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A survey of recent advances in vehicle routing problems

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Abstract

A vehicle routing problem involves finding a set of optimal route for a fleet of capacitated vehicles which are available at a location to service the demands of a set of customers. In its simplest form, a customer is required to be visited once and the capacity of a vehicle must not be exceeded. In this paper, a review of four common and applicable variants of the vehicle routing problem, namely, capacitated vehicle routing problem, vehicle routing problem with time windows, periodic vehicle routing problem and the dynamic vehicle routing problem, are considered based on formulation techniques, methods of solution and areas of application. A summary table is presented for each variant to emphasis some key features that represent direction of current research.

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References

  • Adewumi AO, Arasomwan MA (2016) On the performance of particle swarm optimization with(out) some control parameters for global optimization. Int J Bio-Inspir Comput 8(1):14–32

    Article  Google Scholar 

  • Ai TJ, Kachitvichyamikul V (2009) Particle swarm optimization and two solution representations for solving the capacitated vehicle routing problem. Comput Ind Eng 56:380–387

    Article  Google Scholar 

  • Albareda-Sambola M, Fernandez E, Laporte G (2014) The dynamic multi-period vehicle routing problem with probabilistic information. Comput Oper Res 48:31–39

    Article  MATH  Google Scholar 

  • Alegre J, Laguna M, Pacheco J (2007) Optimizing the periodic pickup of raw materials for a manufacturer of auto parts. Eur J Oper Res 179:736–746

    Article  MATH  Google Scholar 

  • Angelelli E, Speranza MG (2002) The periodic vehicle routing problem with intermediate facilities. Eur J Oper Res 37(2):233–247

    Article  MATH  Google Scholar 

  • Angelelli E, Bianchessi N, Mansini R, Speranza MG (2009) Short term strategies for a dynamic multi-period routing problem. Transp Res Part C Emerg Technol 17(2):106–119

    Article  MATH  Google Scholar 

  • Arasomwan MA, Adewumi AO (2014) Improved particle swarm optimization with a collective local unimodal search for continuous optimization problems. Sci World J 2014:1–23

    Article  Google Scholar 

  • Archetti C, Jabali O, Speranza MG (2015) Multi-period vehicle routing problem with due date. Comput Oper Res 61:122–134

    Article  MathSciNet  MATH  Google Scholar 

  • Armas J, Melian-Batista B (2015) Variable neighbourhood search for dynamic rich vehicle routing problem with time windows. Comput Ind Eng 85:120–131

    Article  Google Scholar 

  • Augerat P, Belenguer JM, Benavent E, Corbern A, Naddef D, Rinaldi R (1995) Computational results with a branch and cut code for the capacitated vehicle routing problem. Research report 949-m, Universite Joseph Fourier, Grenoble, France

    Google Scholar 

  • Azi N, Gendreau M, Potvin J-Y (2007) An exact algorithm for a single-vehicle routing problem with time windows and multiple routes. Eur J Oper Res 178(3):755–766

    Article  MathSciNet  MATH  Google Scholar 

  • Azi N, Gendreau M, Potrin JY (2010) An exact algorithm for a vehicle routing problem with time windows and a multiple use of vehicles. Eur J Oper Res 202:756–763

    Article  MATH  Google Scholar 

  • Baldacci R, Mingozzi A, Roberti R (2012) Recent exact algorithms for solving the vehicle routing problem under capacity and time window constraints. Eur J Oper Res 218(1):1–6

    Article  MathSciNet  MATH  Google Scholar 

  • Balseiro SR, Loiseau I, Ramonet J (2011) An ant colony algorithm hybridized with insertion heuristics for the time dependent vehicle routing problem with time windows. Comput Oper Res 38:954–966

    Article  MathSciNet  MATH  Google Scholar 

  • Belfiore P, Yoshizaki HTY (2013) Heuristic methods for the fleet size and mix vehicle routing problem with time windows and split deliveries. Comput Ind Eng 64:589–601

    Article  Google Scholar 

  • Bock A, Sanita L (2013) On the approximability of two capacitated vehicle routing problems. Electron Notes Discret Math 41:519–526

    Article  Google Scholar 

  • Bortfeldt A (2012) A hybrid algorithm for the capacitated vehicles routing problem with three-dimensional loading constraints. Comput Oper Res 39(9):2248–2257

    Article  MathSciNet  MATH  Google Scholar 

  • Bouthillier AL, Crainic TG (2005) A cooperative parallel metaheuristic for the vehicle routing problem with time windows. Comput Oper Res 32:1685–1708

    Article  MATH  Google Scholar 

  • Branchini RM, Armentano VA, Lokketangen A (2009) Adaptive granular local search heuristic for dynamic vehicle routing problem. Comput Oper Res 36:2955–2968

    Article  MATH  Google Scholar 

  • Calvete HI, Gale C, Oliverros MJ, Sanchez-Valverde B (2007) A goal programming approach to vehicle routing problem with soft time windows. Eur J Oper Res 177:1720–1733

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng CB, Wang KP (2009) Solving a vehicle routing problem with time windows by a decomposition technique and genetic algorithm. Expert Syst Appl 36:7758–7763

    Article  Google Scholar 

  • Chiang TC, Hsu WH (2014) A knowledge-based evolutionary algorithm for the multiobjective vehicle routing problem with time windows. Comput Oper Res 45:25–37

    Article  MATH  Google Scholar 

  • Choi E, Tcha DW (2007) A column generation approach to the heterogeneous fleet vehicle routing problem. Comput Oper Res 34(7):2080–2095

    Article  MATH  Google Scholar 

  • Christiansen CH, Lysgaard J (2007) A branch-and-price algorithm for the capacitated vehicle routing problem with stochastic demands. Oper Res Lett 35(6):773–781

    Article  MathSciNet  MATH  Google Scholar 

  • Christofides N, Eilon S (1969) An algorithm for the vehicle dispatching problem. Oper Res Q 20:309–318

    Article  Google Scholar 

  • Christofides N, Beasley JE (1984) The periodic routing problem. Networks 14(2):237–256

    Article  MATH  Google Scholar 

  • Christofides N, Mingozzi A, Toth P (1979) The vehicle routing problem. In: Christofides N, Mingozzi A, Toth P, Sandi C (eds) Combinatorial optimization. Wiley, Chichester, pp 315–338

    Google Scholar 

  • Clarke G, Wright J (1964) Scheduling of vehicle from central depot to number of delivery points. Oper Res 12(4):568–581

    Article  Google Scholar 

  • Colorni A, Dorigo M, Maniezzo V (1991) Distributed Optimization by ant colonies. First European conference on artificial life, 134–142

  • Cordeau JF, Gendreau M, Laporte G (1997) A tabu search heuristic for periodic and multi-depot vehicle routing problems. Networks 30(2):105–119

    Article  MATH  Google Scholar 

  • Cordeau JF, Laporte G, Mercier A (2001) A unified tabu search heuristic for vehicle routing problems with time windows. J Oper Res Soc 52(8):928–936

    Article  MATH  Google Scholar 

  • Dantzig R, Ramzer J (1959) The truck dispatching problem. Manag Sci 6(1):81–91

    MathSciNet  Google Scholar 

  • Dayarian I, Crainic TG, Gendreau M, Rei W (2015) A branch- and-price approach for a multi-period vehicle routing problem. Comput Oper Res 55:167–184

    Article  MathSciNet  MATH  Google Scholar 

  • Dhahri A, Zidi K, Ghedira K (2014) Variable neighborhood search based set covering ILP model for the vehicle routing problem with time windows. Proc Comput Sci 29:844–854

    Article  Google Scholar 

  • Dror M, Trudeau P (1990) Split vehicle routing. Naval Res Logist 37(3):383–402

    Article  MathSciNet  MATH  Google Scholar 

  • Euchi J, Yassine A, Chabchoub H (2015) The dynamic vehicle routing problem: solution with hybrid metaheuristic approach. Swarm Evolut Comput 21:41–53

    Article  Google Scholar 

  • Fabri A, Recht P (2006) On dynamic pickup and delivery vehicle routing with several time windows and waiting times. Transp Res Part B 40:335–350

    Article  Google Scholar 

  • Ferrucci F, Bock S (2015) A general approach for controlling vehicle en-route diversions in dynamic vehicle routing problems. Transp Res Part B 77:76–87

    Article  Google Scholar 

  • Ferrucci F, Bock S, Gendreau M (2013) A pro-active real-time control approach for dynamic vehicle routing problems dealing with the delivery of urgent goods. Eur J Oper Res 225:130–141

    Article  Google Scholar 

  • Fisher ML (1994) Optimal solution of vehicle routing problems using minimum k-trees. Oper Res 42:626–642

    Article  MathSciNet  MATH  Google Scholar 

  • Fisher ML, Jaikumar R (1981) A generalized assignment heuristic for vehicle routing. Netw 11:109–124

    Article  MathSciNet  Google Scholar 

  • Francis P, Smilowitz K (2006) Modeling techniques for periodic vehicle routing problems. Transp Res Part B 40:872–884

    Article  Google Scholar 

  • Francis P, Smilowitz KR, Tzur M (2008) The periodic vehicle routing problem and its extensions. In: Golden B et al (eds) The vehicle routing problem: latest advances and new challenges. Springer, NewYork, pp 73–102

    Chapter  Google Scholar 

  • Gehring H, Homberger J (1999) A parallel hybrid evolutionary metaheuristic for the vehicle routing problem with time windows. In: Mettinen K, Makela MM, Toivanen J (eds) Proceedings of EUROGEN99-short course on evolutionary algorithms in engineering and computer science. Reports of the Department of Mathematical Information Technology, No. A 2/1999, University of Jyvaskyla, Finland, 57–64

  • Gendreau M, Ilori M, Laporte G, Martello S (2006) A tabu search algorithm for a routing and container loading problem. Transp Sci 40:342–350

    Article  Google Scholar 

  • Ghannadpour SF, Noori S, Tavakkoli-Moghaddam R, Ghoseiri K (2014) A multi-objective dynamic vehicle routing problem with fuzzy time windows: model, solution and application. Appl Soft Comput 14:504–527

    Article  Google Scholar 

  • Ghoseiri K, Ghannadpour SF (2010) Multi-objective vehicle routing problem with time windows using goal programming and genetic algorithm. Appl Soft Comput 10:1096–1107

    Article  Google Scholar 

  • Gillet B, Miller L (1974) Heuristic algorithm for vehicle dispatch problem. Oper Res 22(2):340–349

    Article  MATH  Google Scholar 

  • Glover F (1997) A Template for Scatter Search and Path Relinking. In Hao JK, Lutton E, Ronald E, Schoenauer M, Snyers D (eds) Lect Notes Comput Sci, 1363:13–54

  • Godinho MT, Gouveia L, Magnanti TL (2008) Combined route capacity and route length models for unit demand vehicle routing problem. Discret Optim 5:350–372

    Article  MathSciNet  MATH  Google Scholar 

  • Goel A, Gruhn V (2008) A general vehicle routing problem. Eur J Oper Res 191(3):650–660

    Article  MathSciNet  MATH  Google Scholar 

  • Golden BL (1975) Vehicle routing problems: formulations and heuristic solution techniques. Operations Research Center, MIT, Technical report, No. 113

  • Golden B, Assad A, Levy L, Gheysens FG (1984) The fleet size and mix vehicle routing problem. Comput Oper Res 11:49–66

    Article  MATH  Google Scholar 

  • Golden BL, Wasil EA, Kelly JP, Chao IM (1998) Metaheuristics in vehicle routing. In: Craini TG, Laporte G (eds) Fleet management and logistics. Kluwer, Boston, pp 33–56

    Chapter  Google Scholar 

  • Guner AR, Murat A, Chinnam RB (2012) Dynamic routing under recurrent and non-recurrent congestion using real-time information. Comput Oper Res 39(2):358–373

    Article  Google Scholar 

  • Gutierrez-Jarpa G, Desaulniers G, Laporte G, Marianov V (2010) A branch-and-price algorithm for the vehicle routing problem with deliveries, selective pickups and time windows. Eur J Oper Res 206:341–349

    Article  MATH  Google Scholar 

  • Hadjiconstantinou E, Baldacci R (1998) A multi-depot period vehicle routing problem arising in the utilities sector. J Oper Res Soc 49:1239–1248

    Article  MATH  Google Scholar 

  • Haghani A, Jung S (2005) A dynamic vehicle routing problem with time-dependent travel times. Comput Oper Res 32:2959–2986

    Article  MATH  Google Scholar 

  • Haimovich M, Rinnooy Kan AHG, Stougie L (1988) Analysis of heuristics for vehicle routing problems. In: Golden BL, Assad AA (eds) Vehicle routing: methods and studies. North Holland, Amsterdam, pp 47–61

    Google Scholar 

  • Hammelmayr VC, Doerner KF, Hartl RF (2009) A variable neighborhood search heuristic for periodic routing problems. Eur J Oper Res 195:791–802

    Article  MATH  Google Scholar 

  • Hamzadayi A, Topaloglu S, Kose SY (2013) Nested simulated annealing approach to periodic routing problem of a retail distribution system. Comput Oper Res 40:2893–2905

    Article  MathSciNet  MATH  Google Scholar 

  • Hashimoto H, Yagiura M, Ibaraki T (2008) An iterated local search algorithm for the time-dependent vehicle routing problem with time windows. Discret Optim 5:434–456

    Article  MathSciNet  MATH  Google Scholar 

  • Homberger J, Gehring H (1999) Two evolutionary metaheuristics for the vehicle routing problem with time windows. In: Laporte G, Semet F (eds) Metaheuristics for location and routing problems. Information systems and operational research, 37, (Special issue), 297–318

  • Homberger J, Gehring H (2005) A two-phase hybrid metaheuristic for the vehicle routing problem with time windows. Eur J Oper Res 162:220–238

    Article  MATH  Google Scholar 

  • Hong L (2012) An improved LNS algorithm for real-time vehicle routing problem with time windows. Comput Oper Res 39:151–163

    Article  MATH  Google Scholar 

  • Hu X, Sun L, Liu L (2013) A PAM approach to handling disruptions in real-time vehicle routing problems. Decis Support Syst 54:1380–1393

    Article  Google Scholar 

  • Hvattum LM, Lokketangen A, Laporte G (2007) A branch- and-regret heuristic for stochastic and dynamic vehicle routing problems. Networks 49(3):330–340

    Article  MathSciNet  MATH  Google Scholar 

  • Jiang J, Ng KM, Poh KL, Teo KM (2014) Vehicle routing problem with heterogeneous fleet and time windows. Expert Syst Appl 41:3748–3760

    Article  Google Scholar 

  • Jin J, Crainic TG, Lokketangen A (2012) A parallel multi- neighborhood cooperative tabu search for capacitated vehicles routing problems. Eur J Oper Res 222:441–451

    Article  Google Scholar 

  • Jin J, Crainic TG, Lokketangen A (2014) A cooperative parallel metaheuristic for the capacitated vehicle routing problem. Comput Oper Res 44:33–41

    Article  MathSciNet  MATH  Google Scholar 

  • Juan AA, Faulin J, Ruiz R, Barrios B, Caballe S (2010) The Sr-GCWS hybrid algorithm for solving the capacitated vehicle routing problem. Appl Soft Comput 10:215–224

    Article  Google Scholar 

  • Ke L, Feng Z (2013) A two-phase in metaheuristic for the cumulative capacitated vehicle routing problem. Comput Oper Res 40:633–638

    Article  MATH  Google Scholar 

  • Kek AGH, Cheu RL, Meng Q (2008) Distance-constrained capacitated vehicle routing problems with flexible assignment of start and end depots. Math Comput Model 47:140–152

    Article  MathSciNet  MATH  Google Scholar 

  • Koskosidis YA, Powell WB, Solomon MM (1992) An optimization-based heuristic for vehicle routing and scheduling with sofy time window constraints. Transp Sci 26:69–85

    Article  MATH  Google Scholar 

  • Kumar SV, Thansekhar MR, Saravanan R, Amali SMJ (2014) Solving multi-objective vehicle routing problem with time windows by FAGA. Proced Eng 97:2176–2185

    Article  Google Scholar 

  • Kuo RJ, Zulvia FE, Suryadi K (2012) Hybrid particle swarm optimization with generic algorithm for solving capacitated vehicle routing problem with fuzzy demand: a case study on garbage collection system. Appl Math Comput 219:2574–2588

    MathSciNet  MATH  Google Scholar 

  • Laporte G (1992) The vehicle routing problem: an overview of exact and approximate algorithms. Eur J Oper Res 59(3):345–358

    Article  MATH  Google Scholar 

  • Larsen A (2001) The dynamic vehicle routing problem, Ph.D. thesis, Technical University of Denmark (DTU)

  • Larsen A, Madsen OBG, Solomon MM (2008) Recent developments in dynamic vehicle routing systems. In: Golden B et al (eds) The vehicle routing problem: latest advances and new challenges. Springer, NewYork, pp 199–220

    Chapter  Google Scholar 

  • Lau HC, Sim M, Teo KM (2003) Vehicle routing problem with time windows and a limited number of vehicles. Eur J Oper Res 148:559–569

    Article  MathSciNet  MATH  Google Scholar 

  • Lei H, Laporte G, Guo B (2011) The capacitated vehicle routing problem with stochastic demands and time windows. Comput Oper Res 38(2):1775–1783

    Article  MathSciNet  MATH  Google Scholar 

  • Lenstra JK, Rinnooy Kan AHG (1981) Complexity of vehicle routing and scheduling problems. Networks 11(2):221–227

    Article  MATH  Google Scholar 

  • Lewis HF, Sexton TR (2007) On the tour partitioning heuristic for the unit demand capacitated vehicle routing problem. Oper Res Lett 35:773–781

    Article  MathSciNet  MATH  Google Scholar 

  • Li F, Golden B, Wasil E (2005) Very large-scale vehicle routing: New test problems, algorithms, and results. Comput & Oper Res 32:1165–1179

    Article  MATH  Google Scholar 

  • Li JQ, Mirchandani PB, Borenstein D (2009) A lagrangian heuristic for real-time vehicle rescheduling problem. Transp Res Part E Logist Transp Rev 45(3):419–433

    Article  Google Scholar 

  • Liao TY, Hu TY (2011) An object oriented evaluation frame- work for dynamic vehicle routing problems under real-time information. Expert Syst Appl 38:12548–12558

    Article  Google Scholar 

  • Lin S-W, Lee Z-J, Ying K-C, Lee C-Y (2009) Applying hybrid meta-heuristics for capacitated vehicle routing problem. Expert Syst Appl 36:1505–1512

    Article  Google Scholar 

  • Liu FH, Shen SY (1999) The fleet size and mix vehicle routing problem with time windows. J Oper Res Soc 50(7):721–732

    Article  MATH  Google Scholar 

  • Liu R, Jiang Z, Fung RYK, Chen F, Liu X (2010) An effective memetic algorithm for the cumulative capacitated vehicles routing problem. Comput Oper Res 37:1877–1885

    Article  MathSciNet  Google Scholar 

  • Lorini S, Potvin JY, Zufferey N (2011) Online vehicle routing and scheduling with dynamic travel times. Comput Oper Res 38(7):1086–1090

    Article  MATH  Google Scholar 

  • Lund K, Madsen OBG, Rygaard JM (1996) Vehicle routing problem with varying degrees of dynamism. Technical report, IMM, The Department of Mathematical Modelling, Technical University of Denmark, Lyngby, Denmark

  • Luo Z, Qin H, Che C, Lim A (2015) On service consistency in multi-period vehicle route. Eur J Oper Res 243:731–744

    Article  MATH  Google Scholar 

  • Lysgaard J (2010) The pyramidal capacitated vehicle routing problem. Eur J Oper Res 205:59–64

    Article  MathSciNet  MATH  Google Scholar 

  • Lysgaard J, Wohlk S (2014) A branch-and-cut-and-price algorithm for the cumulative capacitated vehicle routing problem. Eur J Oper Res 236(3):800–810

    Article  MathSciNet  MATH  Google Scholar 

  • Marinakis Y (2012) Multiple phase neighborhood search-GRASP for capacitated vehicle routing problem. Expert Syst Appl 39:6807–6815

    Article  Google Scholar 

  • Marti R, Laguna M, Glover F (2006) Principles of scatter search. Eur J Oper Res 169:359–372

    Article  MathSciNet  MATH  Google Scholar 

  • Mavrovouniotis M, Ynag S (2015) Ant algorithms with immigrants schemes for the dynamic vehicle routing problem. Inf Sci 294:456–477

    Article  MathSciNet  Google Scholar 

  • Mazzeo S, Loiseau I (2004) An ant colony algorithm for the capacitated vehicle routing problem. Electron Notes Discret Math 18:181–186

    Article  MATH  Google Scholar 

  • Mehrjerdi Y, Nadizadeh A (2013) Using greedy clustering method to solve capacitated location-routing problem with fuzzy demands. Eur J Oper Res, 229(1):75–84

    Article  MathSciNet  MATH  Google Scholar 

  • Mester D, Braysy O (2007) Active-guided evolution strategies for large-scale capacitated vehicle routing problems. Comput Oper Res 34:2964–2975

    Article  MATH  Google Scholar 

  • Mester D, Braysy O, Dullaert W (2005) A multi-parametric evolution strategies algorithm for capacitated vehicle routing problem. Working paper, University of Haifa, Israel

  • Michallet J, Prins C, Amodeo L, Yalaoui F, Vitry G (2014) Multi-start iterated local search for the periodic vehicle routing problem with time windows and spread constraints on services. Comput Oper Res 41:196–207

    Article  MathSciNet  MATH  Google Scholar 

  • Mu Q, Fu Z, Lysgaard J, Eglese E (2011) Disruption management of the vehicle routing problem with vehicle breakdown. J Oper Res Soc 64(2):742–749

    Article  Google Scholar 

  • Nagata Y, Braysy O (2009) A powerful route optimization heuristic for the vehicle routing problem with time windows. Oper Res Lett 37:333–338

    Article  MathSciNet  MATH  Google Scholar 

  • Nagata Y, Braysy O, Dullaert W (2010) A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows. Comput Oper Res 37:724–737

    Article  MATH  Google Scholar 

  • Nazif H, Lee LS (2012) Optimised crossover genetic algorithm for capacitated vehicle routing problem. Appl Math Model 36(5):2110–2117

    Article  MathSciNet  MATH  Google Scholar 

  • Ngueveu SU, Prins C, Wolfler Calvo R (2010) An effective memetic algorithm for the cumulative capacitated vehicle routing problem. Comput Oper Res 37(11):1877–1885

    Article  MathSciNet  MATH  Google Scholar 

  • Nguyen PK, Crainic TG, Toulouse M (2011) A hybrid genetic algorithm for periodic vehicle routing problems with time windows. CIRRELT-2011-25

  • Nguyen PK, Crainic TG, Toulouse M (2013) A tabu search for time-dependent multi-zone-multi-trip vehicle routing problem with time windows. Eur J Oper Res 231:43–56

    Article  MathSciNet  MATH  Google Scholar 

  • Olusanya MO, Arasomwan MA, Adewumi AO (2015) Particle swarm optimization algorithm for optimizing assignment of blood in blood banking system. Comput Math Methods Med 2015:1–12

    Article  Google Scholar 

  • Pang KW (2011) An adaptive parallel route construction heuristic for the VRP with time windows constraints. Expert Syst Appl 38:11939–11946

    Article  Google Scholar 

  • Pillac V, Gendreau M, Gueret C, Medaglia AL (2011) A review of dynamic vehicle routing problems. Interuniversity research Centre on Enterprise Networks, Logistics and Transportation, CIRRELT-2011-62

  • Pillac V, Gueret C, Medaglia AL (2012) An event-driven optimization framework for dynamic vehicle routing. Decis Support Syst 54:414–423

    Article  Google Scholar 

  • Potvin JY, Zu Y, Benyahia I (2006) Vehicle routing and scheduling with dynamic travel times. Comput Oper Res 33:1129–1137

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Qureshi AG, Taniguchi E, Yamada T (2010) Exact solution for the vehicle routing problem with semi soft time windows and its application. Proc Soc Behav Sci 2(3):5931–5943

    Article  Google Scholar 

  • Qureshi AG, Taniguchi E, Yamada T (2012) A microsimulation based analysis of exact solution of dynamic vehicle routing with soft time windows. Proc Soc Behav Sci 39:205–216

    Article  Google Scholar 

  • Ribeiro GM, Laporte G (2012) An adaptive large neighborhood search heuristic for the cumulative capacitated vehicles routing problem. Comput Oper Res 39:1419–1431

    Article  MathSciNet  MATH  Google Scholar 

  • Rivera JC, Murat AH, Prins C (2016) Mathematical formulations and exact algorithm for the multi-trip cumulative capacitated single-vehicle routing problem. Eur J Oper Res 249(1):93–104

    Article  MATH  Google Scholar 

  • Rodriguez A, Ruiz R (2012) A study on the effect of the asymmetric on real capacitated vehicle routing problems. Comput Oper Res 39:2142–2151

    Article  MathSciNet  MATH  Google Scholar 

  • Russell RA (1995) Hybrid heuristics for the vehicle routing problem with time windows. Transp Sci 29:156–166

    Article  MATH  Google Scholar 

  • Sarker RA, Newton CS (2008) Optimization modelling: a practical approach. Taylor and Francis, NW

    MATH  Google Scholar 

  • Schyns M (2015) An ant colony system for responsive dynamic vehicle routing. Eur J Oper Res 245:704–718

    Article  MathSciNet  MATH  Google Scholar 

  • Sharma K, Chhamunya V, Gupta PC, Sharma H, Bansal JC (2015) Fitness based particle swarm optimization. Int J Syst Assur Eng Manag 6(3):319–329

    Article  Google Scholar 

  • Solomon MM (1983) Vehicle routing and scheduling with time windows constraints: Models and algorithms. Ph.D. Dissertation, Department of Decision Sciences, University of Pennsylvania

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

    Article  MathSciNet  MATH  Google Scholar 

  • Solomon MM, Desrosiers J (1988) Survey paper—time window constrained routing and scheduling problems. Transp Sci 22(1):1–13

    Article  MATH  Google Scholar 

  • Sorensen K, Schittekat P (2013) Statistical analysis of distance—based path relinking for the capacitated vehicle routing problem. Comput Oper Res 40:3197–3205

    Article  MathSciNet  MATH  Google Scholar 

  • Stanojevic M, Stanojevic B, Vujosevic M (2013) Enhanced savings calculation and its applications for solving capacitated vehicle routing problem. Appl Math Comput 219:10302–10312

    MathSciNet  MATH  Google Scholar 

  • Szeto WY, Wu Y, Ho SC (2011) An artificial bee colony algorithm for the capacitated vehicle routing problems. Eur J Oper Res 215:126–135

    Article  Google Scholar 

  • Taillard E (1993) Parallel iterative search methods for vehicle routing problems. Networks 23:661–673

    Article  MATH  Google Scholar 

  • Taillard E (1995) A heuristic column generation method for the heterogeneous fleet vehicle routing problem. RAIRO 33(1):1–14

    Article  MathSciNet  MATH  Google Scholar 

  • Taillard ÉD (1999) A heuristic column generation method for the heterogeneous fleet VRP. RAIRO-Oper Res, 33(1):1–14

    Article  MathSciNet  MATH  Google Scholar 

  • Tan CCR, Beasley JE (1984) A heuristic algorithm for the period vehicle routing problem. OMEGA, Int J Manage Sci, 12(5):497–504

    Article  Google Scholar 

  • Tarakkoli-Moghaddam R, Safali N, Gholipour Y (2006) A hybrid simulated annealing for capacitated vehicle routing problems with the independent route length. Appl Math Comput 176:445–454

    MathSciNet  MATH  Google Scholar 

  • Tarakkoli-Mohghaddam R, Safali N, Kah MMO, Rabbani M (2007) A new capacitated vehicle routing problem with split service for minimizing float cost by simulated Annealing. J Franklin Inst 344:406–425

    Article  MathSciNet  Google Scholar 

  • Tarantilis CD, Zachariadis EE, Kiranoudis CT (2009) A hybrid metaheuristic algorithm for the integrated vehicle routing and three- dimensional container loading problem. IEEE Trans Intell Transp Syst, 10:255–271

    Article  Google Scholar 

  • Teixeira J, Antunes AP, de Sousa JP (2004) Recyclable waste collection planning—a case study. Eur J Oper Res 158(3):543–554

    Article  MathSciNet  MATH  Google Scholar 

  • Thomas BW (2007) Waiting strategies for anticipating service requests from known customer locations. Transp Sci 41(3):319–331

    Article  Google Scholar 

  • Tlili T, Faiz S, Krichen S (2014) An hybrid metaheuristic for the distance-constrained capacitated vehicle routing problem. Proc Soc Behav Sci 109:779–783

    Article  Google Scholar 

  • Toth T, Vigo D (2002) Models, relaxations and exact approaches for the capacitated vehicle routing problem. Discret Appl Math 123:427–512

    Article  MathSciNet  MATH  Google Scholar 

  • Ursani Z, Essam D, Cornforth D, Stocker R (2011) Localized genetic algorithm for vehicle routing problem with time windows. Appl Soft Comput 11:5375–5390

    Article  Google Scholar 

  • Van Woensel T, Kerbache L, Peremans H, Vandaele N (2008) Vehicle routing with dynamic travel times: a queuing approach. Eur J Oper Res 186:990–1007

    Article  MATH  Google Scholar 

  • Vidal T, Battarra M, Subramanian A, Erdogan G (2014) Hybrid Metaheuristics for the Clustered Vehicle Routing Problem. Comput & Oper Res, 58:87–99

    Article  MathSciNet  MATH  Google Scholar 

  • Vidal T, Crainic TG, Gendreau M, Lahrichi N, Rei W (2010) A hybrid genetic algorithm for multi-depot and periodic vehicle routing problems. CIRRELT-2010-34

  • Wang CH, Lu JZ (2009) A hybrid genetic algorithm that optimizes capacitated vehicle routing problems. Expert Syst Appl 36:2921–2936

    Article  Google Scholar 

  • Wen M, Cordeau JF, Laporte G, Larsen J (2010) The dynamic multi-period vehicle routing problem. Comput Oper Res 37:1615–1623

    Article  MathSciNet  MATH  Google Scholar 

  • Wohlgemuth S, Oloruntoba R, Clausen U (2012) Dynamic vehicle routing with anticipation in disaster relief. Soc Econ Plan Sci 46:261–271

    Article  Google Scholar 

  • Xiao Y, Zhao Q, Kaku I, Xiu Y (2012) Development of a fuel consumption optimization model for the capacitated vehicle routing problem. Comput Oper Res 39:1419–14131

    Article  MathSciNet  MATH  Google Scholar 

  • Yamashita DS, Armento VA, Laguna M (2006) Scatter search for project scheduling with resource availability cost. Eur J Oper Res 169:623–637

    Article  MathSciNet  MATH  Google Scholar 

  • Yu B, Yang ZZ (2011) An ant colony optimization model: the periodic vehicle routing problem with time windows. Transp Res Part E 47:166–181

    Article  Google Scholar 

  • Yurtjuran A, Einel E (2010) A new hybrid electromagnetism-like algorithm for capacitated vehicle routing problems. Expert Syst Appl 37:3427–3433

    Article  Google Scholar 

  • Zhang Z, Che O, Cheang B, Lim A, Qin H (2013) A memetic algorithm for the multi-period vehicle routing problem with profit. Eur J Oper Res 229:573–584

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, University of Kwazulu-Natal, Westville Campus, Private Bag X54001, Durban, 4000, South Africa

    Aderemi Oluyinka Adewumi

  2. Department of Mathematics, Covenant University, Ota PMB 1023, Canaanland, Ota, Ogun State, Nigeria

    Olawale Joshua Adeleke

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  1. Aderemi Oluyinka Adewumi
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  2. Olawale Joshua Adeleke
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Correspondence to Aderemi Oluyinka Adewumi.

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Adewumi, A.O., Adeleke, O.J. A survey of recent advances in vehicle routing problems. Int J Syst Assur Eng Manag 9, 155–172 (2018). https://doi.org/10.1007/s13198-016-0493-4

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  • DOI: https://doi.org/10.1007/s13198-016-0493-4

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