Solving the Inter-Terminal Truck Routing Problem for Delay Minimization Using Simulated Annealing with Normalized Exploration Rate
Abstract
:1. Introduction
2. Literature Review
2.1. Routing Problems and Inter-Terminal Transportation
2.2. Simulated Annealing and Modifications
3. Problem Formulation and Methodology
3.1. Inter-Terminal Truck Routing Problem Formulation
3.2. Simulated Annealing with Normalized Acceptance Rate (SANE)
Algorithm 1 SANE for ITTRP Transport Delay Minimization |
Initialize:
|
3.3. Solution Representation
4. Experiments and Discussion
4.1. Experimental Settings
4.2. Performance Comparison to Baselines
4.3. Exploration Behavior and Property of SANE
4.4. Algorithm Implications
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- UNCTAD UNCTADstat. Available online: https://unctadstat.unctad.org/EN/Index.html (accessed on 5 January 2023).
- Tierney, K.; Voß, S.; Stahlbock, R. A Mathematical Model of Inter-Terminal Transportation. Eur. J. Oper. Res. 2014, 235, 448–460. [Google Scholar] [CrossRef]
- Adi, T.N.; Iskandar, Y.A.; Bae, H. Interterminal Truck Routing Optimization Using Deep Reinforcement Learning. Sensors 2020, 20, 5794. [Google Scholar] [CrossRef] [PubMed]
- Heilig, L.; Lalla-Ruiz, E.; Voß, S. Port-IO: An Integrative Mobile Cloud Platform for Real-Time Inter-Terminal Truck Routing Optimization. Flex. Serv. Manuf. J. 2017, 29, 504–534. [Google Scholar] [CrossRef]
- Kadłubek, M.; Thalassinos, E.; Noja, G.G.; Cristea, M. Logistics Customer Service and Sustainability-Focused Freight Transport Practices of Enterprises: Joint Influence of Organizational Competencies and Competitiveness. J. Green Econ. Low-Carbon Dev. 2022, 1, 2–15. [Google Scholar] [CrossRef]
- Heilig, L.; Voß, S. Inter-Terminal Transportation: An Annotated Bibliography and Research Agenda. Flex. Serv. Manuf. J. 2017, 29, 35–63. [Google Scholar] [CrossRef]
- Heilig, L.; Lalla-Ruiz, E.; Voß, S. Multi-Objective Inter-Terminal Truck Routing. Transp. Res. Part E Logist. Transp. Rev. 2017, 106, 178–202. [Google Scholar] [CrossRef]
- Hu, Q.; Luan, X.; Corman, F.; Lodewijks, G. A Tabu Search Algorithm for Inter-Terminal Container Transport. IFAC-PapersOnLine 2016, 49, 413–418. [Google Scholar] [CrossRef]
- Gharehgozli, A.; Roy, D.; Saini, S.; van Ommeren, J.K. Loading and Unloading Trains at the Landside of Container Terminals. Marit. Econ. Logist. 2022, 25, 549–575. [Google Scholar] [CrossRef]
- Oudani, M. A Simulated Annealing Algorithm for Intermodal Transportation on Incomplete Networks. Appl. Sci. 2021, 11, 4467. [Google Scholar] [CrossRef]
- Weerasinghe, B.A.; Perera, H.N.; Bai, X. Optimizing Container Terminal Operations: A Systematic Review of Operations Research Applications. Marit. Econ. Logist. 2023, 1–35. [Google Scholar] [CrossRef]
- Šedivý, J.; Cejka, J.; Guchenko, M. Possible Application of Solver Optimization Module for Solving Single-Circuit Transport Problems. LOGI Sci. J. Transp. Logist. 2020, 11, 78–87. [Google Scholar] [CrossRef]
- Stopka, O. Modelling Distribution Routes in City Logistics by Applying Operations Research Methods. Promet-Traffic Transportation 2022, 34, 739–754. [Google Scholar] [CrossRef]
- Baals, J.; Emde, S.; Turkensteen, M. Minimizing Earliness-Tardiness Costs in Supplier Networks—A Just-in-Time Truck Routing Problem. Eur. J. Oper. Res. 2023, 306, 707–741. [Google Scholar] [CrossRef]
- Malhotra, S.; Khandelwal, M. Solving XpressBees Logistics Problem by Using Exact and Heuristic Method. LOGI Sci. J. Transp. Logist. 2022, 13, 37–48. [Google Scholar] [CrossRef]
- Nucamendi, S.; Cardona-Valdes, Y.; Angel-Bello Acosta, F. Minimizing Customers’ Waiting Time in a Vehicle Routing Problem with Unit Demands. J. Comput. Syst. Sci. Int. 2015, 54, 866–881. [Google Scholar] [CrossRef]
- Dedović, U.; Gušavac, B.A. Optimal Vehicle Routing in Consumer Goods Distribution: A GNU Linear Programming Kit-Based Analysis. Acadlore Trans. Appl. Math. Stat. 2023, 1, 87–95. [Google Scholar] [CrossRef]
- Jin, X.; Kim, K.H. Collaborative Inter-Terminal Transportation of Containers. Ind. Eng. Manag. Syst. 2018, 17, 407–416. [Google Scholar] [CrossRef]
- Cao, P.; Zheng, Y.; Yuen, K.F.; Ji, Y. Inter-Terminal Transportation for an Offshore Port Integrating an Inland Container Depot. Transp. Res. Part E Logist. Transp. Rev. 2023, 178, 103282. [Google Scholar] [CrossRef]
- Adi, T.N.; Bae, H.; Iskandar, Y.A. Interterminal Truck Routing Optimization Using Cooperative Multiagent Deep Reinforcement Learning. Processes 2021, 9, 1728. [Google Scholar] [CrossRef]
- Suarez, J.; Millan, C.; Millan, E. Improved Modified Simulated Annealing Algorithm for Global Optimization. Contemp. Eng. Sci. 2018, 11, 4789–4795. [Google Scholar] [CrossRef]
- Gonzalez-Ayala, P.; Alejo-Reyes, A.; Cuevas, E.; Mendoza, A. A Modified Simulated Annealing (MSA) Algorithm to Solve the Supplier Selection and Order Quantity Allocation Problem with Non-Linear Freight Rates. Axioms 2023, 12, 459. [Google Scholar] [CrossRef]
- Alnowibet, K.A.; Mahdi, S.; El-Alem, M.; Abdelawwad, M.; Mohamed, A.W. Guided Hybrid Modified Simulated Annealing Algorithm for Solving Constrained Global Optimization Problems. Mathematics 2022, 10, 1312. [Google Scholar] [CrossRef]
- Burke, E.K.; Kendall, G. Search Methodologies; Springer: New York, NY, USA, 2014; ISBN 978-1-4614-6939-1. [Google Scholar]
- Park, N.-K.; Lee, J.-H. The Evaluation of Backhaul Transport with ITT Platform: The Case of Busan New Port. J. Fish. Mar. Sci. Educ. 2017, 29, 354–364. [Google Scholar] [CrossRef]
- Arık, O.A.; Schutten, M.; Topan, E. Weighted Earliness/Tardiness Parallel Machine Scheduling Problem with a Common Due Date. Expert Syst. Appl. 2022, 187, 115916. [Google Scholar] [CrossRef]
- Misztal, W. The Impact of Perturbation Mechanisms on the Operation of the Swap Heuristic. Arch. Automot. Eng. 2019, 86, 27–39. [Google Scholar] [CrossRef]
- Tang, Y.; Agrawal, S.; Faenza, Y. Reinforcement Learning for Integer Programming: Learning to Cut. In Proceedings of the International Conference on Machine Learning, PMLR. Virtual, 13–18 July 2020; pp. 9367–9376. [Google Scholar]
- Qi, M.; Wang, M.; Shen, Z.-J. Smart Feasibility Pump: Reinforcement Learning for (Mixed) Integer Programming. arXiv 2021, arXiv:2102.09663. [Google Scholar]
Sets | |
---|---|
A set of all container terminal locations | |
A set of all trucks | |
A set of all orders | |
A set of truck initial positions described by , where is the initial position of truck |
Parameters | |
---|---|
Index of an order or index of . To avoid ambiguity, we always state whether or when such index is used. | |
Index of a truck, | |
Index of initial position, | |
Source/pick-up location of order , where | |
Destination location of order , where | |
The earliest possible time of delivery of order | |
The time of delivery deadline | |
A penalty per-unit of time given for each late order, see the objective function (2) for more detail | |
Travel time of delivering order right after performing order | |
Big notation to describe a large positive real number |
Decision Variables | |
---|---|
Binary decision variable that returns 1 if order is performed immediately after order and return 0 otherwise | |
Continuous decision variable to represent the time of delivery of order | |
Binary decision variable that returns 1 if order is late and returns 0 otherwise |
From/To | PNIT | PNC | HJNC | HPNT | BNCT |
---|---|---|---|---|---|
PNIT | 0.0% | 6.6% | 0.9% | 3.3% | 9.2% |
PNC | 9.3% | 0.0% | 9.1% | 0.6% | 8.2% |
HJNC | 4.3% | 10.0% | 0.0% | 2.1% | 7.8% |
HPNT | 1.7% | 8.1% | 2.6% | 0.0% | 5.2% |
BNCT | 6.3% | 0.6% | 2.0% | 1.9% | 0.0% |
Dataset | Number of Trucks | Number of Orders |
---|---|---|
ITT010-2 | 2 | 10 |
ITT015-3 | 3 | 15 |
ITT030-6 | 6 | 30 |
ITT060-9 | 9 | 60 |
ITT100-12 | 12 | 100 |
ITT120-15 | 15 | 120 |
Dataset | Averaged Total Delay Cost (Unit Price) | Averaged Solving Time (s) | ||||||
---|---|---|---|---|---|---|---|---|
MIP | TS | SA | SANE | MIP | TS | SA | SANE | |
ITT010-2 | 200.8 | 209.2 | 270.4 | 200.8 | 0.05 | 0.33 | 0.38 | 0.80 |
ITT015-3 | 233.2 | 296.4 | 271.6 | 239.6 | 0.42 | 1.25 | 0.56 | 1.14 |
ITT030-6 | 681.6 | 842.4 | 726.0 | 717.6 | 58.84 | 11.997 | 1.36 | 2.57 |
ITT060-9 | - | 679.2 | 589.2 | 444.8 | - | 109.82 | 3.57 | 5.87 |
ITT100-12 | - | 2350.4 | 2224.4 | 1944.8 | - | 717.60 | 12.83 | 15.15 |
ITT120-15 | - | 3431.6 | 3273.2 | 2674.4 | - | 817.52 | 18.97 | 20.69 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Ramadhan, M.H.; Kamal, I.M.; Kim, D.; Bae, H. Solving the Inter-Terminal Truck Routing Problem for Delay Minimization Using Simulated Annealing with Normalized Exploration Rate. J. Mar. Sci. Eng. 2023, 11, 2103. https://doi.org/10.3390/jmse11112103
Ramadhan MH, Kamal IM, Kim D, Bae H. Solving the Inter-Terminal Truck Routing Problem for Delay Minimization Using Simulated Annealing with Normalized Exploration Rate. Journal of Marine Science and Engineering. 2023; 11(11):2103. https://doi.org/10.3390/jmse11112103
Chicago/Turabian StyleRamadhan, Muhammad Hanif, Imam Mustafa Kamal, Dohee Kim, and Hyerim Bae. 2023. "Solving the Inter-Terminal Truck Routing Problem for Delay Minimization Using Simulated Annealing with Normalized Exploration Rate" Journal of Marine Science and Engineering 11, no. 11: 2103. https://doi.org/10.3390/jmse11112103