Foundations of Location Analysis pp 179-206 | Cite as

# Conditional Location Problems on Networks and in the Plane

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## Abstract

Location decisions are of critical importance to all firms. Opening, closing, and relocating facilities require careful planning due to the strategic nature of these decisions. When customers do not have physical contact with the facilities (such as plants, distribution centers, or call centers), demand for the products or services can be assumed to be relatively independent of location. However, location choices of some stores (such as coffee shops, supermarkets, bank branches, and restaurants) do have a direct impact on demand. Therefore, such decisions should not be made without consideration of consumer behavior and market conditions.

## Keywords

Demand Point Price Decision Competitive Location Vote Theory Attraction Level
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

- Aboolian R, Berman O, Krass D (2007a) Competitive facility location model with concave demand. Eur J Oper Res 181:598–619CrossRefGoogle Scholar
- Aboolian R, Berman O, Krass D (2007b) Competitive facility location and design problem. Eur J Oper Res 182:40–62CrossRefGoogle Scholar
- Achabal D, Gorr WL, Mahajan V (1982) MULTILOCL: a multiple store location decision model. J Retail 58:5–25Google Scholar
- Ahn H-K, Cheng S-W, Cheong O, Golin M, van Oostrum R (2004) Competitive facility location: the Voronoi game. Theor Comput Sci 310:457–467CrossRefGoogle Scholar
- Balakrishnan P, Storbeck J (1991) Mctresh: modeling maximum coverage with threshold constraints. Environ Plan B 18:459–472CrossRefGoogle Scholar
- Bandelt H-J (1985) Networks with Condorcet solutions. Eur J Oper Res 20:314–326CrossRefGoogle Scholar
- Bandelt H-J, Labbe M (1986) How bad can a voting location be? Soc Choice Welf 3:125–145CrossRefGoogle Scholar
- Benati S (1999) The maximum capture problem with heterogeneous customers. Comput Oper Res 26:1351–1367CrossRefGoogle Scholar
- Benati S (2003) An improved branch and bound method for the uncapacitated competitive location problem. Ann Oper Res 122:43–58CrossRefGoogle Scholar
- Benati S, Hansen P (2002) The maximum capture problem with random utilities: problem formulation and algorithms. Eur J Oper Res 143:518–530CrossRefGoogle Scholar
- Benati S, Laporte G (1994) Tabu search algorithms for the (
*r|Xp*)—medianoid and (*r|p*)—centroid problems. Locat Sci 2:193–204Google Scholar - Berman O, Krass D (1998) Flow intercepting spatial interaction model: a new approach to optimal location of competitive facilities. Locat Sci 6:41–65CrossRefGoogle Scholar
- Berman O, Krass D (2002) Locating multiple competitive facilities: spatial interaction models with variable expenditures. Ann Oper Res 111:197–225CrossRefGoogle Scholar
- Bhadury J, Eiselt HA, Jaramillo JH (2003) An alternating heuristic for medianoid and centroid problems in the plane. Comput Oper Res 30:553–565CrossRefGoogle Scholar
- Campos-Rodriguez CM, Moreno-Perez JA (2003) Relaxation of the Condorcet and Simpson conditions in voting location. Eur J Oper Res 145:673–683CrossRefGoogle Scholar
- Cheong O, Har-Peled S, Linial N, Matousek J (2004) The one-round Voronoi game. Discrete Comput Geom 31:125–138Google Scholar
- Colome R, Lourenco HR, Serra D (2003) A new chance-constrained maximum capture location problem. Ann Oper Res 122:121–139CrossRefGoogle Scholar
- Current J, Storbeck J (1994) A multiobjective approach to design franchise outlet networks. J Oper Res Soc 45:71–81Google Scholar
- Dasci A, Laporte G (2005) A continuous model for multistore competitive location. Oper Res 53:263–280CrossRefGoogle Scholar
- Daskin MS (1995) Network and discrete location: models, algorithms, and applications. Wiley, New YorkGoogle Scholar
- Dobson G, Karmarkar US (1987) Competitive location on a network. Oper Res 35:565–574CrossRefGoogle Scholar
- Drezner Z (1982) Competitive location strategies for two facilities. Reg Sci Econ 12:485–493CrossRefGoogle Scholar
- Drezner T (1994a) Locating a single new facility among existing unequally attractive facilities. J Reg Sci 34:237–252CrossRefGoogle Scholar
- Drezner T (1994b) Optimal continuous location of a retail facility, facility attractiveness, and market share: an interactive model. J Retail 70:49–64CrossRefGoogle Scholar
- Drezner T (1998) Location of multiple retail facilities with limited budget constraints—in continuous space. J Retail Consum Serv 5:173–184CrossRefGoogle Scholar
- Drezner T, Drezner Z (1996) Competitive facilities: market share and location with random utility. J Reg Sci 36:1–15CrossRefGoogle Scholar
- Drezner T, Drezner Z (1998) Facility location in anticipation of future competition. Locat Sci 6:155–173CrossRefGoogle Scholar
- Drezner Z, Wesolowsky GO, Drezner T (1998) On the logit approach to competitive facility location. J Reg Sci 38:313–327CrossRefGoogle Scholar
- Drezner T, Drezner Z, Salhi S (2002a) Solving the multiple competitive facilities location problem. Eur J Oper Res 142:138–151CrossRefGoogle Scholar
- Drezner T, Drezner Z, Shiode S (2002b) A threshold satisfying competitive location model. J Reg Sci 42:287–299CrossRefGoogle Scholar
- Eiselt HA (1992) Hotelling’s duopoly on a tree. Ann Oper Res 40:195–207CrossRefGoogle Scholar
- Eiselt HA (1998) Perception and information in a competitive location model. Eur J Oper Res 108:94–105CrossRefGoogle Scholar
- Eiselt HA, Bhadury J (1998) Reachability of locational Nash equilibria. OR Spectrum 20:101–107CrossRefGoogle Scholar
- Eiselt HA, Laporte G (1989) The maximum capture problem in a weighted network. J Reg Sci 29:433–439CrossRefGoogle Scholar
- Eiselt HA, Laporte G (1996) Sequential location problems. Eur J Oper Res 96:217–231CrossRefGoogle Scholar
- Eiselt HA, Laporte G, Thisse J-F (1993) Competitive location models: a framework and bibliography. Transp Sci 27:44–54CrossRefGoogle Scholar
- Fernandez J, Pelegrin B, Plastria F, Toth B (2007a) Solving a Huff-like competitive location and design model for profit maximization in the plane. Eur J Oper Res 179:1274–1287CrossRefGoogle Scholar
- Fernandez J, Pelegrin B, Plastria F, Toth B (2007b) Planar location and design of a new facility with inner and outer competition: an interval lexicographical-like solution procedure. Netw Sp Econ 7:19–44CrossRefGoogle Scholar
- Fekete SP, Meijer H (2005) The one-round Voronoi game replayed. Comput Geom Theory Appl 30:81–94Google Scholar
- Fischer K (2002) Sequential discrete
*p*-facility models for competitive location planning. Ann Oper Res 111:253–270CrossRefGoogle Scholar - Friesz T, Tobin L, Miller T (1989) Existence theory for spatially competitive network facility location models. Ann Oper Res 18:267–276CrossRefGoogle Scholar
- Garcia-Perez MD, Pelegrin BP (2003) All Stackelberg location equilibria in the Hotelling’s duopoly model on a tree with parametric prices. Ann Oper Res 122:177–192CrossRefGoogle Scholar
- Ghosh A, Craig CS (1983) Formulating retail location strategy in a changing environment. J Mark 47:56–68CrossRefGoogle Scholar
- Ghosh A, Craig CS (1991) FRANSYS: a franchise location model. J Retail 67:212–234Google Scholar
- Ghosh A, McLafferty SL (1987) Location strategies for retail and service firms. Lexington Books, LexingtonGoogle Scholar
- Hakimi SL (1983) On locating new facilities in a competitive environment. Eur J Oper Res 12:29–35CrossRefGoogle Scholar
- Hakimi SL (1986)
*p*-median theorems for competitive location. Ann Oper Res 5:79–88Google Scholar - Hakimi SL (1990) Locations with spatial interactions: competitive locations and games. In: Mirchandani PB, Francis RL (eds) Discrete location theory. Wiley, New York, pp 439–478Google Scholar
- Hansen P, Thisse J-F (1981) Outcomes of voting and planning: Condorcet; Weber and Rawls locations. J Public Econ 16:1–15CrossRefGoogle Scholar
- Hansen P, Labbe M (1988) Algorithms for voting and competitive location on a network. Transp Sci 22:278–288CrossRefGoogle Scholar
- Hansen P, Thisse J-F, Wendell RW (1990) Equilibrium analysis for voting and competitive location problems. In: Mirchandani PB, Francis RL (eds) Discrete location theory. Wiley, New York, pp 479–501Google Scholar
- Hotelling H (1929) Stability in competition. Econ J 39:41–57CrossRefGoogle Scholar
- Huff DL (1964) Defining and estimating a trading area. J Mark 28:34–38CrossRefGoogle Scholar
- Karkazis J (1989) Facilities location in a competitive environment: a Promethee-based multiple criteria analysis. Eur J Oper Res 42:294–304CrossRefGoogle Scholar
- Labbe M (1985) Outcomes of voting and planning in single facility location problems. Eur J Oper Res 20:299–313CrossRefGoogle Scholar
- Lee DT, Wu YF (1986) Geometric complexity of some location problems. Algorithmica 1:193–211CrossRefGoogle Scholar
- Marianov V, Serra D (1998) Probabilistic maximal covering location-allocation for congested systems. J Reg Sci 38:401–424CrossRefGoogle Scholar
- Marianov V, Rios M, Taborga P (2004) Finding locations for public service centres that compete with private centres: effects of congestion. Pap Reg Sci 83:631–648Google Scholar
- McGarvey RG, Cavalier TM (2005) Constrained location of competitive facilities in the plane. Comput Oper Res 32:359–378Google Scholar
- Megiddo N, Zemel E, Hakimi SL (1983) The maximum coverage location problem. SIAM J Algebra Discrete Method 4:253–261CrossRefGoogle Scholar
- Miller T, Tobin R, Friez T (1991) Stackelberg games on a network with Cournot-Nash oligopolistic competitors. J Reg Sci 31:435–454CrossRefGoogle Scholar
- Nakanishi M, Cooper LG (1974) Parameter estimate for multiplicative interactive choice model: least squares approach. J Mark Res 11:303–311CrossRefGoogle Scholar
- Noltemeier H, Spoerhase J, Wirth H-C (2007) Multiple voting location and single voting location on trees. Eur J Oper Res 181:654–667CrossRefGoogle Scholar
- Peeters PH, Plastria F (1998) Discretization results for the Huff and Pareto-Huff competitive location models on networks. Top 6:247–260CrossRefGoogle Scholar
- Pelegrin B, Fernandez J, Suarez R, Garcia-Perez MD (2006) Single facility location on a network under mill and delivered pricing. IMA J Manag Math 17:373–385CrossRefGoogle Scholar
- Plastria F (2001) Static competitive facility location: an overview of optimization approaches. Eur J Oper Res 129:461–470CrossRefGoogle Scholar
- Plastria F, Vanhaverbeke L (2009) Maximal covering location problem with price decision for revenue maximization in a competitive environment. OR Spectrum 31:555–571CrossRefGoogle Scholar
- Redondo JL, Fernández J, García I, Ortigosa PM (2009a) Solving multiple competitive facilities location and design problem on the plane. Evolutionary Computation 17:21–53CrossRefGoogle Scholar
- Redondo JL, Fernández J, García I, Ortigosa PM (2009b) A robust and efficient algorithm for planar competitive location problems. Ann Oper Res 167:87–105CrossRefGoogle Scholar
- ReVelle C (1986) The maximum capture or “sphere of influence” location problem: Hotelling revisited on a network. J Reg Sci 26:343–358CrossRefGoogle Scholar
- Saiz ME, Hendrix EMT, Fernandez J, Pelegrin B (2007) On a branch-and-bound approach doe a Huff-like Stackelberg location problem. Discussion paper No. 37, Mansolt Graduate SchoolGoogle Scholar
- Santos-Penate DR, Suarez-Vega R (2003) Submodular capture functions in competitive location: the (
*r|Xp*)—medianoid and the (*r|p*)—centroid problems. 27 Congreso SEIO, LeridaGoogle Scholar - Santos-Penate DR, Suarez-Vega R, Dorta-Gonzalez P (2007) The leader--follower location model. Netw Sp Econ 7:45–61CrossRefGoogle Scholar
- Serra D, Colome R (2001) Consumer choice and optimal location models: formulations and heuristics. Pap Reg Sci 80:439–464CrossRefGoogle Scholar
- Serra D, ReVelle C (1994) Market capture by two competitors: the preemptive location problem. J Reg Sci 34:549–561CrossRefGoogle Scholar
- Serra D, ReVelle C (1999) Competitive location and pricing on networks. Geogr Anal 31:109–129CrossRefGoogle Scholar
- Serra D, ReVelle C, Rosing K (1999a) Surviving in a competitive spatial market: the threshold capture model. J Reg Sci 39:637–650CrossRefGoogle Scholar
- Serra D, Eiselt HA, Laporte G, ReVelle C (1999b) Market capture models under various customer choice rules. Environ Plan B 26:741–750CrossRefGoogle Scholar
- Shiode S, Drezner Z (2003) A competitive facility location problem on a tree network with stochastic weights. Eur J Oper Res 149:47–52CrossRefGoogle Scholar
- Silva F, Serra D (2007) Incorporating waiting time in competitive location models. Netw Sp Econ 7:63–76CrossRefGoogle Scholar
- Slater PJ (1975) Maximin facility location. J Nat Bureau Stand B 79:107–115Google Scholar
- Suarez-Vega R, Santos-Penate DR, Dorta-Gonzalez P (2004a) Competitive multi-facility location on networks: the (
*r*|*Xp*)-medianoid problem. J Reg Sci 44:569–588CrossRefGoogle Scholar - Suarez-Vega R, Santos-Penate DR, Dorta-Gonzalez P (2004b) Discretization and resolution of the (
*r*|*Xp*)—medianoid problem involving quality criteria. Top 12:111–133CrossRefGoogle Scholar - Suarez-Vega R, Santos-Penate DR, Dorta-Gonzalez P (2007) The follower location problem with attraction thresholds. Pap Reg Sci 86:123–137CrossRefGoogle Scholar
- Tobin R, Friesz T (1986) Spatial competition facility location models: definition, formulation and solution approach. Ann Oper Res 6:49–74CrossRefGoogle Scholar
- Toth B, Fernandez J, Pelegrin B, Plastria F (2008) Sequential versus simultaneous approach in the location and design of two new facilities using planar Huff-like model. Comput Oper Res (to appear)Google Scholar
- Wendell RE, Thorson SJ (1974) Some generalizations of social decisions under majority rule. Econometrica 42:893–912CrossRefGoogle Scholar
- Wendell RE, McKelvey R (1981) New perspectives in competitive location theory. Eur J Oper Res 6:174–182CrossRefGoogle Scholar
- Wu TH, JN Lin (2003) Solving the competitive discretionary service facility location problem. Eur J Oper Res 144:366–378CrossRefGoogle Scholar
- Zhang S (2001) On a profit maximizing location model. Ann Oper Res 103:251–260CrossRefGoogle Scholar
- Zhang L, Rushton G (2008) Optimizing the size and locations of facilities in competitive multi-site service systems. Comput Oper Res 35:327–338CrossRefGoogle Scholar

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