Skip to main content
SpringerLink
Log in

A computational study of solution approaches for the resource constrained elementary shortest path problem

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

We present the results of a computational investigation of solution approaches for the resource constrained elementary shortest path problem (\(\mathcal{RCESPP}\)). In particular, the best known algorithms are tested on several problem instances taken from literature. The main aims are to provide a detailed state of the art and to evaluate methods that turn out to be the most promising for solving the problem under investigation. This work represents the first attempt to computationally compare solution approaches for the \(\mathcal{RCESPP}\).

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Algorithm 1
Algorithm 2
Algorithm 3
Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Aneja, Y. P., Aggarwal, V., & Nair, K. P. K. (1983). Shortest chain subject to side constraints. Networks, 13, 295–302.

    Article  Google Scholar 

  • Barnhart, C., Boland, N., Clarke, L., Johnson, E. L., Nemhauser, G. L., & Shenoi, R. G. (1998). Flight string models for aircraft fleeting and routing. Transportation Science, 32, 208–220.

    Article  Google Scholar 

  • Beasley, J. E., & Christofides, N. (1989). An algorithm for the resource constrained shortest path problem. Networks, 19, 379–394.

    Article  Google Scholar 

  • Boland, N., Dethridge, J., & Dumitrescu, I. (2006). Accelerated label setting algorithms for the elementary resource constrained shortest path problem. Operations Research Letters, 34, 58–68.

    Article  Google Scholar 

  • Cherkassky, B. V., Goldberg, A. V., & Radzik, T. (1996). Shortest paths algorithms: theory and experimental evaluation. Mathematical Programming, 73(2), 129–174.

    Article  Google Scholar 

  • Christofides, N., Mingozzi, A., & Toth, P. (1981). Exact algorithms for the vehicle routing problem based on spanning tree and shortest path relaxations. Mathematical Programming, 20, 255–282.

    Article  Google Scholar 

  • Cordeau, J. F., Desaulniers, G., Desrosiers, J., Solomon, M. M., & Soumis, F. (2002). VRP with time windows. In P. Toth & D. Vigo (Eds.), The vehicle-routing problem (pp. 157–193).

    Chapter  Google Scholar 

  • Dell’Amico, M., Righini, G., & Salani, M. (2006). A branch-and-price approach to the vehicle-routing problem with simultaneous distribution and collection. Transportation Science, 40(2), 235–247.

    Article  Google Scholar 

  • Desrochers, M. (1988). An algorithm for the shortest path problem with resource constraints (Technical report G-88-27). GERAD.

  • Desrochers, M., & Soumis, F. (1988). A generalized permanent labeling algorithm for the shortest path problem with time windows. INFOR. Information Systems and Operational Research, 26, 191–212.

    Google Scholar 

  • Desrosiers, J., Pelletier, P., & Soumis, F. (1983). Plus court chemin avec constraints d’horaires. RAIRO—Theoretical Informatics and Applications, 17, 357–377 (in French).

    Google Scholar 

  • Desrochers, M., Desrosiers, J., & Solomon, M. (1992). A new optimization algorithm for the vehicle routing problem with time windows. Operations Research, 40(2), 342–354.

    Article  Google Scholar 

  • Dror, M. (1994). Note on the complexity of the shortest path models for column generation in VRPTW. Operational Research, 42, 977–978.

    Google Scholar 

  • Dumitrescu, I., & Boland, N. (2003). Improved preprocessing, labeling and scaling algorithms for the weight-constrained shortest path problem. Networks, 42(3), 135–153.

    Article  Google Scholar 

  • Feillet, D., Dejax, P., Gendreau, M., & Gueguen, C. (2004). An exact algorithm for the elementary shortest path problem with resource constraints: application to some vehicle routing problems. Networks, 43(3), 216–229.

    Article  Google Scholar 

  • Handler, G. Y., & Zang, I. (1980). A dual algorithm for the constrained shortest path problem. Networks, 10, 293–309.

    Article  Google Scholar 

  • Houck, D. J., Picard, J. C., Queyranne, M., & Vemuganti, R. R. (1980). The travelling salesman problem as a constrained shortest path problem: theory and computational experience. Operational Research, 17, 93–109.

    Google Scholar 

  • Irnich, S. (2008). Resource extension functions: properties, inversion and generalization to segments. OR-Spektrum, 30(1), 113–148.

    Article  Google Scholar 

  • Jaumard, B., Semet, F., & Vovor, T. (1996). A two-phase resource constrained shortest path algorithm for acyclic graphs (Technical report G-96-48). Les Cahier du GERAD.

  • Joksch, H. C. (1966). The shortest route problem with constraints. Journal of Mathematical Analysis and Applications, 14, 191–197.

    Article  Google Scholar 

  • Kohl, N. (1995). Exact methods for time constrained routing and related scheduling problems. PhD thesis, Institute of Mathematical Modelling, Technical University of Denmark, DK-2800 Lyngby. Dissertation no. 16.

  • Lawler, E. L. (1976). Combinatorial optimization: networks and matroids. New York: Holt, Rinehart and Winston.

    Google Scholar 

  • Mehlhorn, K., & Ziegelmann, M. (2000). Resource constraint shortest paths. In LNCS: Vol. 1879. 7 th ann. European symp. on algorithms (ESA2000) (pp. 326–337).

    Google Scholar 

  • Qureshi, A. G., Taniguchi, E., & Yamada, T. (2007). Elementary shortest path problem with resource constraints and time dependent late arrival penalties. Doboku Gakkai Ronbunshuu D, 63(4), 579–590.

    Article  Google Scholar 

  • Righini, G., & Salani, M. (2006). Symmetry helps: bounded bidirectional dynamic-programming for the elementary shortest path problem with resource constraints. Discrete Optimization, 3(3), 255–273.

    Article  Google Scholar 

  • Righini, G., & Salani, M. (2008). New dynamic programming algorithms for the resource constrained elementary shortest path problem. Networks, 51(3), 155–170.

    Article  Google Scholar 

  • Righini, G., & Salani, M. (2009). Decremental state space relaxation strategies and initialization heuristics for solving the orienteering problem with time windows with dynamic programming. Computers & Operations Research, 36, 1191–1203.

    Article  Google Scholar 

  • Santos, L., Coutinho-Rodrigues, J., & Current, J. R. (2007). An improved solution algorithm for the constrained shortest path problem. Transportation Research. Part B, 41, 756–771.

    Article  Google Scholar 

  • Skiscim, C. C., & Golden, B. (1989). Solving the k-shortest and constrained shortest path problem efficiently. Annals of Operations Research, 20, 249–282.

    Article  Google Scholar 

  • Solomon, M. M. (1983). Vehicle routing and scheduling with time window constraints: models and algorithms. PhD thesis, Department of Decision Science, University of Pennsylvania.

  • Toth, P., & Vigo, D. (2002). Capacitated vehicle-routing problems in the vehicle-routing problem. In P. Toth & D. Vigo (Eds.), SIAM monographs on discrete mathematics and applications.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronics, Computer Science and Systems, University of Calabria, 87036, Rende (CS), Italy

    Luigi Di Puglia Pugliese & Francesca Guerriero

Authors
  1. Luigi Di Puglia Pugliese
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francesca Guerriero
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luigi Di Puglia Pugliese.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Di Puglia Pugliese, L., Guerriero, F. A computational study of solution approaches for the resource constrained elementary shortest path problem. Ann Oper Res 201, 131–157 (2012). https://doi.org/10.1007/s10479-012-1162-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-012-1162-x

Keywords

Search

Navigation