusions: The computational results show that the proposed discrete-time model formulation can solve problem instances of medium size to proven optimality within less than one minute. The continuous-time model formulation, on the other hand, can solve small instances to optimality. However, it requires longer solution times than the discrete-time formulation. Furthermore, it is unable to solve medium-sized instances within a 5-minute time limit. Thus, it can be summarized that the proposed discrete-time model formulation is clearly superior to the continuous-time model formulation.

Keywords: cross-docking; truck scheduling; mixed-integer programming; logistics; optimization
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For citation:

MLA Wolff, Pascal, et al. "Mixed-integer programming formulations for the truck scheduling problem with fixed outbound departures ." Logforum 17.2 (2021): 6. DOI: https://doi.org/10.17270/J.LOG.2021.572
APA Pascal Wolff, Jiazhen Huo, Hans-Christian Pfohl (2021). Mixed-integer programming formulations for the truck scheduling problem with fixed outbound departures . Logforum 17 (2), 6. DOI: https://doi.org/10.17270/J.LOG.2021.572
ISO 690 WOLFF, Pascal, HUO, Jiazhen, PFOHL, Hans-Christian. Mixed-integer programming formulations for the truck scheduling problem with fixed outbound departures . Logforum, 2021, 17.2: 6. DOI: https://doi.org/10.17270/J.LOG.2021.572