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A Novel Model for the Time Dependent Competitive Vehicle Routing Problem: Modified Random Topology Particle Swarm Optimization

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Abstract

This paper presents a novel model for a time dependent vehicle routing problem when there is a competition between distribution companies for obtaining more sales. In a real-world situation many factors cause the time dependency of travel times, for example traffic condition on peak hours plays an essential role in outcomes of the planned schedule in urban areas. This problem is named as “Time dependent competitive vehicle routing problem” (TDVRPC) which a model is presented to satisfy the “non-passing” property. The main objectives are to minimize the travel cost and maximize the sale in order to serve customers before other rival distributors. To solve the problem, a Modified Random Topology Particle Swarm Optimization algorithm (RT-PSO) is proposed and the results are compared with branch and bound algorithm in small size problems. In large scales, comparison is done with original PSO. The results show the capability of the proposed RT-PSO method for handling this problem.

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References

  • Ai TJ, Kachitvichyanukul V (2009) A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery. Comput Oper Res 36:1693–1702

    Article  Google Scholar 

  • Beasley JE (1981) Adapting the savings algorithm for varying inter-customer travel times. Omega 9:658–659

    Article  Google Scholar 

  • Chang CT, & Chang CC (2000) A linearization method for mixed 0–1 polynomial programs. Computers & Operations Research, 27(10), 1005–1016

  • Chen HK, Hsueh CF, Chang MS (2006a) The real-time time dependent vehicle routing problem. Transp Res E 42:383–408

    Article  Google Scholar 

  • Chen AL, Yang GK, Wu ZM (2006b) Hybrid discrete particle swarm optimization algorithm for capacitated vehicle routing problem. J. Zhejiang Univ. Sci. A 7(4):607–614

    Article  Google Scholar 

  • Chu JC, Yan S, Huang HJ (2015) A multi-trip split-delivery vehicle routing problem with time windows for inventory replenishment under stochastic travel times. Netw Spat Econ 1(17):41–68

    Google Scholar 

  • Clarke G, Wright JW (1964) Scheduling of vehicles from a central depot to a number of delivery points. Oper Res 12:568–589

    Article  Google Scholar 

  • Clerc M (2006) Particle swarm optimization. ISTE, London

    Book  Google Scholar 

  • Clerc M (2007) Back to random topology. Technical report, March. http://www.clerc.maurice.fr/pso/

  • Cooke KL, Halsey E (1966) The shortest route through a network with time-dependent internodal transit times. J Math Anal Appl 14:492–498

    Google Scholar 

  • Dantzig G, Ramser JH (1959) The truck dispatching problem. Manag Sci 6:80–91

    Article  Google Scholar 

  • Fleischmann B, Gietz M, Gnutzmann S (2004) Time-varying travel times in vehicle routing. Transp Sci 38:160–173

    Article  Google Scholar 

  • Ford LR Jr, Fulkerson DR (1958) Constructing maximal dynamic flows from static flows. Oper Res 6:419–433

    Article  Google Scholar 

  • Geiger MJ (2003) Multi-criteria und Fuzzy Systeme in Theorie und Praxis, in: A computational study of genetic crossover operators for multi-objective vehicle routing problem with soft time windows, Deutscher Universities-Verlag, 191–207

  • Glover F, & Woolsey E (1974) Converting the 0-1 polynomial programming problem to a 0-1 linear program. Operations research, 22(1), 180–182

  • Golden BL, Assad AA (1988) Vehicle routing: methods and studies (studies in management science and systems, vol 16). J Oper Res Soc 39(10):979–980

  • Hill AV, Benton WC (1992) Modelling intra-city time-dependent travel speeds for vehicle scheduling problems. J Oper Res Soc 43:343–351

    Article  Google Scholar 

  • Ichoua S, Gendreau M, Potvin JY (2003) Vehicle dispatching with timedependent travel times. Eur J Oper Res 144:379–396

    Article  Google Scholar 

  • Jin W, Ji HS, Srikanthan T (2011) Algorithm for time-dependent shortest safe path on transportation networks. Procedia Computer Science 4:958–966

    Article  Google Scholar 

  • Kennedy J, Eberhart R (1995) Particle swarm optimization. Proceedings of IEEE International Conference on Neural Networks 4:1942–1948

    Article  Google Scholar 

  • Kennedy J, Eberhart RC (2001) Swarm intelligence. Morgan Kaufman Publishers, San Francisco

    Google Scholar 

  • Kim J, Han W-S, Oh J, Kim S, Yu H (2014) Processing time-dependent shortest path queries without pre-computed speed information on road networks. Inf Sci 255:135–154

    Article  Google Scholar 

  • Kuo Y (2010) Using simulated annealing to minimize fuel consumption for the time-dependent vehicle routing problem. Comput Ind Eng 59:157–165

    Article  Google Scholar 

  • Lenstra JK, Rinnooy Kan AHG (1981) Complexity of vehicle routing and scheduling problems. Networks 11:221–227

    Article  Google Scholar 

  • Malandraki C (1989) Time dependent vehicle routing problems: Formulations, solution algorithms and computations experiments. Ph.D. Dissertation, Northwestern University, Evanston, III

  • Malandraki C, Daskin MS (1992) Time dependent vehicle routing problems: formulations, properties and heuristic algorithms. Transp Sci 26(3):185–200

    Article  Google Scholar 

  • Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidiscip Optim 26:369–395

    Article  Google Scholar 

  • Mirmohammadsadeghi S, Ahmed S (2015) Memetic heuristic approach for solving truck and trailer routing problems with stochastic demands and time windows. Netw Spat Econ 15(4):1093

    Article  Google Scholar 

  • Norouzi N, Tavakkoli-Moghaddam R, Ghazanfari M, Alinaghian M, Salamatbakhsh A (2011) A new multi-objective competitive open vehicle routing problem solved by particle swarm optimization. Netw Spat Econ. https://doi.org/10.1007/s11067-011-9169-4

  • Ombuki B, Ross BJ, Hanshar F (2006) Multi-objective genetic algorithm for vehicle routing problem with time windows. Appl Intell 24:17–30

    Article  Google Scholar 

  • Osman IH (1993) Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem. Ann Oper Res 41:421–451

    Article  Google Scholar 

  • Pan Y, Sun L, Ge M (2013) Finding reliable shortest path in stochastic time-dependent network. Procedia Soc Behav Sci 96:451–460

    Article  Google Scholar 

  • Park YB (2000) A solution of the bicriteria vehicle scheduling problems with time and area-depend travel speeds. Comput Ind Eng 38:173–187

    Article  Google Scholar 

  • Park YB, Song SH (1997) Vehicle scheduling problems with time-varying speed. Comput Ind Eng 33:853–856

    Article  Google Scholar 

  • Qureshi AG, Taniguchi E, Yamada T (2009) An exact solution approach for vehicle routing and scheduling problems with soft time windows. Transport Res E-Log 45:960–977

    Article  Google Scholar 

  • Solomon MM (1987) Algorithms for the vehicle routing and scheduling problem with time windows constraints. Oper Res 35:254–265

    Article  Google Scholar 

  • Taillard E, Badeau P, Guertin F, Gendreau M, Potvin J (1997) A tabu search heuristic for the vehicle routing problem with soft time windows. Transp Sci 31:170–186

    Article  Google Scholar 

  • Tavakkoli-Moghaddam R, Ghazanfari M, Alinaghian M, Salamatbakhsh A, Norouzi N (2011) A new mathematical model for a competitive vehicle routing problem with time windows solved by simulated annealing. J Manuf Syst 30:83–92

    Article  Google Scholar 

  • Toyoglu H, Karasan OE, Kara BY (2012) A new formulation approach for location-routing problems. Netw Spat Econ 12(4):635–659

  • Yan S, Hsiao FY, Chen YC (2015) Inter-school bus scheduling under stochastic travel times. Netw Spat Econ 15(4):1049

    Article  Google Scholar 

  • Zhang J, William H, Lam K, Chen BY (2013) A stochastic vehicle routing problem with travel time uncertainty: trade-off between cost and customer service. Netw Spat Econ 13(4):471

    Article  Google Scholar 

  • Zhu Q, Qian L, Li Y, Zhu S (2006) An improved particle swarm optimization algorithm for vehicle routing problem with time windows”, IEEE Congress on Evolutionary Computation

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    M. Alinaghian

  2. Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

    M. Ghazanfari

  3. Department of Industrial Engineering, School of Engineering, University of Tehran, Tehran, Iran

    N. Norouzi

  4. School of Progress Engineering, Iran University of Science and Technology, Tehran, Iran

    H. Nouralizadeh

Authors
  1. M. Alinaghian
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  2. M. Ghazanfari
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  3. N. Norouzi
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  4. H. Nouralizadeh
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Correspondence to M. Alinaghian.

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Alinaghian, M., Ghazanfari, M., Norouzi, N. et al. A Novel Model for the Time Dependent Competitive Vehicle Routing Problem: Modified Random Topology Particle Swarm Optimization. Netw Spat Econ 17, 1185–1211 (2017). https://doi.org/10.1007/s11067-017-9364-z

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  • DOI: https://doi.org/10.1007/s11067-017-9364-z

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