The maximum capture problem with heterogeneous customers

Computers and Operations Research

Volumn 26, Issue 14, 1999, Pages 1351-1367

  Benati, Stefano ^a  

^a UNIVERSITY OF TRENTO   (Italy)

Author keywords

Competitive location; Lagrangian relaxation; Random utility theory; Submodular functions

Indexed keywords

DATA REDUCTION; DECISION MAKING; FUNCTIONS; LAGRANGE MULTIPLIERS; MARKETING; PROBABILITY; PROBLEM SOLVING; RANDOM PROCESSES; RELAXATION PROCESSES; RESOURCE ALLOCATION; STRATEGIC PLANNING;

BRANCH-AND-BOUND METHODS; RANDOM UTILITY THEORY; SUBMODULAR FUNCTIONS;

OPERATIONS RESEARCH;

COMPETITIVENESS; FACILITY LOCATION; LOCATION-ALLOCATION MODEL;

EID: 0033485277     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0305-0548(99)00040-4     Document Type: Article

References (34)

1. ReVelle C. The maximum capture or 'Sphere of influence' location problem: Hotelling revisited on a network. Journal of Regional Science 1986;26:305-21.
2. ReVelle C, Serra. Competitive location in discrete space. In: Drezner Z, editor. Facility Location: A Survey of Applications and Methods. Berlin: Springer, 1995.
3. Dobson D, Karmarkar US. Competitive location on a network. Operations Research 1987;35:565-74.
4. Hakimi SL. Locations with spatial interactions: Competitive location and games. In: Mirchandani, Francis, editors. Discrete Location Theory. New York: Wiley, 1990.
5. p)-medianoid and the (r/p)-centroid. Location Science 1995;2:193-204.
6. Eiselt H, Laporte G, Thisse JF. Competitive location models: A framework and bibliography. Transportation Science 1993;27:44-54.
7. Luce RD. Individual choice behavior. A Theoretic Analysis. New York: Wiley, 1959.
8. Leonardi G. The use of random utility theory in building location-allocation models. In: Thisse JF, Zoller HG, editors. Locational Analysis of Public Facilities. Amsterdam: North-Holland, 1983.
9. Fotheringham AS, O'Kelly ME. Spatial Interaction Models: Formulations and Applications. Netherland: Kluwer, 1989.
10. Huff DL. Defining and estimating a trading area. Journal of Marketing 1964;28:34-8.
11. Eiselt HA, Laporte G. The maximum capture problem in a weighted network. Journal of Regional Science 1989;29:433-9.
12. AA VV. Some personal views on the current state and the future of locational analysis. European Journal of Operational Research 1998;104:269-87.
13. Eiselt HA, Laporte G. Equilibrium Results for Competitive Location Models. Working paper 96-04, Centre de recherche sur les transports, Université de Montréal, 1996.
14. Choi DS, Desarbo WS, Harker PT. Product positioning under price competition. Management Science 1990;38:175-99.
15. Drezner T, Drezner Z. Competitive facilities: Market share and location with random utility. Journal of Regional Science 1996;36:1-15.
16. de Palma A, Ginsburgh V, Labbé M, Thisse JF. Competitive location with random utilities. Transportation Science 1989;23:244-52.
17. In: Cornuejols G, Nemhauser GL, Wolsey LA. The uncapacitated facility location problem. In: Mirchandani, Francis, editors. Discrete Location Theory, New York: Wiley-Interscience, 1990.
18. Benati S. Submodularity in competitive location problems. Ricerca Operativa, The Journal of the Italian Operational Research Society 1997;26:3-34.
19. Ben-Akiva M, Lerman S. Discrete Choice Analysis: Theory and Application to Predict Travel Demand. Cambridge, MA: MIT Press, 1985.
20. van Lierop W, Nijkamp P. Disaggregate models of choice in a spatial context. Sistemi Urbani 1982;3:331-69.
21. Carlton DW. The location and employment choices of new firms: An ecomometric model with discrete and continuous endogenous variables. The Review of Economics and Statistics 1983;65:440-9.
22. McFadden D. Conditional logit analysis of qualitative choice behaviour. In: Zarembka P, editor. Frontiers in Econometrics. New York: Academic Press, 1974.
23. Eiselt HA, Laporte G. Demand Allocation Functions. Working paper 97-01, Centre de recherche sur les transports, Université de Montréal, 1997.
24. Benati S. Modelli per la localizzazione ottimale di nuove filiali bancarie (The optimal location of new bank branches). Quaderni di Statistica e Matematica Applicata 1996;18:341-50.
25. De Bonis R, Farabullini F, Fornari F. L'apertura di sportelli bancari dopo la liberalizzazione: Andamento e determinanti. Temi di Discussione del Servizio Studi della Banca d'Italia 1994;(235).
26. Nemhauser GL, Wolsey LA. Integer and Combinatorial Optimization. New York: Wiley Interscience, 1988.
27. Lee H, Nemhauser GL, Wang Y. Maximizing a submodular function by integer programming: Polyhedral results for the quadratic case. European Journal of Operational Research 1996;94:154-66.
28. Galvão RD. The use of lagrangean relaxation in the solution of uncapacitated facility location problem. Location Science 1993;1:57-79.
29. Beasley JE. A note on solving large p-median problem. European Journal of Operational Research 1985;21:270-3.
30. Hanjoul P, Peeters D. A comparison of two dual-based procedures for solving the p-median problem. European Journal of Operational Research 1985;20:387-96.
31. Boffey TB, Karkazis J. p-medians and multi-medians. Journal of the Operational Research Society 1984;35:57-64.
32. Christofides N, Beasley JE. A tree search algorithm for the p-median problem. European Journal of Operational Research 1982;10:196-204.
33. Mirchandani PB, Oudjit A, Wong RT. Multidimensional extension and nested dual approach for the m-median problem. European Journal of Operational Research 1985;21:121-37.
34. Nemhauser GL, Wolsey LA. Maximizing submodular set functions: Formulations and analysis of algorithms. Annals of Discrete Mathematics 1981;11:279-301.