Skip to main content

Advertisement

Springer Nature Link
Log in

Artificial neural networks integrated mixed integer mathematical model for multi-fleet heterogeneous time-dependent cash in transit problem with time windows

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

The cash in transit (CIT) problem is a version of the vehicle routing problem (VRP), which deals with the planning of money distribution from the depot(s) to the automated teller machines (ATMs) safely and quickly. This study investigates a novel CIT problem, which is a variant of time-dependent VRP with time windows. To establish a more realistic approach to the time-dependent CIT problem, vehicle speed varying according to traffic density is considered. The problem is formulated as a mixed-integer mathematical model. Artificial neural networks (ANNs) are used to forecast the money demand for each ATM. For this purpose, key factors are defined, and a formulation is proposed to determine the money deposited to and withdrawn into ATMs. The mathematical model is run for different scenarios, and optimum routes are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
€32.70 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (France)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Availability of data and materials

Not applicable.

Code availability

Not applicable.

References

  1. Abidi H, Hassine K, Mguis F (2018) Genetic algorithm for solving a dynamic vehicle routing problem with time windows. In: Proceedings—2018 international conference on high performance computing and simulation, HPCS 2018, pp 782–788. https://doi.org/10.1109/HPCS.2018.00126

  2. Aggarwal D, Kumar V (2019) Mixed integer programming for vehicle routing problem with time windows. Int J Intell Syst Technol Appl 18(1–2):4–19. https://doi.org/10.1504/IJISTA.2019.097744

    Article  Google Scholar 

  3. Akansu YE, Sarioglu M, Seyhan M (2016) Aerodynamic drag force estimation of a truck trailer model using artificial neural network. Int J Automot Eng Technol 5(4):168–175. https://doi.org/10.18245/IJAET.287182

    Article  Google Scholar 

  4. Akkaya G, Demireli E, Yakut, H. Ü. (2009). İşletmelerde Finansal Başarısızlık Tahminlemesi: Yapay Sinir Ağları Modeli İle IMKB Üzerine Bir Uygulama. Eskişehir Osmangazi Üniversitesi Sosyal Bilimler Dergisi 10(2): 187–216

    Google Scholar 

  5. Al Amin MA, Hoque MA (2019) Comparison of ARIMA and SVM for short-term load forecasting. In: IEMECON 2019—9th annual information technology, electromechanical engineering and microelectronics conference, pp 205–210. https://doi.org/10.1109/IEMECONX.2019.8877077

  6. Anbuudayasankar SP, Ganesh K, Lenny Koh SC, Ducq Y (2012) Modified savings heuristics and genetic algorithm for bi-objective vehicle routing problem with forced backhauls. Expert Syst Appl 39(3):2296–2305. https://doi.org/10.1016/j.eswa.2011.08.009

    Article  Google Scholar 

  7. Archetti C, Fernández E, Huerta-Muñoz DL (2017) The flexible periodic vehicle routing problem. Comput Oper Res 85:58–70. https://doi.org/10.1016/j.cor.2017.03.008

    Article  MathSciNet  MATH  Google Scholar 

  8. Ayyildiz E, Erdogan M, Taskin A (2021) Forecasting COVID-19 recovered cases with artificial neural networks to enable designing an effective blood supply chain. Comput Biol Med 139:105029. https://doi.org/10.1016/J.COMPBIOMED.2021.105029

    Article  Google Scholar 

  9. Bahmani-Oskooee M, Chi Wing Ng R (2002) Long-run demand for money in Hong Kong: an application of the ARDL model. Int J Bus Econ 1(2):147–155

    Google Scholar 

  10. Bati S, Gozupek D (2019) Joint optimization of cash management and routing for new-generation automated teller machine networks. IEEE Trans Syst Man Cybern Syst 49(12):2724–2738. https://doi.org/10.1109/TSMC.2017.2710359

    Article  Google Scholar 

  11. Belloso J, Juan AA, Faulin J (2019) An iterative biased-randomized heuristic for the fleet size and mix vehicle-routing problem with backhauls. Int Trans Oper Res 26(1):289–301. https://doi.org/10.1111/itor.12379

    Article  MathSciNet  Google Scholar 

  12. Bernal J, Escobar JW, Paz JC, Linfati R, Gatica G (2018) A probabilistic granular tabu search for the distance constrained capacitated vehicle routing problem. Int J Ind Syst Eng 29(4):453–477

    Google Scholar 

  13. Caceres-Cruz J, Arias P, Guimarans D, Riera D, Juan AA (2014) Rich vehicle routing problem: survey. ACM Comput Surv 47(2):1–28. https://doi.org/10.1145/2666003

    Article  Google Scholar 

  14. Çam ÖN, Sezen HK (2020) Linear programming formulation for vehicle routing problem which is minimized idle time. Decis Mak Appl Manag Eng. https://doi.org/10.31181/dmame2003132h

    Article  Google Scholar 

  15. Coelho VN, Grasas A, Ramalhinho H, Coelho IM, Souza MJF, Cruz RC (2016) An ILS-based algorithm to solve a large-scale real heterogeneous fleet VRP with multi-trips and docking constraints. Eur J Oper Res 250(2):367–376. https://doi.org/10.1016/j.ejor.2015.09.047

    Article  MathSciNet  MATH  Google Scholar 

  16. Dabia S, Lai D, Vigo D (2019) An exact algorithm for a rich vehicle routing problem with private fleet and common carrier. Transp Sci 53(4):986–1000. https://doi.org/10.1287/trsc.2018.0852

    Article  Google Scholar 

  17. Dantzig GB, Ramser JH (1959) The truck dispatching problem. Manag Sci 6(1):80–91. https://doi.org/10.1287/mnsc.6.1.80

    Article  MathSciNet  MATH  Google Scholar 

  18. De Armas J, Melián-Batista B, Moreno-Pérez JA, Brito J (2015) GVNS for a real-world rich vehicle routing problem with time windows. Eng Appl Artif Intell 42:45–56. https://doi.org/10.1016/j.engappai.2015.03.009

    Article  Google Scholar 

  19. Dechampai D, Tanwanichkul L, Sethanan K, Pitakaso R (2017) A differential evolution algorithm for the capacitated VRP with flexibility of mixing pickup and delivery services and the maximum duration of a route in poultry industry. J Intell Manuf 28(6):1357–1376. https://doi.org/10.1007/s10845-015-1055-3

    Article  Google Scholar 

  20. Ertuğrul ÖF, Tağluk ME (2018) Forecasting financial indicators by generalized behavioral learning method. Soft Comput 22(24):8259–8272. https://doi.org/10.1007/s00500-017-2768-3

    Article  Google Scholar 

  21. Ertuğrul ÖF, Tekin H, Tekin R (2021) A novel regression method in forecasting short-term grid electricity load in buildings that were connected to the smart grid. Electr Eng 103(1):717–728. https://doi.org/10.1007/s00202-020-01114-3

    Article  Google Scholar 

  22. Gao F, Shao X (2021) Forecasting annual natural gas consumption via the application of a novel hybrid model. Environ Sci Pollut Res 28(17):21411–21424. https://doi.org/10.1007/s11356-020-12275-w

    Article  Google Scholar 

  23. Ge X, Jin Y, Zhang L (2022) Genetic-based algorithms for cash-in-transit multi depot vehicle routing problems: economic and environmental optimization. Environ Dev Sustain. https://doi.org/10.1007/S10668-021-02066-9

    Article  Google Scholar 

  24. Ghannadpour SF, Zandiyeh F (2020) A new game-theoretical multi-objective evolutionary approach for cash-in-transit vehicle routing problem with time windows (a real life case). Appl Soft Comput 93:106378. https://doi.org/10.1016/J.ASOC.2020.106378

    Article  Google Scholar 

  25. Ghannadpour SF, Zandiyeh F (2020) An adapted multi-objective genetic algorithm for solving the cash in transit vehicle routing problem with vulnerability estimation for risk quantification. Eng Appl Artif Intell 96:103964. https://doi.org/10.1016/j.engappai.2020.103964

    Article  Google Scholar 

  26. Haykin S (1994) Neural networks: a comprehensive foundation, 1st edn. Prentice Hall PTR, Hoboken

    MATH  Google Scholar 

  27. Herrero R, Rodríguez A, Cáceres-Cruz J, Juan AA (2015) Solving vehicle routing problems with asymmetric costs and heterogeneous fleets. Int J Adv Oper Manag 6(1):58–80. https://doi.org/10.1504/IJAOM.2014.059620

    Article  Google Scholar 

  28. Hooshmand F, MirHassani SA (2019) Time dependent green VRP with alternative fuel powered vehicles. Energy Syst 10(3):721–756. https://doi.org/10.1007/s12667-018-0283-y

    Article  Google Scholar 

  29. Huang Y, Zhao L, Van Woensel T, Gross JP (2017) Time-dependent vehicle routing problem with path flexibility. Transp Res Part B: Methodol 95:169–195. https://doi.org/10.1016/j.trb.2016.10.013

    Article  Google Scholar 

  30. Istanbul Metropolitan Municipality (2014) Büyükşehir Belediyesi UKOME Kararları. Istanbul Metropolitan Municipality, Istanbul

    Google Scholar 

  31. Jabali O, Van Woensel T, De Kok AG (2012) Analysis of travel times and CO2 emissions in time-dependent vehicle routing. Prod Oper Manag 21(6):1060–1074. https://doi.org/10.1111/j.1937-5956.2012.01338.x

    Article  Google Scholar 

  32. Khalid N, dan Pengurusan FE, Thelata MH (2017) Forecasting of money demand in Malaysia using neural networks and econometric model. In: Proceedings of international conference on economics (ICE 2017), pp 43–56

  33. Koç Ç, Erbaş M, Özceylan E (2018) A rich vehicle routing problem arising in the replenishment of automated teller machines. Int J Optim Control: Theor Appl 8(2):276–287. https://doi.org/10.11121/ijocta.01.2018.00572

    Article  MathSciNet  Google Scholar 

  34. Larrain H, Coelho LC, Cataldo A (2017) A variable MIP neighborhood descent algorithm for managing inventory and distribution of cash in automated teller machines. Comput Oper Res 85:22–31. https://doi.org/10.1016/j.cor.2017.03.010

    Article  MathSciNet  MATH  Google Scholar 

  35. Liu C, Kou G, Zhou X, Peng Y, Sheng H, Alsaadi FE (2020) Time-dependent vehicle routing problem with time windows of city logistics with a congestion avoidance approach. Knowl-Based Syst 188:104813. https://doi.org/10.1016/j.knosys.2019.06.021

    Article  Google Scholar 

  36. Liu Z, Loo CK, Pasupa K (2020) A novel error-output recurrent two-layer extreme learning machine for multi-step time series prediction. Sustain Cities Soc 66:102613. https://doi.org/10.1016/j.scs.2020.102613

    Article  Google Scholar 

  37. Lysgaard J, López-Sánchez AD, Hernández-Díaz AG (2020) A matheuristic for the MinMax capacitated open vehicle routing problem. Int Trans Oper Res 27(1):394–417. https://doi.org/10.1111/itor.12581

    Article  MathSciNet  Google Scholar 

  38. Mahmoudi M, Zhou X (2016) Finding optimal solutions for vehicle routing problem with pickup and delivery services with time windows: a dynamic programming approach based on state-space-time network representations. Transp Res Part B: Methodol 89:19–42. https://doi.org/10.1016/j.trb.2016.03.009

    Article  Google Scholar 

  39. Marques A, Soares R, Santos MJ, Amorim P (2020) Integrated planning of inbound and outbound logistics with a Rich Vehicle Routing Problem with backhauls. Omega (UK) 92:102172. https://doi.org/10.1016/j.omega.2019.102172

    Article  Google Scholar 

  40. Nur M, Yulyanti S, Nur NM (2017) Analysis of factors affecting money demand in Indonesia year 2006–2015 with approach error corection model (ECM). J Ekon KIAT 28(1):91–100. https://doi.org/10.25299/KIAT.2017.VOL28(1).3005

    Article  Google Scholar 

  41. Osaba E, Yang XS, Diaz F, Onieva E, Masegosa AD, Perallos A (2017) A discrete firefly algorithm to solve a rich vehicle routing problem modelling a newspaper distribution system with recycling policy. Soft Comput 21(18):5295–5308. https://doi.org/10.1007/s00500-016-2114-1

    Article  Google Scholar 

  42. Osaba E, Yang XS, Fister I, Del Ser J, Lopez-Garcia P, Vazquez-Pardavila AJ (2019) A Discrete and Improved Bat Algorithm for solving a medical goods distribution problem with pharmacological waste collection. Swarm Evol Comput 44:273–286. https://doi.org/10.1016/j.swevo.2018.04.001

    Article  Google Scholar 

  43. Ozsahin S, Murat M (2018) Prediction of equilibrium moisture content and specific gravity of heat treated wood by artificial neural networks. Eur J Wood Wood Prod 76(2):563–572. https://doi.org/10.1007/s00107-017-1219-2

    Article  Google Scholar 

  44. Paradiso R, Roberti R, Lagana D, Dullaert W (2020) An exact solution framework for multitrip vehicle-routing problems with time windows. Oper Res 68(1):180–198. https://doi.org/10.1287/OPRE.2019.1874

    Article  MathSciNet  MATH  Google Scholar 

  45. Ritzinger U, Puchinger J, Hartl RF (2016) A survey on dynamic and stochastic vehicle routing problems. Int J Prod Res 54(1):215–231. https://doi.org/10.1080/00207543.2015.1043403

    Article  MATH  Google Scholar 

  46. Royo B, Fraile A, Larrodé E, Muerza V (2016) Route planning for a mixed delivery system in long distance transportation and comparison with pure delivery systems. J Comput Appl Math 291:488–496. https://doi.org/10.1016/j.cam.2015.03.042

    Article  MathSciNet  MATH  Google Scholar 

  47. Sattar AMA, Ertuğrul ÖF, Gharabaghi B, McBean EA, Cao J (2019) Extreme learning machine model for water network management. Neural Comput Appl 31(1):157–169. https://doi.org/10.1007/s00521-017-2987-7

    Article  Google Scholar 

  48. Sawik B, Faulin J, Pérez-Bernabeu E (2017) A multicriteria analysis for the Green VRP: a case discussion for the distribution problem of a Spanish retailer. Transp Res Procedia 22:305–313. https://doi.org/10.1016/j.trpro.2017.03.037

    Article  Google Scholar 

  49. Seyhan M, Akansu YE, Murat M, Korkmaz Y, Akansu SO (2017) Performance prediction of PEM fuel cell with wavy serpentine flow channel by using artificial neural network. Int J Hydrog Energy 42(40):25619–25629. https://doi.org/10.1016/j.ijhydene.2017.04.001

    Article  Google Scholar 

  50. Sicilia JA, Quemada C, Royo B, Escuín D (2016) An optimization algorithm for solving the rich vehicle routing problem based on Variable Neighborhood Search and Tabu Search metaheuristics. J Comput Appl Math 291:468–477. https://doi.org/10.1016/j.cam.2015.03.050

    Article  MathSciNet  MATH  Google Scholar 

  51. Song BD, Ko YD (2016) A vehicle routing problem of both refrigerated- and general-type vehicles for perishable food products delivery. J Food Eng 169:61–71. https://doi.org/10.1016/j.jfoodeng.2015.08.027

    Article  Google Scholar 

  52. Song L, Huang H (2017) The Euclidean vehicle routing problem with multiple depots and time windows. In: Lecture notes in computer science (including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics), 10628 LNCS, pp 449–456. https://doi.org/10.1007/978-3-319-71147-8_31

  53. Soysal M, Bloemhof-Ruwaard JM, Bektaş T (2015) The time-dependent two-echelon capacitated vehicle routing problem with environmental considerations. Int J Prod Econ 164:366–378. https://doi.org/10.1016/j.ijpe.2014.11.016

    Article  Google Scholar 

  54. Talarico L, Sörensen K, Springael J (2015) Metaheuristics for the risk-constrained cash-in-transit vehicle routing problem. Eur J Oper Res 244(2):457–470. https://doi.org/10.1016/j.ejor.2015.01.040

    Article  MATH  Google Scholar 

  55. Talarico L, Springael J, Sörensen K, Talarico F (2017) A large neighbourhood metaheuristic for the risk-constrained cash-in-transit vehicle routing problem. Comput Oper Res 78:547–556. https://doi.org/10.1016/j.cor.2016.04.003

    Article  MathSciNet  MATH  Google Scholar 

  56. Tikani H, Setak M, Demir E (2021) Multi-objective periodic cash transportation problem with path dissimilarity and arrival time variation. Expert Syst Appl 164:114015. https://doi.org/10.1016/j.eswa.2020.114015

    Article  Google Scholar 

  57. Van Anholt RG, Coelho LC, Laporte G, Vis IFA (2016) An inventory-routing problem with pickups and deliveries arising in the replenishment of automated teller machines. Transp Sci 50(3):1077–1091. https://doi.org/10.1287/trsc.2015.0637

    Article  Google Scholar 

  58. Wang F, Liu X, Liu C, Li H, Han Q (2018) Remaining useful life prediction method of rolling bearings based on Pchip-EEMD-GM(1, 1) model. Shock Vib 2018:3013684. https://doi.org/10.1155/2018/3013684

    Article  Google Scholar 

  59. Wang R, Zhou J, Yi X, Pantelous AA (2019) Solving the green-fuzzy vehicle routing problem using a revised hybrid intelligent algorithm. J Ambient Intell Humaniz Comput 10(1):321–332. https://doi.org/10.1007/s12652-018-0703-9

    Article  Google Scholar 

  60. Xu G, Li Y, Szeto WY, Li J (2019) A cash transportation vehicle routing problem with combinations of different cash denominations. Int Trans Oper Res 26(6):2179–2198. https://doi.org/10.1111/itor.12640

    Article  MathSciNet  Google Scholar 

  61. Yan S, Wang SS, Chang YH (2014) Cash transportation vehicle routing and scheduling under stochastic travel times. Eng Optim 46(3):289–307. https://doi.org/10.1080/0305215X.2013.768240

    Article  MathSciNet  Google Scholar 

  62. Yandex (2018) Veriler ve Raporlar—Yandex İstanbul için 3 Yıllık Trafik Analizi. https://yandex.com.tr/company/press_center/infographics/istanbul_traffic

  63. Yu J, Zhang X, Xu L, Dong J, Zhangzhong L (2021) A hybrid CNN-GRU model for predicting soil moisture in maize root zone. Agric Water Manag 245:106649. https://doi.org/10.1016/j.agwat.2020.106649

    Article  Google Scholar 

  64. Yu VF, Jewpanya P, Redi AANP (2016) Open vehicle routing problem with cross-docking. Comput Ind Eng 94:6–17. https://doi.org/10.1016/j.cie.2016.01.018

    Article  Google Scholar 

  65. Zelenka J, Budinska I, Didekova Z (2012) A combination of heuristic and non-heuristic approaches for modified Vehicle Routing Problem. In: LINDI 2012—4th IEEE international symposium on logistics and industrial informatics, proceedings, pp 107–112. https://doi.org/10.1109/LINDI.2012.6319471

  66. Zulvia FE, Kuo RJ, Nugroho DY (2020) A many-objective gradient evolution algorithm for solving a green vehicle routing problem with time windows and time dependency for perishable products. J Clean Prod 242:118428. https://doi.org/10.1016/j.jclepro.2019.118428

    Article  Google Scholar 

Download references

Funding

No competing interest, funding, or other support were received.

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Karadeniz Technical University, Trabzon, Turkey

    Ertuğrul Ayyıldız

  2. Department of Industrial Engineering, Yıldız Technical University, Istanbul, Turkey

    Alev Taşkın, Aslıhan Yıldız & Coşkun Özkan

Authors
  1. Ertuğrul Ayyıldız
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alev Taşkın
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aslıhan Yıldız
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Coşkun Özkan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ertuğrul Ayyıldız.

Ethics declarations

Conflict of interest

All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.

Ethics approval

Ethics committee approval is not required.

Consent to participate

Not applicable.

Consent to publish

The authors confirm that the final version of the manuscript has been reviewed, approved, and consented to for publication by all authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ayyıldız, E., Taşkın, A., Yıldız, A. et al. Artificial neural networks integrated mixed integer mathematical model for multi-fleet heterogeneous time-dependent cash in transit problem with time windows. Neural Comput & Applic 34, 21891–21909 (2022). https://doi.org/10.1007/s00521-022-07659-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-022-07659-7

Keywords

Search

Navigation