Abstract
In location-routing problems, the objective is to locate one or many depots within a set of sites (representing customer locations or cities) and to construct delivery routes from the selected depot or depots to the remaining sites at least system cost. The objective function is the sum of depot operating costs, vehicle acquisition costs and routing costs. This paper considers one such problem in which a weight is assigned to each site and where sites are to be visited by vehicles having a given capacity. The solution must be such that the sum of the weights of sites visited on any given route does not exceed the capacity of the visiting vehicle. The formulation of an integer linear program for this problem involves degree constraints, generalized subtour elimination constraints, and chain barring constraints. An exact algorithm, using initial relaxation of most of the problem constraints, is presented which is capable of solving problems with up to twenty sites within a reasonable number of iterations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L.D. Bodin, B.L. Golden, A. Assad and M. Ball, Routing and scheduling of vehicles and crews. The state of the art, Computers and Operations Research 10(1983)69.
G.B. Dantzig, R. Fulkerson and S.M. Johnson, Solution of a large-scale travelling salesman problem, Oper. Res. 2(1954)393.
R. Gomory, An algorithm for integer solutions to linear programs, in:Recent Advances in Mathematical Programming (McGraw-Hill, 1963) p. 269.
Y.G. Handler and P.B. Mirchandani,Location on Networks. Theory and Algorithms (MIT Press, Cambridge, MA, 1979).
J. Krarup and T.M. Pruzan, Selected families of location problems, Ann. Disc. Math. 5(1979) 327.
J. Krarup and T.M. Pruzan, The simple plant location problem: Survey and synthesis, Eur. J. Oper. Res. 12(1983)36.
A.H. Land and S. Powell,FORTRAN Codes for Mathematical Programming: Linear, Quadratic and Discrete (Wiley, 1973).
G. Laporte and Y. Nobert, A cutting planes algorithm for them-salesmen problem, J. Oper. Res. Soc. 31(1980)1017.
G. Laporte and Y. Nobert, An exact algorithm for minimizing routing and operating costs in depot location, Eur. J. Oper. Res. 6(1981)224.
G. Laporte and Y. Nobert, A branch and bound algorithm for the capacitated vehicle routing problem, Operations Research Spektrum 5(1983)77.
G. Laporte and Y. Nobert, Les problèmes mixtes de localisation et de construction de tournées: un état de la question, Ecole des Hautes Etudes Commerciales de Montréal (1985).
G. Laporte, Y. Nobert and D. Arpin, Optimal solutions to capacitated multidepot vehicle routing problems, Congressus Numerantium 44(1984)283.
G. Laporte, Y. Nobert and M. Desrochers, Optimal routing under capacity and distance restrictions, Oper. Res. 33(1985)1050.
G. Laporte, Y. Nobert and P. Pelletier, Hamiltonian location problems, Eur. J. Oper. Res. 12(1983)82.
O.B.G. Madsen, Methods for solving combined two-level location-routing problems of realistic dimensions, Eur. J. Oper. Res. 12(183)295.
D.R. McLain, M.L. Durchholz and W.B. Wilborn, U.S.A.F. EDSA routing and operating location selection study, Report No. XPSR84-3, Operations Research Division, Directorate of Studies and Analysis, Scott Air Force Base, Illinois (1984).
P. Miliotis, G. Laporte and Y. Nobert, Computational comparison of two methods for finding the shortest complete cycle or circuit in a graph, RAIRO 15(1981)233.
J. Nambiar and L.G. Chalmet, A location and vehicle scheduling problem in collecting and processing rubber, paper presented at the TIMS/ORSA Conference, New Orleans (1979).
Y. Nobert, Construction d'algorithmes optimaux pour des extensions au problème du voyageur de commerce, Thèse de doctorat, Département d'Informatique et de Recherche Opérationnelle, Université de Montréal (1982)
I. Or and W.P. Pierskalla, A transportation location-allocation model for regional blood banking, AIIE Trans. 2(1979)86.
J. Perl, A unified warehouse location-routing problem, Ph.D. Dissertation, Department of Civil Engineering, Northwestern University, Evanston, Illinois (1983).
G.K. Rand, Methodological choices in depot location studies, Operational Research Quarterly 27(1976)241.
TDF (Transportforskningsdelegationen), Distribution planning using mathematical methods, Report 1977: 1, Contract Research Group for Applied Mathematics, Royal Institute of Technology, Sweden (1977).
C.D.T. Watson-Gandy and P.J. Dorn, Depot location with van salesmen. A practical approach, Omega 1(1973)321.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Laporte, G., Nobert, Y. & Arpin, D. An exact algorithm for solving a capacitated location-routing problem. Ann Oper Res 6, 291–310 (1986). https://doi.org/10.1007/BF02023807
Issue Date:
DOI: https://doi.org/10.1007/BF02023807