Aggregation in Location

Location problems occurring in urban or regional settings may involve many tens of thousands of “demand points,” usually individual residences. In modeling such problems it is common to aggregate demand points to obtain tractable models. We discuss aggregation approaches to a large class of location models, consider various aggregation error measures, and identify some effective measures. In particular, we focus on an upper bounding methodology for the error associated with aggregation. The chapter includes an example application.

[1]  Timothy J. Lowe,et al.  Aggregation error for location models: survey and analysis , 2009, Ann. Oper. Res..

[2]  A. Tamir,et al.  Exploiting self‐canceling demand point aggregation error for some planar rectilinear median location problems , 2003 .

[3]  Micha Sharir,et al.  Vertical Decomposition of Shallow Levels in 3-Dimensional Arrangements and Its Applications , 1999, SIAM J. Comput..

[4]  Stefan Nickel,et al.  Location Software and Interface with GIS and Supply Chain Management , 2001 .

[5]  C. Reeves.  Modern heuristic techniques for combinatorial problems , 1993 .

[6]  O. Kariv,et al.  An Algorithmic Approach to Network Location Problems. II: The p-Medians , 1979 .

[7]  Erhan Erkut,et al.  Analysis of aggregation errors for the p-median problem , 1999, Comput. Oper. Res..

[8]  R. L. Francis,et al.  Comparative error bound theory for three location models: continuous demand versus discrete demand , 2014 .

[9]  E. Hillsman,et al.  Errors in measuring distances from populations to service centers , 1978 .

[10]  John N. Hooker,et al.  Finite Dominating Sets for Network Location Problems , 1991, Oper. Res..

[11]  Justo Puerto,et al.  Location Theory - A Unified Approach , 2005 .

[12]  Yosef Sheffi,et al.  Urban Transportation Networks: Equilibrium Analysis With Mathematical Programming Methods , 1985 .

[13]  Igor Vasil'ev,et al.  An aggregation heuristic for large scale p-median problem , 2012, Comput. Oper. Res..

[14]  S. Salhi,et al.  AGGREGATION AND NON AGGREGATION TECHNIQUES FOR LARGE FACILITY LOCATION PROBLEMS - A SURVEY , 2015 .

[15]  Timothy J. Lowe,et al.  A framework for demand point and solution space aggregation analysis for location models , 2004, Eur. J. Oper. Res..

[16]  Kasturi R. Varadarajan.  A divide-and-conquer algorithm for min-cost perfect matching in the plane , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[17]  Alon Itai,et al.  Geometry Helps in Bottleneck Matching and Related Problems , 2001, Algorithmica.

[18]  Alan T. Murray,et al.  The Influence of Data Aggregation on the Stability of p-Median Location Model Solutions , 2010 .

[19]  A. Tamir,et al.  Aggregation Decomposition and Aggregation Guidelines for a Class of Minimax and Covering Location Models , 2004 .

[20]  Pitu B. Mirchandani,et al.  Location on networks : theory and algorithms , 1979 .

[21]  Frank Plastria,et al.  On the choice of aggregation points for continuousp-median problems: A case for the gravity centre , 2001 .

[22]  H. A. Eiselt,et al.  Foundations of Location Analysis , 2011 .

[23]  Chandra Ade Irawan,et al.  An adaptive multiphase approach for large unconditional and conditional p-median problems , 2014, Eur. J. Oper. Res..

[24]  A. Frieze,et al.  A simple heuristic for the p-centre problem , 1985 .

[25]  Mariel S. Lavieri,et al.  A Florida County Locates Disaster Recovery Centers , 2005, Interfaces.

[26]  Gerhard J. Woeginger,et al.  Uncapacitated single and multiple allocation p-hub center problems , 2009, Comput. Oper. Res..

[27]  Timothy J. Lowe,et al.  Aggregation Error Bounds for a Class of Location Models , 2000, Oper. Res..

[28]  Panos M. Pardalos,et al.  Handbook of applied optimization , 2002 .

[29]  S. L. Hakimi,et al.  Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph , 1964 .

[30]  Jorge Pinho de Sousa,et al.  Metaheuristics: Computer Decision-Making , 2010 .

[31]  Arthur M. Geoffrion,et al.  Objective function approximations in mathematical programming , 1977, Math. Program..

[32]  Mark S. Daskin,et al.  Network and Discrete Location: Models, Algorithms, and Applications, Second Edition , 2013 .

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

[34]  R. L. Francis,et al.  Demand point aggregation analysis for a class of constrained location models: a penalty function approach , 2004 .

[35]  M. Daskin,et al.  Aggregation effects in maximum covering models , 1990 .

[36]  Timothy J. Lowe,et al.  A Synthesis of Aggregation Methods for Multifacility Location Problems: Strategies for Containing Error , 1999 .

[37]  Chandra Ade Irawan,et al.  Solving large $$p$$p-median problems by a multistage hybrid approach using demand points aggregation and variable neighbourhood search , 2015, J. Glob. Optim..

[38]  Erhan Erkut,et al.  Analytical models for locating undesirable facilities , 1989 .

[39]  Paul D. Domich,et al.  Locating tax facilities: a graphics based microcomputer optimization model , 1991 .

[40]  Nimrod Megiddo,et al.  On the Complexity of Some Common Geometric Location Problems , 1984, SIAM J. Comput..

[41]  Timothy J. Lowe,et al.  On worst-case aggregation analysis for network location problems , 1993, Ann. Oper. Res..

[42]  Bhaba R. Sarker,et al.  Discrete location theory , 1991 .