A branch-and-cut method for the obnoxious p-median problem

The obnoxious p-median (OpM) problem is the repulsive counterpart of the ore known attractive p-median problem. Given a set I of cities and a set J of possible locations for obnoxious plants, a p-cardinality subset Q of J is sought, such that the sum of the distances between each city of I and the nearest obnoxious site in Q is maximised. We formulate (OpM) as a {0,1} linear programming problem and propose three families of valid inequalities whose separation problem is polynomial. We describe a branch-and-cut approach based on these inequalities and apply it to a set of instances found in the location literature. The computational results presented show the effectiveness of these inequalities for (OpM).

[1]  I. Moon,et al.  An Analysis of Network Location Problems with Distance Constraints , 1984 .

[2]  E. Erkut.  The discrete p-dispersion problem , 1990 .

[3]  Arie Tamir,et al.  Obnoxious Facility Location on Graphs , 1991, SIAM J. Discret. Math..

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

[5]  Abilio Lucena,et al.  Branch and cut algorithms , 1996 .

[6]  Manfred Körkel.  On the exact solution of large-scale simple plant location problems , 1989 .

[7]  Rex K. Kincaid,et al.  Technical Note - The Discrete Anti-P-Center Problem , 1994, Transp. Sci..

[8]  R. Garfinkel,et al.  Locating an Obnoxious Facility on a Network , 1978 .

[9]  Mauro Dell'Amico,et al.  Solution of the Cumulative Assignment Problem With a Well-Structured Tabu Search Method , 1999, J. Heuristics.

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

[11]  J. Kindle,et al.  An internal report , 2004 .

[12]  E. Erkut,et al.  Comparison Of Four Models For dispersing Facilities , 1991 .

[13]  Pierre Hansen,et al.  Dispersing Facilities on a Network , 1995 .

[14]  Edward Minieka,et al.  Anticenters and antimedians of a network , 1983, Networks.

[15]  Said Salhi,et al.  The obnoxious p facility network location problem with facility interaction , 1997 .

[16]  Francesco Maffioli,et al.  Discrete facility location and routing of obnoxious activities , 2003, Discret. Appl. Math..

[17]  Eduardo Conde,et al.  A fractional model for locating semi-desirable facilities on networks , 2002, Eur. J. Oper. Res..

[18]  Emanuel Melachrinoudis,et al.  The Maximin-Maxisum Network Location Problem , 2001, Comput. Optim. Appl..

[19]  John E. Beasley,et al.  OR-Library: Distributing Test Problems by Electronic Mail , 1990 .

[20]  Zvi Drezner,et al.  Facility location - applications and theory , 2001 .

[21]  Erhan Erkut,et al.  The discrete p-Maxian location problem , 1990, Comput. Oper. Res..

[22]  Rainer E. Burkard,et al.  Optimierung Und Kontrolle Projektbereich Diskrete Optimierung 2-medians in Networks with Pos/neg Weights , 1999 .

[23]  C. Revelle,et al.  A Lagrangean heuristic for the maximal covering location problem , 1996 .

[24]  D. Shier.  A Min-Max Theorem for p-Center Problems on a Tree , 1977 .

[25]  Rainer E. Burkard,et al.  2-Medians in trees with pos/neg weights , 2000, Discret. Appl. Math..

[26]  Zvi Drezner,et al.  An Efficient Genetic Algorithm for the p-Median Problem , 2003, Ann. Oper. Res..

[27]  Gilbert Laporte,et al.  OBJECTIVES IN LOCATION PROBLEMS. , 1995 .