Abstract
Discrete facility location problems are attractive candidates for decomposition procedures since two types of decisions have to be performed: on the one hand the yes/no-decision where to locate the facilities, on the other hand the decision how to allocate the demand to the selected facilities. Nevertheless, Benders' decomposition seems to have a rather slow convergence behaviour when applied for solving location problems. In the following, a procedure will be presented for strengthening the Benders' cuts for the capacitated facility location problem. Computational results show the efficiency of the modified Benders' decomposition algorithm. Furthermore, the paretooptimality of the strengthened Benders' cuts in the sense of [Magnanti and Wong 1990] is shown under a weak assumption.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Balas E (1965) An additive algorithm for solving linear programs with zero-one variables. Operations Research 13:517–546
Balas E, Martin CH (1980) Pivot and complement — A heuristic for 0-1 programming. Management Science 26(1): 86–96
Beasley JE (1988) An algorithm for solving large scale capacitated warehouse location problems. European Journal of Operational Research 33:314–325
Beasley JE (1990) OR-library: Distributing test problems by electronic mail. Journal of the Operational Research Society 41(11): 1069–1072
Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4:238–252
Boffey TB (1989) Location problems arising in computer networks. Journal of the Operational Research Society 40(4): 347–354
Christofides N, Beasley JE (1983) Extensions to a lagrangean relaxation approach for the capacitated warehouse location problem. European Journal of Operational Research 12:19–28
Cornuejols G, Sridharan R, Thizy JM (1991) A comparison of heuristics and relaxations for the capacitated plant location problem. European Journal of Operational Research 50:280–297
Domschke W (1989) Logistik: Transport (third edition). Oldenbourg Verlag, München
Geoffrion AM, Graves GW (1974) Multicommodity distribution system design by Benders decomposition. Management Science 20(5):822–844
Jacobsen SK (1983) Heuristics for the capacitated plant location model. European Journal of Operational Research 12:253–261
Kochmann GA, McCallum CJ (1981) Facility location models for planning a transatlantic communications network. European Journal of Operational Research 6:205–211
Lasdon LS (1970) Optimization theory for large systems. Macmillan, London
Magnanti TL, Wong RT (1981) Accelerating Benders decomposition: Algorithmic enhancement and model selection criteria. Operations Research 29(3): 464–484
Magnanti TL, Wong RT (1990) Decomposition methods for facility location problems. In: Mirchandani PB, Francis RL (Eds) Discrete Location Theory, chapter 5, 209–262. John Wiley & Sons, New York et al
McDaniel D, Devine M (1977) A modified Benders' partitioning algorithm for mixed integer programming. Management Science 24(3): 312–319
Minoux M (1986) Mathematical programming — Theory and algorithms. John Wiley & Sons, Chichester et al
Mirzaian A (1985) Lagrangian relaxation for the star-star concentrator location problem: Approximation algorithm and bounds. Networks 15:1–20
Nauss RM (1978) An improved algorithm for the capacitated facility location problem. Journal of the Operational Research Society 29(12): 1195–1201
Pochey Y, Wolsey LA (1988) Lot-size models with backlogging: Strong reformulations and cutting planes. Mathematical Programming 40:317–335
Ryu C (1993) Capacity-oriented planning and scheduling in production and distribution systems. PhD thesis, University of Pennsylvania
Van Roy TJ (1986) A cross decomposition algorithm for capacitated facility location. Operations Research 34(1): 145–163
Wentges P (1994) Standortprobleme mit Berücksichtigung von Kapazitätsrestriktionen: Modellierung und Lösungsverfahren. PhD thesis Nr. 1620 University of St. Gallen
Author information
Authors and Affiliations
Additional information
This paper was written when the author was at the Institute for Operations Research, University of St. Gallen, Switzerland, and partly supported by “Schweizerischer Nationalfond zur Förderung der wissenschaftlichen Forschung (Grant 12-30140.90)”.
Rights and permissions
About this article
Cite this article
Wentges, P. Accelerating Benders' decomposition for the capacitated facility location problem. Mathematical Methods of Operations Research 44, 267–290 (1996). https://doi.org/10.1007/BF01194335
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01194335