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An extension of the relaxation algorithm for solving a special case of capacitated arc routing problems

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Abstract

In this paper, we propose an exact method for solving a special integer program associated with the classical capacitated arc routing problems (CARPs) called split demand arc routing problems (SDARP). This method is developed in the context of monotropic programming theory and bases a promising foundation for developing specialized algorithms in order to solve general integer programming problems. In particular, the proposed algorithm generalizes the relaxation algorithm developed by Tseng and Bertsekas (Math. Oper. Res. 12(4):569–596, 1987) for solving linear programming problems. This method can also be viewed as an alternative for the subgradient method for solving Lagrangian relaxed problems. Computational experiments show its high potential in terms of efficiency and goodness of solutions on standard test problems.

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References

  • Archetti C, Speranza MG, Hertz A (2006a) A tabu search algorithm for split delivery vehicle routing problem. Transp Sci 40(1):64–73

    Article  Google Scholar 

  • Archetti C, Savelsbergh MWP, Speranza MG (2006b) Worst-case analysis for split delivery vehicle routing problems. Transp Sci 40(2):226–234

    Article  Google Scholar 

  • Ball MO, Magnanti TL, Monma CL, Nemhauser GL (eds) (1995) Network routing: handbook in operations research and management science, vol 8. Elsevier Science/North-Holland, Amsterdam

    Google Scholar 

  • Barnhart C, Johnson EL, Nemhauser GL, Salvelsbergh MWP, Vance PH (1998) Branch and price: column generation for solving huge integer programs. Oper Res 46(3):316–329

    Article  MATH  MathSciNet  Google Scholar 

  • Belenguer JM, Benavent E (2003) A cutting plane algorithm for capacitated arc routing problem. Comput Oper Res 30:705–728

    Article  MATH  MathSciNet  Google Scholar 

  • Belenguer JM, Martinez MC, Mota E (2000) A lower bound for the split delivery vehicle routing problem. Oper Res 48(5):801–810

    Article  MATH  MathSciNet  Google Scholar 

  • Belenguer JM, Benavent E, Lacomme P, Prins C (2006) Lower and upper bounds for mixed capacitated arc routing problem. Comput Oper Res 33:3363–3383

    Article  MATH  MathSciNet  Google Scholar 

  • Bertsekas DP (1985) A unified framework for primal-dual methods in minimum cost network flow problems. Math Program 32(2):125–145

    Article  MATH  MathSciNet  Google Scholar 

  • Bertsekas DP (1995) Nonlinear programming. Athena Scientific, Belmont

    MATH  Google Scholar 

  • Chen SI, Golden B, Wasil E (2007) The split delivery vehicle routing problem: applications, algorithms, test problems and computational results. Networks 49(4):318–329

    Article  MATH  MathSciNet  Google Scholar 

  • Dror M, Trudeau P (1989) Savings by split delivery routing. Transp Sci 23:141–145

    Article  MATH  MathSciNet  Google Scholar 

  • Dror M, Trudeau P (1990) Split delivery routing. Nav Res Logist 37:383–402

    MATH  MathSciNet  Google Scholar 

  • Dror M, Laporte G, Trudeau P (1994) Vehicle routing with split deliveries. Discrete Appl Math 50:239–254

    Article  MATH  MathSciNet  Google Scholar 

  • Frizzell PW, Giffin JW (1992) The bounded split vehicle routing problem with grid networks distances. Asia Pac J Oper Res 9:101–116

    MATH  MathSciNet  Google Scholar 

  • Frizzell PW, Giffin JW (1995) The split delivery vehicle scheduling problem with time windows and grid network distance. Comput Oper Res 22:655–667

    Article  MATH  Google Scholar 

  • Hiriart-Urruty JB, Lemarechal C (1993) Convex analysis and minimization algorithm I. Springer, Berlin

    Google Scholar 

  • Lacomme P, Prins C, Ramdane-Cherif W (2004) Competitive memtic algorithms for arc routing problems. Ann Oper Res 131:159–185

    Article  MATH  MathSciNet  Google Scholar 

  • Longo H, Poggi de Aragao M, Uchoa E (2006) Solving capacitated arc routing problems using a transformation to the CVRP. Comput Oper Res 33:1823–1837

    Article  MATH  Google Scholar 

  • Mingzhou J, Kai L, Bowden RO (2007) A two stage algorithm with valid inequalities for the split delivery vehicle routing problem. Int J Prod Econ 105:228–242

    Article  Google Scholar 

  • Mullaseril PA, Dror M, Leung J (1997) Split delivery routing heuristics in livestock feed distribution. J Oper Res Soc 48:107–116

    Article  MATH  Google Scholar 

  • Nowak MA (2005) The pickup and delivery problem with split loads. PhD thesis, Georgia Institute of Technology

  • Rockafellar RT (1970) Convex analysis. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Rockafellar RT (1981) Monotropic programming: descent algorithms and duality. In: Mangasarian OL, Meyer R, Robinson S (eds) Nonlinear programming, vol 4. Academic Press, New York, pp 327–366

    Google Scholar 

  • Rockafellar RT (1983) Network flows and monotropic programming. Wiley-Interscience, New York

    Google Scholar 

  • Sierksma G, Tijssen GA (1998) Routing helicopters for crew exchange on off-shore locations. Ann Oper Res 76:261–286

    Article  MATH  Google Scholar 

  • Song SH, Lee KS, Kim GS (2002) A practical approach to solving a newspaper logistics problem using a digital map. Comput Ind Eng 43:315–330

    Article  Google Scholar 

  • Tseng P, Bertsekas DP (1987) Relaxation methods for linear programs. Math Oper Res 12(4):569–596

    Article  MATH  MathSciNet  Google Scholar 

  • Vanderbeck F (1994) Decomposition and column generation for integer programs. PhD thesis, Universite Catholique de Louvain, Belguim

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Authors and Affiliations

  1. Engineering Optimization Research Group and Department of Industrial Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran

    Saman Eskandarzadeh & Reza Tavakkoli-Moghaddam

  2. Department of Industrial Engineering, Dalhousie University, Halifax, Nova Scotia, Canada

    Amir Azaron

Authors
  1. Saman Eskandarzadeh
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  2. Reza Tavakkoli-Moghaddam
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  3. Amir Azaron
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Corresponding author

Correspondence to Reza Tavakkoli-Moghaddam.

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Eskandarzadeh, S., Tavakkoli-Moghaddam, R. & Azaron, A. An extension of the relaxation algorithm for solving a special case of capacitated arc routing problems. J Comb Optim 17, 214–234 (2009). https://doi.org/10.1007/s10878-007-9109-x

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  • DOI: https://doi.org/10.1007/s10878-007-9109-x

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