Covering models with time-dependent demand

In this paper a covering model for locating facilities with time-dependent demand is introduced. Not only the facility locations, but also the instants at which such facilities become operative, are considered as decision variables in order to determine the maximal-profit decision. Expressed as a mixed nonlinear integer program, structural properties are derived for particular demand patterns, and a metaheuristic procedure is proposed as optimization tool.

[1]  G. O. Wesolowsky,et al.  Facility location when demand is time dependent , 1991 .

[2]  Terry L. Friesz,et al.  COMPETITIVE NETWORK FACIUTY LOCATION MODELS: A SURVEY , 2005 .

[3]  Vladimir Marianov,et al.  Location Problems in the Public Sector , 2002 .

[4]  Tammy Drezner,et al.  Locating a single new facility among existing unequally attractive facilities , 1994 .

[5]  George O. Wesolowsky,et al.  Dynamic Facility Location , 1973 .

[6]  Mark S. Daskin,et al.  Network and Discrete Location: Models, Algorithms and Applications , 1995 .

[7]  E. Carrizosa,et al.  LOCATION AND DESIGN OF A COMPETITIVE FACILITY FOR PROFIT MAXIMISATION , 2003 .

[8]  Lee G. Cooper,et al.  Parameter Estimation for a Multiplicative Competitive Interaction Model—Least Squares Approach , 1974 .

[9]  Richard L. Church,et al.  The maximal covering location problem , 1974 .

[10]  Gilbert Laporte,et al.  Sequential location problems , 1997 .

[11]  Jesús T. Pastor,et al.  Two new heuristics for the location set covering problem , 1994 .

[12]  Frank Plastria,et al.  Static competitive facility location: An overview of optimisation approaches , 2001, Eur. J. Oper. Res..

[13]  Ram C. Rao,et al.  Preempting an Alert Rival: Strategic Timing of the First Plant by Analysis of Sophisticated Rivalry , 1979 .

[14]  Zvi Drezner.  Dynamic facility location: The progressive p-median problem , 1995 .

[15]  John R. Current,et al.  Dynamic facility location when the total number of facilities is uncertain: A decision analysis approach , 1998, Eur. J. Oper. Res..

[16]  Alan S. Manne,et al.  Sufficient Conditions for Optimality in an Infinite Horizon Development Plan , 1970 .

[17]  Gilbert Laporte,et al.  Competitive spatial models , 1989 .

[18]  T. Drezner.  Optimal continuous location of a retail facility, facility attractiveness, and market share: An interactive model , 1994 .

[19]  David L. Huff,et al.  Defining and Estimating a Trading Area , 1964 .

[20]  François V. Louveaux,et al.  Discrete stochastic location models , 1986 .

[21]  Donald Erlenkotter,et al.  A comparative study of approaches to dynamic location problems , 1981 .

[22]  Reza Barkhi,et al.  A REVIEW OF COVERING PROBLEMS IN FACILITY LOCATION. , 1993 .

[23]  C. Craig,et al.  Formulating Retail Location Strategy in a Changing Environment , 1983 .

[24]  Said Salhi,et al.  Facility Location: A Survey of Applications and Methods , 1996 .

[25]  M. J. Hodgson.  A location—allocation model maximizing consumers' welfare , 1981 .

[26]  G. O. Wesolowsky,et al.  The Multiperiod Location-Allocation Problem with Relocation of Facilities , 1975 .

[27]  Tammy Drezner,et al.  Competitive Facility Location in the Plane , 1995 .

[28]  Vladimir Marianov,et al.  The maximum-capture hierarchical location problem , 1992 .

[29]  R. Suárez-Vega,et al.  Discretization and resolution of the (r|Xp)-medianoid problem involving quality criteria , 2004 .

[30]  Gamini Gunawardane,et al.  Dynamic versions of set covering type public facility location problems , 1982 .

[31]  Robert G. Cromley,et al.  Integrating the maximum capture problem into a GIS framework , 2007, J. Geogr. Syst..

[32]  Martine Labbé,et al.  Locations on time‐varying networks , 1999 .

[33]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[34]  Terry L. Friesz,et al.  Reaction Function Based Dynamic Location Modeling in Stackelberg–Nash–Cournot Competition , 2007 .

[35]  Atsuyuki Okabe,et al.  Sequential location—allocation of public facilities in one- and two-dimensional space: Comparison of several policies , 1991, Math. Program..