Abstract
In this paper, we introduce the stop-and-drop problem (SDRP), a new variant of location-routing problems, that is mostly applicable to nonprofit food distribution networks. In these distribution problems, there is a central warehouse that contains food items to be delivered to agencies serving the people in need. The food is delivered by trucks to multiple sites in the service area and partner agencies travel to these sites to pick up their food. The tactical decision problem in this setting involves how to jointly select a set of delivery sites, assign agencies to these sites, and schedule routes for the delivery vehicles. The problem is modeled as an integrated mixed-integer program for which we delineate a two-phase sequential solution approach. We also propose two Benders decomposition-based solution procedures, namely a linear programming relaxation based Benders implementation and a logic-based Benders decomposition heuristic. We show through a set of realistic problem instances that given a fixed time limit, these decomposition based methods perform better than both the standard branch-and-bound solution and the two-phase approach. The general problem and the realistic instances used in the computational study are motivated by interactions with food banks in southeastern United States.
Similar content being viewed by others
References
Beasley, J. E., & Nascimento, E. M. (1996). The vehicle routing-allocation problem: A unifying framework. Top, 4, 65–86.
Black, R., Morris, S., & Bryce, J. (2003). Where and why are 10 million children dying every year? The Lancet, 361, 2226–2234.
Clarke, G., & Wright, J. (1964). Scheduling of vehicles from a central depot to a number of delivery points. Operations Research, 12, 568–581.
Codato, G., & Fischetti, M. (2006). Combinatorial Benders cuts for mixed-integer linear programming. Operations Research, 54(4), 756–766.
de Souza, L. V., & Siqueira, P. H. (2010). Heuristic methods applied to the optimization school bus transportation routes: a real case. In Proceedings of the 23rd international conference on industrial engineering and other applications of applied intelligent systems: part II (pp. 247–256). Berlin: Springer.
Desrochers, M., & Laporte, G. (1991). Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints. Operations Research Letters, 10, 27–36.
Fazel-Farandi, M. M., & Beck, J. C. (2009). Solving a location-allocation problem with logic-based Benders decomposition. In Principles and practice of constraint programming—CP 2009 (pp. 344–351). Berlin: Springer.
Feeding America (2009). Local Impact Study, September 2009. http://feedingamerica.org/newsroom/local-impact-study.aspx. Accessed 22 February 2010.
Food and Agriculture Organization of the United Nations (2009). Food security statistics. http://www.fao.org/economic/ess/food-security-statistics/en/. Accessed 22 February 2010.
Gillett, B., & Miller, L. (1974). A heuristic algorithm for the vehicle-dispatch problem. Operations Research, 22(2), 340–349.
Gunes, C., van Hoeve, W.-J., & Tayur, S. (2010). Vehicle routing for food rescue programs: A comparison of different approaches. In Proceedings of the seventh international conference on integration of AI and OR techniques in constraint programming for combinatorial optimization problems (CPAIOR) (pp. 287–291). Berlin: Springer.
Hooker, J. N. (2000). Logic-based methods for optimization: combining optimization and constraint satisfaction. New York: Wiley.
Hooker, J. N. (2007). Planning and scheduling by logic-based Benders decomposition. Operations Research, 55(3), 588–602.
Hooker, J. N., & Ottosson, G. (2003). Logic-based Benders decomposition. Mathematical Programming, 96, 33–60.
Hooker, J. N., & Yan, H. (1995). Logic circuit verification by Benders decomposition. In V. Saraswat & P. Van Hentenryck (Eds.), Principles and practice of constraint programming: The newport papers (pp. 267–288). Cambridge: MIT Press.
Jain, V., & Grossmann, I. E. (2001). Algorithms for hybrid MILP/CLP models for a class of optimization problems. INFORMS Journal on Computing, 13, 258–276.
Johnson, M. P., & Smilowitz, K. (2008). Community-based operations research. OR/MS Today, 35(1), 22–25.
Kara, I., Laporte, G., & Bektas, T. (2004). A note on the lifted Miller–Tucker–Zemlin subtour elimination constraints for the capacitated vehicle routing problem. European Journal of Operational Research, 158, 793–795.
Labbé, M., & Laporte, G. (1986). Maximizing user convenience and postal service efficiency in post box location. Belgian Journal of Operations Research, Statistics, and Computer Science, 26(2), 24–33.
Labbé, M., Laporte, G., Martin, I. R., & Gonzalez, J. J. S. (2005). Locating median cycles in networks. European Journal of Operational Research, 160, 457–470.
Laporte, G., & Louveaux, F. (1993). The integer L-shaped method for stochastic integer programs with complete recourse. Operations Research Letters, 13, 133–142.
le Blanc, H. M., Fleuren, H. A., & Krikke, H. R. (2004). Redesign of a recycling system for LPG-tanks. OR-Spektrum, 26, 283–304.
Lien, R., Iravani, S., & Smilowitz, K. (2010). Sequential resource allocation for nonprofit operations (Working paper). Available online at http://www.iems.northwestern.edu/docs/working_papers/WP_10-02.pdf.
Miller, C. E., Tucker, A. W., & Zemlin, R. A. (1960). Integer programming formulations and traveling salesman problems. Journal of the Association for Computing Machinery, 7, 326–329.
Murty, K., & Djang, P. (1999). The US army national guard’s mobile training simulators location and routing problem. Operations Research, 47(2), 175–182.
Nagy, G., & Salhi, S. (2007). Location-routing: Issues, models and methods. European Journal of Operational Research, 177(2), 649–672.
Nord, M., Andrews, M., & Carlson, S. (2008). Household food security in the United States. USDA Economic Research Report No. ERR-83.
Sherali, H. D., & Smith, J. C. (2001). Improving discrete model representations via symmetry considerations. Management Science, 47, 1396–1407.
Acknowledgements
This work has been supported by the University of Massachusetts Amherst Faculty Research Grant/Healey Endowment Grant Award Number P1FRG0000000055 and the National Science Foundation Broadening Participation Research Initiation Grants in Engineering (BRIGE) Award number 0927095.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Solak, S., Scherrer, C. & Ghoniem, A. The stop-and-drop problem in nonprofit food distribution networks. Ann Oper Res 221, 407–426 (2014). https://doi.org/10.1007/s10479-012-1068-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-012-1068-7