Two New Location Covering Problems: The Partial P‐Center Problem and the Partial Set Covering Problem

Two new covering problems are introduced. The partial covering P-center problem minimizes a coverage distance in such a way that a given fraction of the population is covered. The partial set covering problem seeks the minimum number of facilities needed to cover an exogenously specified fraction of the population within a given coverage distance. The problems are formulated as integer linear programming problems. Bisection search algorithms are outlined for the two problems. The search algorithm repeatedly solves a Lagrangian relaxation of the maximal covering problem. Computational results for the Lagrangian relaxation of the maximal covering problem and for the bisection search algorithms are presented on problems with up to 150 nodes.

[1]  M. Daskin,et al.  Integration of Multiple, Excess, Backup, and Expected Covering Models , 1988 .

[2]  Charles S. ReVelle,et al.  The Location of Emergency Service Facilities , 1971, Oper. Res..

[3]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

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

[5]  Mark S. Daskin,et al.  APPLICATION OF AN EXPECTED COVERING MODEL TO EMERGENCY MEDICAL SERVICE SYSTEM DESIGN , 1982 .

[6]  Vladimir Marianov,et al.  A probabilistic fire-protection siting model with joint vehicle reliability requirements , 1992 .

[7]  Mark S. Daskin,et al.  A Maximum Expected Covering Location Model: Formulation, Properties and Heuristic Solution , 1983 .

[8]  Charles S. ReVelle,et al.  The Maximum Availability Location Problem , 1989, Transp. Sci..

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

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

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

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

[13]  Kathleen Hogan,et al.  The maximum reliability location problem and α-reliablep-center problem: Derivatives of the probabilistic location set covering problem , 1990 .

[14]  M. Brandeau,et al.  An overview of representative problems in location research , 1989 .

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

[16]  David A. Schilling,et al.  DYNAMIC LOCATION MODELING FOR PUBLIC‐SECTOR FACILITIES: A MULTICRITERIA APPROACH , 1980 .

[17]  Marshall L. Fisher,et al.  An Applications Oriented Guide to Lagrangian Relaxation , 1985 .

[18]  S. Hakimi.  Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems , 1965 .