Abstract
We consider a special class of large-scale, network-based, resource allocation problems under uncertainty, namely that of multi-commodity flows with time-windows under uncertainty. In this class, we focus on problems involving commodity pickup and delivery with time-windows. Our work examines methods of proactive planning, that is, robust plan generation to protect against future uncertainty. By a priori modeling uncertainties in data corresponding to service times, resource availability, supplies and demands, we generate solutions that are more robust operationally, that is, more likely to be executed or easier to repair when disrupted. We propose a novel modeling and solution framework involving a decomposition scheme that separates problems into a routing master problem and Scheduling Sub-Problems; and iterates to find the optimal solution. Uncertainty is captured in part by the master problem and in part by the Scheduling Sub-Problem. We present proof-of-concept for our approach using real data involving routing and scheduling for a large shipment carrier’s ground network, and demonstrate the improved robustness of solutions from our approach.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ahuja, R., Magnanti, T., & Orlin, J. (1993). Network flows: Theory, algorithms and applications. New York: Prentice Hall.
Barnhart, C., Hane, C. A., Johnson, E. L., Sigismondi, G. (1994). A column generation and partitioning approach for multi-commodity flow problems. Telecommunication Systems, 3, 239–258, ISSN 1018–4864. doi:10.1007/BF02110307.
Barnhart, C., Johnson, E., Nemhauser, G., Savelsbergh, M., & Vance, P. (1998a). Branch-and-price: Column generation for solving huge integer programs. Operations Research, 46, 316–329.
Ben-Tal, A., & Nemirovski, A. (1999). Robust solutions to uncertain programs. Operations Research Letters, 25, 1–13.
Ben-Tal, A., & Nemirovski, A. (2000). Robust solutions of linear programming problems contaminated with uncertain data. Mathematical Programming, 88, 411–424.
Bertsimas, D., & Sim, M. (2003). Robust discrete optimization and network flows. Mathematical Programming Series B, 98, 49–71.
Bertsimas, D., & Sim, M. (2004). The price of robustness. Operations Research, 52(1), 35–53.
Bertsimas, D., & Simchi-Levi, D. (1996). A new generation of vehicle routing research: Robust algorithms, addressing uncertainty. Operations Research, 44(2), 286–304.
Birge, J., & Louveaux, F. (1997). Introduction to stochastic programming. New York: Springer.
Charnes, A., & Cooper, W. W. (1959). Chance constrained programming. Management Science, 6(1), 73–79.
Charnes, A., & Cooper, W. W. (1963). Deterministic equivalents for optimizing and satisficing under chance constraints. Operations Research, 11(1), 18–39.
Cordeau, J., Laporte, G., Potvin, J., & Savelsbergh, M. (2006). Transportation on demand. Section: Handbook of operations research (Vol. 2). Montreal, QC: Centre for Research on Transportation.
Cordeau, J.-F., Laporte, G., Potvin, J.-Y., & Savelsbergh, M. W. P. (2007). Transportation on demand. In C. Barnhart & G. Laporte (Eds.), Transportation, Handbooks in operations research and management science (Vol. 14, pp. 429–466). Amsterdam: Elsevier.
Desrosiers, J., Dumas, Y., Solomon, M. M., & Soumis, F. (1995). Time constrained routing and scheduling. In M. Ball (Ed.), Handbook in operations research/ management science, network routing. Amsterdam: North-Holland.
Dessouky, M., Hall, R., Nowroozi, A., & Mourikas, K. (1999). Bus dispatching at timed transfer transit stations using bus tracking technology. Transportation Research Part C: Emerging Technologies, 7, 187–208.
Dror, M., Laporte, G., & Trudeau, P. (1989). Vehicle routing with stochastic demands: Properties and solution frameworks. Transportation Science, 23(3), 166–176.
Dumas, Y., Desrosiers, J., & Soumis, F. (1991). The pickup and delivery problem with time windows. European Journal of Operational Research, 54(1), 7–22.
Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: A guide to the THEORY of NP-completeness. San Francisco: Freeman.
Jiang, H., & Barnhart, C. (2009). Dynamic airline scheduling. Transportation Science, 43(3), 336–354.
Kang, L. S., & Clarke, J.-P. (2002). Degradable airline scheduling. Working paper. Operations Research Center, Massachusetts Institute of Technology.
Lan, S., Clarke, J.-P., & Barnhart, C. (2006). Planning for robust airline operations: Optimizing aircraft routings and flight departure times to minimize passenger disruptions. Transportation Science, 40(1), 15–28.
Mahr, T. (2011). Vehicle routing under uncertainty. Master’s thesis, Budapest University of Technology and Economics.
Marla, L. (2007). Robust optimization for network-based resource allocation problems. Masters thesis, Massachusetts Institute of Technology.
Marla, L. (2010). Airline schedule planning and operations: Optimization-based approaches for delay mitigation. PhD thesis, Massachusetts Institute of Technology.
Marla, L., & Barnhart, C. (2011). A decomposition approach to dynamic airline scheduling. Working paper.
Mulvey, J. M., Vanderbei, R. J., & Zeinos, S. A. (1981). Robust optimization of large-scale systems. Operations Research, 43, 34–56.
Nuutila, E., & Soisalon-Soininen, E. (1994). On finding the strongly connected components in a directed graph. Information Processing Letters, 49, 9–14.
Ordonez, F., & Zhao, J. (2011). Robust capacity expansion of network flows. Technical report, University of Southern California.
Paraskevopoulos, D., Karakitsos, E., & Rustem, B. (1991). Robust capacity planning under uncertainty. Management Science, 37(7), 787–800.
Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. The Journal of Risk, 2(3), 21–41.
Shebalov, S., & Klabjan, D. (2004). Robust airline crew pairing: Move-up crews. Working paper, The University of Illinois at Urbana-Champaign. http://netfiles.uiuc.edu/klabjan/www
Soyster, A. L. (1973). Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations Research, 21(5), 1154–1157.
Sungur, I., Ordonez, F., Dessouky, M. M., Ren, Y., & Zhong, H. (2010). A model and algorithm for the courier delivery problem with uncertainty. Transportation Science, 44, 193–205.
Tarjan, R. (1972). Depth first search and linear graph algorithms. Journal of Computing, 1(2), 146–160.
Wollmer, R. D. (1980). Investment in stochastic minimum cost generalized multicommodity networks with application to coal transport. Networks, 10(4), 351–362, ISSN 1097–0037. doi:10.1002/net.3230100406.
Wood, D. (1997). An algorithm for finding a maximum clique in a graph. Operations Research Letters, 21, 211–217.
Yang, J., Jaillet, P., & Mahmassani, H. (2004). Real-time multivehicle truckload pickup and delivery problems. Transportation Science, 38(2), 135–148.
Acknowledgments
We sincerely thank the anonymous reviewers for their time in reading our paper and for their valuable comments and suggestions, which significantly contributed to improving the quality of this manuscript.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Marla, L., Barnhart, C. & Biyani, V. A decomposition approach for commodity pickup and delivery with time-windows under uncertainty. J Sched 17, 489–506 (2014). https://doi.org/10.1007/s10951-013-0317-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10951-013-0317-1