DOI: 10.5937/jaes0-47651
This is an open access article distributed under the CC BY 4.0
Volume 22 article 1179 pages: 199-214
Vehicle routing, with its many variants, is one of the most important and frequently solved problems in transportation engineering. The aim of this paper is to develop a decision-making support tool for addressing the issue of dispatching vehicles in scenarios characterized by uncertain demands within soft time windows. In real-world scenarios, it is not uncommon for customer demands to exhibit flexibility, where certain early arrivals or delays may be deemed acceptable. Therefore, this paper introduces vehicle routing in more realistic contexts, offering potential practical implementations. The methodology for solving the problem is based on a fuzzy logic system whose membership functions are additionally adjusted using a neural network. Such a tool, neuro-fuzzy logic, is suitable for solving a defined routing problem since it can consider all the mentioned uncertainties in the distribution systems. Each user is assigned a performance index that considers travel time, demand, and delivery time windows. Then, the performance index is used as input data in the proposed vehicle routing tool based on the Clarke-Wright algorithm. The described approach has been tested on a concrete example, mimicking a distribution network resembling real-world conditions, incorporating estimated travel times between customers. The results demonstrate that the proposed approach can effectively handle customer demands, with an average delay of 5.05 minutes during the 80-minute distribution. In future research, some environmental factors could be included in the proposed model. In addition, one of the directions of future research could be vehicle re-routing using the ideas from this paper.
1.
U.S. Transportation. Climate
Impact Index, ranking the top 100 metro areas in the United States. (2019),
from https://www.streetlightdata.com/, accessed on 2023-05-06.
2. Sawik B,
Faulin J, Pérez-Bernabeu E. (2017). Multi-criteria optimization for fleet size with
environmental aspects. Transportation Research
Procedia, vol. 27, 61-68. DOI: https://doi.org/10.1016/j.trpro.2017.12.056
3. Qian J, Eglese R. Fuel
emissions optimization in vehicle routing problems with time-varying speeds. (2016).
European
Journal of Operational Research,
vol. 248, no. 3, 840-848. DOI: https://doi.org/10.1016/j.ejor.2015.09.009
4.
Zadeh L. (1965). Fuzzy sets. Information
and Control, vol.8, 338–353.
5. Jang JS. (1993). ANFIS:
adaptive-network-based fuzzy inference system. IEEE Transactions on Systems, Man, and Cybernetics, vol. 23, no.
3, 665-685. DOI: 10.1109/21.256541
6. Balinski ML, Quandt RE. (1964).
On an integer program for a delivery problem. Operations Research, vol. 12, no. 2, 300-304. DOI:
https://doi.org/10.1287/opre.12.2.300
7. Laporte G, Nobert Y.
(1987). Exact algorithms for the vehicle routing problem. North-Holland Mathematics Studies, vol. 132, 147-184. DOI:
https://doi.org/10.1016/S0304-0208(08)73235-3
8. Prins C. (2004). A simple
and effective evolutionary algorithm for the vehicle routing problem. Computers & Operations Research,
vol. 31, no. 12, 1985-2002. https://doi.org/10.1016/S0305-0548(03)00158-8
9. Toth P, Vigo D. (2002). An
overview of vehicle routing problems. In The vehicle routing problem.
Philadelphia, USA: Society for Industrial and Applied Mathematics.
10. Konstantakopoulos
GD, Gayialis SP, Kechagias EP. (2020). Vehicle routing problem and related algorithms
for logistics distribution: A literature review and classification. Operational Research, vol. 22,
2033-2062.
11. Dantzig GB, Ramser JH.
(1959). The truck dispatching problem. Management
Science, vol. 6, no. 1, 80-91. DOI: https://doi.org/10.1287/mnsc.6.1.80
12. Christofides NA. (1979).
The vehicle routing problem. Combinatorial Optimization.
13. Laporte G, Semet F. (2002).
Classical heuristics for the capacitated vehicle routing problem. Philadelphia,
USA: Society for Industrial and Applied Mathematics.
14. Gendreau M. (2002). Metaheuristics
for the capacitated vehicle routing problem. Philadelphia, USA: Society for
Industrial and Applied Mathematics.
15. Cordeau JF, et al. (2004). New
heuristics for the vehicle routing problem. GERAD Montreal, Canada. Report
number: G-2004-33.
16. Mester D, Braysy O. (2005).
Active guided evolution strategies for large-scale vehicle routing problems
with time windows. Computers &
Operations Research, vol. 32, 1593-1614. DOI:
https://doi.org/10.1016/j.cor.2003.11.017
17. Potvin JY, et al. (2005). The
vehicle routing problem with time windows part I: Tabu search. INFORMS Journal on Computing, vol. 8,
no. 2, 158-164. DOI: https://doi.org/10.1287/ijoc.8.2.158
18. Chiang WC, Russell R. (1996).
Simulated annealing meta-heuristics for the vehicle routing problem with time
windows. Annals of Operations Research,
vol. 93, no. 1, 3-27.
19. Thangiah SR, et al. (1991).
GIDEON: A Genetic Algorithm System for routing problems with time windows.
Proceedings of the 7th IEEE Conference on Artificial Intelligence Applications
1991, Miami Beach, FL, USA. p. 322-328.
20. Potvin JY, Bengio S. (1996).
The vehicle routing problem with time windows part II: Genetic Search. INFORMS Journal on Computing, vol. 8,
no. 2, 165-172. DOI: https://doi.org/10.1287/ijoc.8.2.165
21. Nikolić M, Teodorović D. (2015).
The vehicle rerouting problem with time windows and split delivery. Proceedings
of the 2nd Logistics International Conference 2015, Belgrade, Serbia. 2015. p.
55-60.
22. Taillard E, et al. (1997). A
Tabu search heuristic for the vehicle routing problem with soft time windows. Transportation Science, vol. 31, no. 2,
170-186. DOI: https://doi.org/10.1287/trsc.31.2.170
23. Figliozzi MA. (2010). An
iterative route construction and improvement algorithm for the vehicle routing
problem with soft time windows. Transportation
Research Part C: Emerging Technologies, vol. 18, no. 5, 668-679. DOI:
https://doi.org/10.1016/j.trc.2009.08.005
24. Tang J, et al. (2009). Vehicle
routing problem with fuzzy time windows. Fuzzy
Sets and Systems, vol. 160, no. 5, 683-695. DOI:
https://doi.org/10.1016/j.fss.2008.09.016
25. Teodorović D, Pavković G. (1996).
The fuzzy set theory approach to the vehicle routing problem when demand at
nodes is uncertain. Fuzzy Sets and
Systems, vol. 82, no. 3, 307-317. DOI:
https://doi.org/10.1016/0165-0114(95)00276-6
26. Lučić P, Teodorović D. (2003).
Vehicle routing problem with uncertain demand at nodes: The bee system and
fuzzy logic approach. In: Verdegay JL. (eds.) Fuzzy sets based heuristics for
optimization. Berlin, Heidelberg: Springer, p. 67-82. DOI:
https://doi.org/10.1007/978-3-540-36461-0_5
27. Sungur I, Ordónez F,
Dessouky M. (2008). A robust optimization approach for the capacitated vehicle
routing problem with demand uncertainty. IIE
Transactions, vol. 40, no. 5, 509-523.DOI:
https://doi.org/10.1080/07408170701745378
28. Tas D, et al. (2013). Vehicle
routing problem with stochastic travel times including soft time windows and
service costs. Computers & Operations
Research, vol. 40, no. (1), 214-224. DOI:
https://doi.org/10.1016/j.cor.2012.06.008
29. Xu J, Yan F, Li S. (2011). Vehicle
routing optimization with soft time windows in a fuzzy random environment. Transportation Research Part E: Logistics
and Transportation Review, vol. 47, no. 6, 1075-1091. DOI:
https://doi.org/10.1016/j.tre.2011.04.002
30. Yang T,
Wang W, Wu Q. (2022). Fuzzy demand vehicle routing problem with soft time windows. Sustainability, vol. 14, no. 9, 5658.
DOI: https://doi.org/10.3390/su14095658
31.
Khodashenas M, et al. (2023). Providing
an integrated multi-depot vehicle routing problem model with simultaneous
pickup and delivery and package layout under uncertainty with fuzzy-robust box
optimization method. Decision Making: Applications in Management and
Engineering, vol. 6, no. 2, 372-403. DOI: https://doi.org/10.31181/dmame622023640
32. Yadegari
Z, et al. (2024). Designing a Fuzzy Mathematical Model for a Two-Echelon
Allocation-Routing Problem by Applying Route Conditions: A New Interactive
Fuzzy Approach. Decision Making: Applications in Management and
Engineering, vol. 7, no. 2, 172-196. DOI:
https://doi.org/10.31181/dmame7220241029
33. Munjal P, Pahl J. (1969). An
analysis of the Boltzmann-type statistical models for multi-lane traffic flow. Transportation Research, vol. 3, no. 1,
151-163.
34. Highway Capacity Manual
(HCM). (2010). Transportation Research Board. National Research Council, Washington,
DC.
35. Dijkstra EW. (1959). A note
on two problems in connection with graphs. Numerische
Mathematik, vol.1, no. 1, 269-271.
36. Rumelhart DE, Hinton GE,
Williams RJ. (1985). Learning internal representations by error propagation.
California University San Diego La Jolla Institut for Cognitive Science. Report
number: ICS-8506.
37. Clarke G, Wright JW. (1964).
Scheduling of vehicles from a central depot to a number of delivery points. Operations
Research, vol. 12, no. 4, 568-581. DOI:
https://doi.org/10.1287/opre.12.4.568