Planar location and design of a new facility with inner and outer competition: An interval lexicographical-like solution procedure

Networks and Spatial Economics

Volumn 7, Issue 1, 2007, Pages 19-44

  Fernández, José ^a   Pelegrín, Blas ^a   Plastria, Frank ^b   Tóth, Boglárka ^a  

^a UNIVERSITY OF MURCIA   (Spain)

^b VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

Author keywords

Biobjective optimization; Cannibalization; Competition; Continuous location; Efficient set; Facility design; Global optimization; Interval analysis; Lexicographic method; Profit optimization

Indexed keywords

BI-OBJECTIVE OPTIMIZATION; CANNIBALIZATION; CONTINUOUS LOCATIONS; EFFICIENT SETS; FACILITY DESIGNS; INTERVAL ANALYSIS; LEXICOGRAPHIC METHODS; PROFIT OPTIMIZATION;

BRANCH AND BOUND METHOD; COMPETITION; GLOBAL OPTIMIZATION; LOCATION; PRODUCT DESIGN; PROFITABILITY;

CHAINS;

EID: 33947608210     PISSN: 1566113X     EISSN: 15729427     Source Type: Journal    
DOI: 10.1007/s11067-006-9005-4     Document Type: Article

References (50)

1. Achabal D, Gorr WL, Mahajan V (1982) MULTILOC: A multiple store location model. J Retail 58:5-25
2. Centro Regional de Estadística de Murcia (2003) Anuario estadístico de la Región de Murcia: Dirección General de Economía, Planificación y Estadística, Centro Regional de Estadística de Murcia (2003)
3. Colomé R, Serra D (2001) Consumer choice and optimal location models: Formulations and heuristics. Pap Reg Sci 80:439-464
4. Current JR, Storbeck JE (1994) A multiobjective approach to design franchise outlet networks. J Oper Res Soc 45:71-81
5. Drezner T (1994a) Locating a single new facility among existing, unequally attractive facilities. J Reg Sci 34:237-252
6. Drezner T (1994b) Optimal continuous location of a retail facility, facility attractiveness, and market share: An interactive model. J Retail 70:49-64
7. Drezner T, Drezner Z (2004) Finding the optimal solution to the Huff based competitive location model. Comput Manage Sci 1:193-208
8. Drezner T, Drezner Z, Salhi S (2002) Solving the multiple competitive facility location problem. Eur J Oper Res 142:138-151
9. Drezner Z (ed) (1995) Facility Location: A Survey of Applications and Methods. Springer, Berlin Heidelberg New York
10. Eiselt HA, Laporte G, Thisse J-F (1993) Competitive location models: A framework and bibliography. Transp Sci 27:44-54
11. Ehrgott M (2005) Multicriteria Optimization, 2nd edn. Springer, Berlin Heidelberg New York
12. Fernández J, Fernández P, Pelegrín B (2000) A continuous location model for siting a non-noxious undesirable facility within a geographical region. Eur J Oper Res 121:259-274
13. b1,b2,θ-norm and a study about the selection of the data set. Comput Oper Res 29:609-623
14. Fernández J, Pelegrín B (2000) Sensitivity analysis in continuous location models via interval analysis. Stud Locat Anal 14:121-136
15. Fernández J, Pelegrín B (2001) Using interval analysis for solving planar single-facility location problems: New discarding tests. J Glob Optim 19:61-81
16. Fernández J, Pelegrín B, Plastria F, Tóth B (2005) Solving a Huff-like competitive location and design model for profit maximization in the plane. Eur J Oper Res DOI: 10.1016/ j.ejor.2006.02.005. (to appear)
17. Fernández J, Pelegrín B, Plastria F, Tóth B (2004) Sensitivity of optimal solutions to a Huff-type competitive location and design problem (Working paper)
18. Fernández J, Tóth B, Plastria F, Pelegrín B (2006) Reconciling franchisor and franchisee: A planar biobjective competitive location and design model. In: Recent Advances in Optimization. Lectures Notes in Economics and Mathematical Systems vol. 563. Springer, Berlin Heidelberg New York, pp375-398
19. Fishburn PC (1974) Lexicographic orders, utilities and decision rules: A survey. Manage Sci 20:1442-1471
20. Friesz TL, Miller T, Tobin RL (1988) Competitive networks facility location models: A survey. Pap Reg Sci Assoc 65:47-57
21. Ghosh A, Craig CS (1991) FRANSYS: A franchise distribution system location model. J Retail 67:466-495
22. Hammer R, Hocks M, Kulisch U, Ratz D (1995) C++ Toolbox for Verified Computing. Springer, Berlin Heidelberg New York
23. Hansen E (1992) Global Optimization Using Interval Analysis. Marcel Dekker, New York
24. Hansen P, Jaumard B (1995) Lipschitz optimization. In: Handbook of Global Optimization. Kluwer, Dordrecht, The Netherlands, pp407-494
25. Hansen P, Jaumard B, Tuy H (1995) Global optimization in location. In: Facility Location: A Survey of Applications and Methods. Springer, Berlin Heidelberg New York, pp 43-68
26. Hodgson MJ (1981) A location-allocation model maximizing consumers' welfare. Reg Stud 15:493-506
27. Huff DL (1964) Defining and estimating a trading area. J Mark 28:34-38
28. Huff DL (1966) A programmed solution for approximating an optimum reail location. Land Econ 42:293-303
29. Jain AK, Mahajan V (1979) Evaluating the competitive environment in retailing using multiplicative competitive interactive models. In: Sheth J (ed) Research in Marketing. JAI Press, Greenwich, Connecticut, pp 217-235
30. Kearfott RB (1996) Rigorous Global Search: Continuous Problems. Kluwer, Dordrecht, The Netherlands
31. Kearfott RB, Nakao MT, Neumaier A, Rump SM, Shary SP, van Hentenryck P (2002) Standardized notation in interval analysis. Reliab Comput. Submitted for publication, available at http://www.mat.univie.ac.at/~neum/software/int/
32. Kilkenny M, Thisse JF (1999) Economics of location: A selective survey. Comput Oper Res 26:1369-1394
33. Knüppel O (1994) PROFIL/BIAS - a fast interval library. Comput 53:277-287
34. Markót MC, Fernández J, Casado LG, Csendes T (2006) New interval methods for constrained global optimization. Math Prog Ser A 106:287-318
35. Martínez JA, Casado LG, García I, Tóth B, AMIGO: Advanced Multidimensional Interval analysis Global Optimization algorithm. In: Frontiers in Global Optimization. Nonconvex Optimization and its Applications, vol. 74. Kluwer, pp313-326 (2003)
36. Miettinen KS (1998) Nonlinear multiobjective optimization. Kluwer, Boston, Massachusetts
37. Miller TC, Friez TL, Tobin RL (1996) Equilibrium Facility Location on Networks. Springer, Berlin Heidelberg New York
38. Nakanishi M, Cooper LG (1974) Parameter estimate for mutiplicative interactive choice model: Least square approach. J Mark Res 11:303-311
39. Peeters PH, Plastria F (1992) Discretization results for the Huff and Pareto-Huff competitive location models on networks. Top 6:247-260
40. Plastria F (1992) GBSSS: The generalized big square small square method for planar single-facility location. Eur J Oper Res 62:163-174
41. Plastria F (2001) Static competitive facility location: An overview of optimisation approaches. Eur J Oper Res 129:461-470
42. Plastria F (2005) Avoiding cannibalization and/or competitor reaction in planar single facility location. J Oper Res Soc Jpn 48:148-157
43. Ratschek H, Rokne J (1984) Computer Methods for the Range of Functions. Ellis Horwood, Chichester, UK
44. Ratschek H, Rokne J (1988) New Computer Methods for Global Optimization. Ellis Horwood, Chichester, UK
45. Schmalensee R, Thisse JF (1988) Perceptual maps and the optimal location of new products: An integrative essay. Int J Res Mark 5:225-249
46. p) medianoid problem involving quality criteria. Top 12:111-133
47. Tóth B, Csendes T (2005) Empirical investigation of the convergence speed of inclusion functions. Reliab Comput 11:253-273
48. Tóth B, Fernández J, Csendes T (2007) Empirical convergence speed of inclusion functions for facility location problems. J Comput Appl Math 199:384-389 DOI: 10.1016/j.cam.2005.07.037
49. Visual GIS Engineering (2003) VisualMap. Basauri 17 (La Florida) 28023 Madrid
50. Wendell RE, McKelvey RD (1981) New perspectives in competitive location theory. Eur J Oper Res 6:174-182