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The risk-averse traveling repairman problem with profits

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Abstract

In this paper, we study a stochastic variant of the traveling repairman problem with profits in which travel times are random. The introduction of the arrival time in the objective function instead of the travel time, which is common in most vehicle routing problems, poses compelling challenges, emphasized by the incorporation of the stochasticity in travel times and by the presence of profits. A risk-averse perspective is considered in the model, which is then formulated as a nonlinear integer model and heuristically solved by means of a beam search heuristic. Experimental results have been performed on instances adapted from the available deterministic datasets, to show the effectiveness of the solution approach.

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References

  • Adulyasak Y, Jaillet P (2014) Models and algorithms for stochastic and robust vehicle routing with deadlines. Transp Sci 50(2):608–626

    Article  Google Scholar 

  • Agra A, Christiansen M, Hvattum LM, Figueiredo R, Poss M, Requejo C (2012) Layered formulation for the robust vehicle routing problem with time windows. Lect Notes Comput Sci 7422:249–260

    Article  MathSciNet  MATH  Google Scholar 

  • Agra A, Christiansen M, Hvattum LM, Figueiredo R, Poss M, Requejo C (2013) The robust vehicle routing problem with time windows. Comput Oper Res 40(3):856–866

    Article  MathSciNet  MATH  Google Scholar 

  • Ando N, Taniguchi E (2006) Travel time reliability in vehicle routing and scheduling with time windows. Netw Spat Econ 6(3–4):293–311

    Article  MathSciNet  MATH  Google Scholar 

  • Araya I, Riff MC (2014) A beam search approach to the container loading problem. Comput Oper Res 43:100–107

    Article  MATH  Google Scholar 

  • Ausiello G, Leonardi S, Marchetti-Spaccamela A (1994) On salesman repairmen spiders and other traveling agents. In: Proceeding of the Italian conference on algorithms and complexity, pp 1–16

  • Baldi MM, Crainic TG, Perboli G, Tadei R (2014) Branch and price and beam search algorithms for the variable cost and size bin packing problem with optional items. Ann Oper Res 222(1):125–141

    Article  MathSciNet  MATH  Google Scholar 

  • Beraldi P, Bruni ME (2010) An exact approach for solving integer problem under probabilistic constraints with random technology matrix. Ann Oper Res 177(1):127–137

    Article  MathSciNet  MATH  Google Scholar 

  • Beraldi P, Ruszczyński A (2002a) A branch and bound method for stochastic integer problems under probabilistic constraints. Optim Methods Softw 17:359–382

    Article  MathSciNet  MATH  Google Scholar 

  • Beraldi P, Ruszczyński A (2002b) The probabilistic set-covering problem. Oper Res 50(6):956–967

    Article  MathSciNet  MATH  Google Scholar 

  • Beraldi P, Ruszczyński A (2005) Beam search heuristic to solve stochastic integer problems under probabilistic constraints. Eur J Oper Res 167(1):35–47

    Article  MathSciNet  MATH  Google Scholar 

  • Beraldi P, Ghiani G, Laporte G, Musmanno R (2005) Efficient neighborhood search for the probabilistic pickup and delivery travelling salesman problem. Networks 45(4):195–198

    Article  MathSciNet  MATH  Google Scholar 

  • Beraldi P, Bruni ME, Violi A (2012) Capital rationing problems under uncertainty and risk. Comput Optim Appl 51(3):1375–1396

    Article  MathSciNet  MATH  Google Scholar 

  • Beraldi P, Bruni ME, Laganà D, Musmanno R (2015) The mixed capacitated general routing problem under uncertainty. Eur J Oper Res 240(2):382–392

    Article  MathSciNet  MATH  Google Scholar 

  • Beraldi P, Bruni ME, Manerba D, Mansini R (2017) A stochastic programming approach for the traveling purchaser problem. IMA J Manag Math 28(1):41–63

    Article  MathSciNet  MATH  Google Scholar 

  • Bigras LP, Gamache M, Savard G (2008) The time-dependent traveling salesman problem and single machine scheduling problems with sequence dependent setup times. Discrete Optim 5(4):685–699

    Article  MathSciNet  MATH  Google Scholar 

  • Birge J, Louveaux F (1997) Introduction to stochastic programming. Springer, Berlin

    MATH  Google Scholar 

  • Birgin EG, Ferreira JE, Ronconi DP (2015) List scheduling and beam search methods for the flexible job shop scheduling problem with sequencing flexibility. Eur J Oper Res 247(2):421–440

    Article  MathSciNet  MATH  Google Scholar 

  • Blum C, Miralles C (2011) On solving the assembly lineworker assignment and balancing problem via beam search. Comput Oper Res 38:328–339

    Article  MathSciNet  MATH  Google Scholar 

  • Bock S (2015) Solving the traveling repair problem on a line with general processing times and deadlines. Eur J Oper Res 24(3):690–703

    Article  MATH  MathSciNet  Google Scholar 

  • Bruni ME, Beraldi P, Laganà D (2013) The express heuristic for probabilistically constrained integer problems. J Heuristics 19(3):423–441

    Article  Google Scholar 

  • Bruni ME, Guerriero F, Beraldi P (2014) Designing robust routes for demand-responsive transport systems. Transp Res Part E Logist Transp Rev 70:1–16

    Article  Google Scholar 

  • Bruni ME, Beraldi P, Khodaparasti S (2018) A heuristic approach for the k-traveling repairman problem with profits under uncertainty. Electron Notes Discrete Math 69:221–228

    Article  MathSciNet  Google Scholar 

  • Bruni ME, Beraldi P, Khodaparasti S (2018) A fast heuristic for routing in post-disaster humanitarian relief logistics. Transp Res Procedia 30:304–313

    Article  Google Scholar 

  • Caceres H, Hwang H, He Q (2016) Estimating freeway route travel time distributions with consideration to time-of-day, inclement weather, and traffic incidents. J Adv Transp 50:967–987

    Article  Google Scholar 

  • Calafiore G, El Ghaoui L (2006) On distributionally robust chance-constrained linear programs. J Optim Theory Appl 130(1):1–22

    Article  MathSciNet  MATH  Google Scholar 

  • Campbell A, Vandenbussche D, Hermann W (2008) Routing for relief efforts. Transp Sci 42(2):127–145

    Article  Google Scholar 

  • Dewilde T, Cattrysse D, Coene S, Spieksma FCR, Vansteenwegen P (2013) Heuristics for the traveling repairman problem with profits. Comput Oper Res 40(7):1700–1707

    Article  MathSciNet  MATH  Google Scholar 

  • Fang KT, Kotz S, Ng KW (1990) Symmetric multivariate and related distributions. Chapman & Hall, London. ISBN: 9781315897943

  • Fernandez-Viagas V, Framinan JM (2017) A beam-search-based constructive heuristic for the PFSP to minimise total flowtime. Comput Oper Res 81:167–177

    Article  MathSciNet  MATH  Google Scholar 

  • Fischetti M, Laporte G, Martello S (1993) The delivery man problem and cumulative matroids. Oper Res 41(6):1055–1064

    Article  MathSciNet  MATH  Google Scholar 

  • Gomez A, Marino R, Akhavan-Tabatabaei R, Medaglia AL, Mendoza JE (2016) On modeling stochastic travel and service times in vehicle routing. Transp Sci 50(2):627–641

    Article  Google Scholar 

  • Henrion R, Strugarek C (2008) Convexity of chance constraints with independent random variables. Comput Optim Appl 412(2):263–276

    Article  MathSciNet  MATH  Google Scholar 

  • Jaillet P, Qi J, Sim M (2016) Routing optimization under uncertainty. Oper Res 64(1):186–200

    Article  MathSciNet  MATH  Google Scholar 

  • Jung S, Haghani A (2001) Genetic algorithm for the time-dependent vehicle routing problem. Transp Res Rec J Transp Res Board 1771(1):164–171

    Article  Google Scholar 

  • Kenyon A, Morton D (2003) Stochastic vehicle routing with random travel times. Transp Sci 37(1):69–82

    Article  Google Scholar 

  • Khokhlov V (2016) Conditional value at risk for elliptical distributions. Evropsky Casopis Ekonomiky a Managementu 2(6):70–79

    Google Scholar 

  • Krokhmal P, Zabarankin M, Uryasev S (2011) Modeling and optimization of risk. Surv Oper Res Manag Sci 16(2):49–66

    Google Scholar 

  • Laporte G, Louveaux F, Mercure H (1992) The vehicle routing problem with stochastic travel times. Transp Sci 26(3):161–70

    Article  MATH  Google Scholar 

  • Lecluyse C, Van Woensel T, Peremans H (2009) Vehicle routing with stochastic time-dependent travel times. 4OR-Q J Oper Res 7:363–377

    Article  MathSciNet  MATH  Google Scholar 

  • Lee C, Lee K, Park S (2004) Robust vehicle routing problem with deadlines and travel time/demand uncertainty. J Oper Res Soc 63(9):1294–306

    Article  Google Scholar 

  • Li X, Stephen PT, Leung CH (2010) Vehicle routing problems with time windows and stochastic travel and service times: models and algorithm. Int J Prod Econ 125(1):137–145

    Article  Google Scholar 

  • Lucena A (1990) Time-dependent traveling salesman problem—the deliveryman case. Networks 20(6):753–763

    Article  MathSciNet  MATH  Google Scholar 

  • Maggioni F, Perboli G, Tadei R (2014) The multi-path traveling salesman problem with stochastic travel costs: building realistic instances for city logistics applications. Transp Res Procedia 3:528–536

    Article  Google Scholar 

  • Oyola J, Arntzen H, Woodruff DL (2017) The stochastic vehicle routing problem, a literature review, part II: solution methods. EURO J Transp Logist 6(4):349–388

    Article  Google Scholar 

  • Oyola J, Arntzen H, Woodruff DL (2018) The stochastic vehicle routing problem, a literature review, part I: models. EURO J Transp Logist 7(3):193–221

    Article  Google Scholar 

  • Perboli G, Gobbato L, Maggioni F (2017) A progressive hedging method for the multi-path traveling salesman problem with stochastic travel times. IMA J Manag Math 28(1):65–86

    Article  MathSciNet  MATH  Google Scholar 

  • Solano-Charris EL, Prins C, Santos AC (2016) Solving the bi-objective robust vehicle routing problem with uncertain costs and demands. RAIRO Oper Res 50(4–5):689–714

    Article  MathSciNet  MATH  Google Scholar 

  • Sungur I, Ordóñez F, Dessouky M (2008) A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty. IIE Trans 40(5):509–523

    Article  Google Scholar 

  • Susilawati S, Taylor M, Somenahalli S (2013) Distributions of travel time variability on urban roads. J Adv Transp 47(8):720–736

    Article  Google Scholar 

  • Taş D, Dellaert N, Van Woensel T, de Kok AG (2013) Vehicle routing problem with stochastic travel times including soft time windows and service costs. Comput Oper Res 40(1):214–224

    Article  MathSciNet  MATH  Google Scholar 

  • Taş D, Gendreau M, Dellaert N, Van Woensel T, de Kok AG (2014) Vehicle routing with soft time windows and stochastic travel times: a column generation and branch-and-price solution approach. Eur J Oper Res 236(3):789–799

    Article  MathSciNet  MATH  Google Scholar 

  • Tulabandhula T, Rudin C, Jaillet P (2011) The machine learning and traveling repairman problem. Algorithm Decis Theory Lect Notes Comput Sci 6992:262–276

    Article  MathSciNet  MATH  Google Scholar 

  • Yavuz M (2017) An iterated beam search algorithm for the green vehicle routing problem. Networks 69(3):317–328

    Article  MathSciNet  Google Scholar 

  • Zhang T, Chaovalitwongse WA, Zhang Y (2012) Scatter search for the stochastic travel-time vehicle routing problem with simultaneous pick-ups and deliveries. Comput Oper Res 39(10):2277–2290

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to M. E. Bruni.

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Communicated by P. Beraldi, M. Boccia, C. Sterle.

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Beraldi, P., Bruni, M.E., Laganà, D. et al. The risk-averse traveling repairman problem with profits. Soft Comput 23, 2979–2993 (2019). https://doi.org/10.1007/s00500-018-3660-5

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