Abstract
Multi-depot Location-Routing Problem (MDLRP) is about finding the optimal number and locations of depots while allocating customers to depots and determining vehicle routes to visit all customers. In this study we propose a nested Lagrangian relaxation-based method for the discrete uncapacitated MDLRP. An outer Lagrangian relaxation embedded in subgradient optimization decomposes the parent problem into two subproblems. The first subproblem is a facility location-like problem. It is solved to optimaliy with Cplex 9.0. The second one resembles a capacitated and degree constrained minimum spanning forest problem, which is tackled with an augmented Lagrangian relaxation. The solution of the first subproblem reveals a depot location plan. As soon as a new distinct location plan is found in the course of the subgradient iterations, a tabu search algorithm is triggered to solve the multi-depot vehicle routing problem associated with that plan, and a feasible solution to the parent problem is obtained. Its objective value is checked against the current upper bound on the parent problem’s true optimal objective value. The performance of the proposed method has been observed on a number of test problems, and the results have been tabulated.
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References
Ahipasaoglu, S.D., Erdogan, G. and Tansel, B., “Location-routing problems: a review and assessment of research directions”, Working Paper IEOR 2003-07, Department of Industrial Engineering, Bilkent University, Ankara, Türkiye (2004).
Aksen, D. and Altinkemer, K., “Efficient frontier analysis and heuristics for etailing logistics”, Working Paper, Purdue University, Krannert Graduate School of Management: West Lafayette, Indiana, USA (2003).
Aksen, D. and Altinkcmer, K., “A location-routing problem for the conversion to the ‘click-and-mortar’ retailing: the static case”, Working Paper, College of Administrative Science and Economics, Koç University, Istanbul, Türkiye (2005).
Aksen, D., Özyurt, Z. and Aras, N., “Open vehicle routing problem with driver nodes and time windows”, available online in Journal of Operational Research Society, August 2006, (doi:10.1057/palgrave.jors.2602249).
Albareda-Sambola, M., Díaz, J. A. and Fernández, E., “A compact model and tight bounds for a combined location-routing problem”, Computers & Operations Research 32, 407–428 (2005).
Ambrosino, D. and Scutellà, M. G., “Distribution network design: new problems and related models”, European Journal of Operational Research 165, 610–624 (2005).
Crainic, T. G. and Laporte, G., “Planning models for freight transportation”, European Journal of Operational Research 97, 409–438 (1997).
Garey, G. and Johnson, D. S., “Computers and intractability: a guide to the theory of NP-completeness”, W. H. Freeman and Company: New York (1979).
Gavish, B., “Augmented Lagrangian based algorithms for centralized network design”, IEEE Transactions on Communications COM-33, 1247–1257 (1985).
Geoffrion, A. M., “Lagrangian relaxation and its uses in integer programming”, Mathematical Programming Study 2, 82–114 (1974).
Jacobsen, S.K. and Madsen, O. B. G., “A comparative study of heuristics for a two-level routing-location problem”, European Journal of Operational Research 5, 378–387 (1980).
Laporte, G., Nobert, Y. and Taillefer, S., “Solving a family of multi-depot vehicle routing and location-routing problems”, Transportation Science 22, 161–172 (1988).
Melechovský, J., Prins, C. and Calvo, R. W., “A metaheuristic to solve a location-routing problem with non-linear costs”, Journal of Heuristics 11, 375–391 (2005).
Min, H., Jayaraman, V. and Srivastava, R., “Combined location-routing: a synthesis and future research directions”, European Journal of Operational Research 108, 1–15(1998).
Salhi, S. and Rand, G. K., “The effect of ignoring routes when locating depots”, European Journal of Operational Research 39, 150–156 (1989).
Srivastava, R., “Alternate solution procedures for the location routing problem”, Omega International Journal of Management Science 21, 497–506 (1993).
Tüzün, D., and Burke, L. I., “A two-phase tabu search approach to the location routing problem”, European Journal of Operational Research 116, 87–99 (1999).
Wu, T.H., Low, C. and Bai, J.W., “Heuristic solutions to multi-depot location-routing problems”, Computers & Operations Research 29, 1393–1415 (2002).
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Özyurt, Z., Aksen, D. (2007). Solving the Multi-Depot Location-Routing Problem with Lagrangian Relaxation. In: Baker, E.K., Joseph, A., Mehrotra, A., Trick, M.A. (eds) Extending the Horizons: Advances in Computing, Optimization, and Decision Technologies. Operations Research/Computer Science Interfaces Series, vol 37. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-48793-9_9
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DOI: https://doi.org/10.1007/978-0-387-48793-9_9
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