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64 Emilio Carrizosa, José Gordillo, and Dolores R. Santos-Peñatefor τ 1 < . . . < τ r the facilities will become operative in exactly r different instants. Allowingdifferent τ i to coincide collapses the number of different instants considered. In other words,the problem of determining sites for at most q facilities, to become operative in at most rdifferent instants, can be written asmaxr∑ { ∑x k v [g v(τ k+1 ) − g v (τ k )] − ∑ yf k[h f (τ k+1 ) − h f (τ k )] }k=1v∈V(x, y) ∈ S r0 ≤ τ 1 ≤ τ 2 ≤ . . . ≤ τ r ≤ T,or equivalently as the bilevel problemf∈F(6)or equivalently as the bilevel problemmax (x,y)∈Srmaxk=1max Π r (τ 1 , . . . , τ r )0 ≤ τ 1 ≤ τ 2 ≤ . . . ≤ τ r ≤ T,r∑ { ∑x k v [g v(τ k+1 ) − g v (τ k )] − ∑ yf k[h f (τ k+1 ) − h f (τ k )] }v∈V0 ≤ τ 1 ≤ τ 2 ≤ . . . ≤ τ r ≤ T.f∈F(7)(8)Since (6), (7) and (8) are simply different writings of the same problem, we will use one orother at our convenience.Our problem, namely, the determination of optimal locations and opening times for at mostq facilities corresponds to (6), (7) or (8) with r = q.General properties concerning the optimal sites and times are derived. These results arestrengthened for different particular instances of demand patterns, namely, the cases in whichthe demand of a given consumer is constant, varies linearly in time, is increasing or is decreasing.A heuristic procedure is proposed to determine the optimal policy, and numericalexperiences are provided.References[1] Benati, S. and P. Hansen (2002): The maximum capture problem with random utilities: Problem formulationand algorithms, European Journal of Operational Research 143, 518-530.[2] Craig, S., A. Ghosh and S. McLafferty (1984): Models of the retail location process: a review, Journal of Retailing,60, 1, pp. 5-36.[3] Drezner, T. (1995): Competitive facility location in the plane, in Facility Location. A survey of applications andmethods, Z. Drezner (Ed.), Springer, Berlin, 285-300.[4] Drezner Z. and G.O. Wesolowsky (1991): Facility Location When Demand is Time Dependent, Naval ResearchLogistics, 38, 763-777.[5] Eiselt, H.A. and G. Laporte (1989): Competitive spatial models, European Journal of Operational Research, 39,pp.231-242.[6] Eiselt, H.A., G. Laporte and J-F. Thisse (1993): Competitive location models: A framework and bibliography,Transportation Science, 27, nž 1, pp.44-54.[7] Friesz, T.L., T. Miller and R.L. Tobin (1988): Competitive network facility location models: A survey, Papersof the Reginal Science Association, 65, pp. 47-57.[8] Hakimi, S.L. (1983): On locating new facilities in a competitive environment, European Journal of OperationalResearch, 12, pp. 29-35.[9] Hakimi, S.L. (1990): Location with spatial interactions: Competitive locations and games, in Mirchandani,P.B. and R.L. Francis (editors), Discrete Location Theory, John Wiley & Sons, Nueva York, pp. 439-478.[10] Hansen, P., Peeters, D. and Thisse, J.-F., (1995): The profit-maximizing Weber Problem, Location Science 3, 2,67-85.[11] Plastria, F. (1997): Profit maximising single competitive facility location in the plane, Studies in LocationalAnalysis, 11, 115-126.
Locating competitive facilities 65[12] Plastria, F. (2001): Static competitive facility location: an overview of optimisation approaches, EuropeanJournal of Operational Research, 129, 461-470.[13] Plastria, F. and E. Carrizosa (2004): Location and design of a competitive facility for profit maximisation,Mathematical Programming 100, 345-353.[14] Santos-Peñate, D.R. (2004): Competencia espacial en redes. In Pelegrín, B. (editor), Avances en localización deservicios y sus aplicaciones, Servicio de Publicaciones de la Universidad de Murcia, pp. 219-248.[15] Wey, W.-M. and C.-T. Liao (2001): A study of parking facility location when demand is time dependent.Presented at INFORMS Anual Meeting 2001, Maui, Hawaii, USA.[16] Wesolowsky, G.O. (1973): Dynamic facility location, Management Science 19, 1241-1247.[17] Wesolowsky, G.O. and W.G. Truscott (1975): The multiperiod location-allocation problem with relocation offacilities, Management Science 22, 57-65.
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PROCEEDINGS OF THEINTERNATIONAL WOR
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ContentsPrefaceiiiPlenary TalksYaro
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ContentsviiFuh-Hwa Franklin Liu, Ch
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PLENARY TALKS
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4 Yaroslav D. Sergeyevto work with
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EXTENDED ABSTRACTS
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10 Bernardetta Addis and Sven Leyff
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12 Bernardetta Addis and Sven Leyff
Page 22 and 23: 14 Bernardetta Addis and Sven Leyff
Page 24 and 25: 16 Bernardetta Addis, Marco Locatel
Page 26 and 27: 18 April K. Andreas and J. Cole Smi
Page 32 and 33: 24 Charles Audet, Pierre Hansen, an
Page 38 and 39: 30 János Balogh, József Békési,
Page 44 and 45: 36 Balázs Bánhelyi, Tibor Csendes
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Page 49 and 50: MGA Pruning Technique 41Figure 1. A
Page 51 and 52: MGA Pruning Technique 43O(n) = k 2
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Page 56 and 57: 48 Edson Tadeu Bez, Mirian Buss Gon
Page 62 and 63: 54 R. Blanquero, E. Carrizosa, E. C
Page 64 and 65: 56 R. Blanquero, E. Carrizosa, E. C
Page 66 and 67: 58 Sándor Bozókiwhere for any i,
Page 68 and 69: 60 Sándor Bozóki[6] Budescu, D.V.
Page 70 and 71: 62 Emilio Carrizosa, José Gordillo
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Page 77: Globally optimal prototypes 69Refer
Page 80 and 81: 72 Leocadio G. Casado, Eligius M.T.
Page 82 and 83: 874 Leocadio G. Casado, Eligius M.T
Page 84 and 85: 76 Leocadio G. Casado, Eligius M.T.
Page 86 and 87: 78 András Erik Csallner, Tibor Cse
Page 88 and 89: 80 András Erik Csallner, Tibor Cse
Page 90 and 91: 82 Tibor Csendes, Balázs Bánhelyi
Page 92 and 93: 84 Tibor Csendes, Balázs Bánhelyi
Page 94 and 95: 86 Bernd DachwaldFor spacecraft wit
Page 96 and 97: 88 Bernd Dachwaldcurrent target sta
Page 98 and 99: 90 Bernd Dachwaldreference launch d
Page 100 and 101: 92 Mirjam Dür and Chris TofallisMo
Page 102 and 103: 94 Mirjam Dür and Chris Tofallis2.
Page 104 and 105: 96 Mirjam Dür and Chris Tofallis[3
Page 106 and 107: 98 José Fernández and Boglárka T
Page 108 and 109: 100 José Fernández and Boglárka
Page 110 and 111: 102 José Fernández and Boglárka
Page 112 and 113: 104 Erika R. Frits, Ali Baharev, Zo
Page 118 and 119: 110 Juergen Garloff and Andrew P. S
Page 120 and 121: 112 Juergen Garloff and Andrew P. S
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Proceedings of GO 2005, pp. 115 - 1
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Global multiobjective optimization
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Global multiobjective optimization
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Conditions for ε-Pareto Solutions
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Conditions for ε-Pareto Solutions
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128 Eligius M.T. Hendrix1.1 Effecti
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130 Eligius M.T. Hendrix4h(x)3.532.
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132 Eligius M.T. Hendrixneighbourho
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134 Kenneth Holmströmcomputed by R
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136 Kenneth Holmströmα(x) =∑i=1
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138 Kenneth HolmströmGL-step Phase
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140 Kenneth Holmströmsurrogate mod
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142 Dario Izzo and Mihály Csaba Ma
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148 Leo Liberti and Milan DražićV
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150 Leo Liberti and Milan Dražićs
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Set-covering based p-center problem
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Set-covering based p-center problem
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On the Solution of Interplanetary T
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On the Solution of Interplanetary T
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Parametrical approach for studying
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Parametrical approach for studying
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An Interval Branch-and-Bound Algori
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An Interval Branch-and-Bound Algori
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A New approach to the Studyof the S
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A New approach to the Studyof the S
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184 Katharine M. Mullen, Mikas Veng
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190 Niels J. Olieman and Eligius M.
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196 Andrey V. Orlovwhere A is (m 1
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198 Andrey V. OrlovStep 4. Beginnin
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200 Blas Pelegrín, Pascual Fernán
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208 Deolinda M. L. D. Rasteiro and
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214 José-Oscar H. Sendín, Antonio
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220 Ya. D. Sergeyev and D. E. Kvaso
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226 J. Cole Smith, Fransisca Sudarg
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232 Fazil O. Sonmezcost of a config
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234 Fazil O. Sonmezhere f h is the
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236 Fazil O. SonmezThe optimal shap
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238 Alexander S. StrekalovskyDevelo
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PSfrag replacementsPruning a box fr
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Pruning a box from Baumann point in
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A Hybrid Multi-Agent Collaborative
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A Hybrid Multi-Agent Collaborative
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Improved lower bounds for optimizat
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258 Graham R. Wood, Duangdaw Sirisa
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264 Yinfeng Xu and Wenqiang Daiopti
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266 Yinfeng Xu and Wenqiang DaiThe
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Author IndexAddis, BernardettaDipar
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Author Index 271Nasuto, S.J.Departm
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