An overview of representative problems in location research

We present a survey of over 50 representative problems in location research. Our goal is not to review all variants of different location models or to describe solution results, but rather to provide a broad overview of major location problems that have been studied, indicating briefly how they are formulated and how they relate to one another. We review standard problems such as median, center, and warehouse location problems, as well as less traditional location problems which have emerged in recent years. Our primary focus is on problems for which operations research-type models have been developed. Most of the problems we review have been formulated as optimization problems.

[1]  H. Hotelling Stability in Competition , 1929 .

[2]  A. Smithies Optimum Location in Spatial Competition , 1941, Journal of Political Economy.

[3]  William Grant Ireson Factory planning and plant layout , 1952 .

[4]  A. Lösch The economics of location , 1954 .

[5]  David Valinsky Symposium on Applications of Operations Research to Urban Services—A Determination of the Optimum Location of Fire-Fighting Units in New York City , 1955 .

[6]  Walter Isard,et al.  Location and Space-Economy , 1956 .

[7]  Richard Muther,et al.  Practical Plant Layout , 1956 .

[8]  Edwin Mansfield,et al.  A Model for the Location of a Railroad Classification Yard , 1958 .

[9]  Leon N. Moses,et al.  Location and the Theory of Production , 1958 .

[10]  W. Miehle Link-Length Minimization in Networks , 1958 .

[11]  Benjamin H. Steven,et al.  An application of game theory to a problem in location strategy , 1961 .

[12]  P. Gilmore Optimal and Suboptimal Algorithms for the Quadratic Assignment Problem , 1962 .

[13]  J. E. Sussams,et al.  Evaluation of Transport Costs for Alternative Factory Sites — A Case Study , 1962 .

[14]  E. Lawler The Quadratic Assignment Problem , 1963 .

[15]  Alfred A. Kuehn,et al.  A Heuristic Program for Locating Warehouses , 1963 .

[16]  Elwood S. Buffa,et al.  A Heuristic Algorithm and Simulation Approach to Relative Location of Facilities , 1963 .

[17]  L. Cooper Location-Allocation Problems , 1963 .

[18]  Henry A. Young On the Optimum Location of Checking Stations , 1963 .

[19]  Leon Cooper,et al.  Heuristic Methods for Location-Allocation Problems , 1964 .

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

[21]  A. Manne Plant Location Under Economies-of-Scale---Decentralization and Computation , 1964 .

[22]  F. E. Maranzana,et al.  On the Location of Supply Points to Minimize Transport Costs , 1964 .

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

[24]  J. W. Gavett,et al.  The Optimal Assignment of Facilities to Locations by Branch and Bound , 1966, Oper. Res..

[25]  H. Frank,et al.  Optimum Locations on a Graph with Probabilistic Demands , 1966, Oper. Res..

[26]  T. L. Ray,et al.  A Branch-Bound Algorithm for Plant Location , 1966, Oper. Res..

[27]  F. Hillier,et al.  Quadratic Assignment Problem Algorithms and the Location of Indivisible Facilities , 1966 .

[28]  T. L. Ray,et al.  Warehouse Location Under Continuous Economies of Scale , 1966 .

[29]  Roger C. Vergin,et al.  An Algorithm and Computational Procedure for Locating Economic Facilities , 1967 .

[30]  Leon Cooper,et al.  SOLUTIONS OF GENERALIZED LOCATIONAL EQUILIBRIUM MODELS , 1967 .

[31]  Kurt Ernst Weil Plant layout and design , 1967 .

[32]  Richard L. Francis,et al.  Letter to the Editor - Some Aspects of a Minimax Location Problem , 1967, Oper. Res..

[33]  Polly Bart,et al.  Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph , 1968, Oper. Res..

[34]  E. S. Savas,et al.  Simulation and Cost-Effectiveness Analysis of New York's Emergency Ambulance Service , 1969 .

[35]  Graciano Sá,et al.  Branch-and-Bound and Approximate Solutions to the Capacitated Plant-Location Problem , 1969, Oper. Res..

[36]  Kurt Spielberg,et al.  Algorithms for the Simple Plant-Location Problem with Some Side Conditions , 1969, Oper. Res..

[37]  Guy L. Curry,et al.  A Dynamic Programming Algorithm for Facility Location and Allocation , 1969 .

[38]  E. Minieka The m-Center Problem , 1970 .

[39]  D. H. Marks,et al.  An Analysis of Private and Public Sector Location Models , 1970 .

[40]  G. O. Wesolowsky,et al.  Location of facilities with rectangular distances among point and area destinations , 1971 .

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

[42]  A. J. Goldman Optimal Center Location in Simple Networks , 1971 .

[43]  Nicos Christofides,et al.  Distribution management : mathematical modelling and practical analysis , 1971 .

[44]  Robert S. Garfinkel,et al.  Technical Note - An Improved Algorithm for the Bottleneck Assignment Problem , 1971, Oper. Res..

[45]  S. L. Hakimi,et al.  Optimum Locations of Centers in Networks , 1972, Oper. Res..

[46]  G. O. Wesolowsky,et al.  A Nonlinear Approximation Method for Solving a Generalized Rectangular Distance Weber Problem , 1972 .

[47]  Leon Cooper,et al.  The Transportation-Location Problem , 1972, Oper. Res..

[48]  Richard M. Soland,et al.  Exact and approximate solutions to the multisource weber problem , 1972, Math. Program..

[49]  G. O. Wesolowsky Rectangular Distance Location under the Minimax Optimality Criterion , 1972 .

[50]  Richard L. Francis,et al.  A Generalized Assignment Approach to Optimal Facility Layout , 1972 .

[51]  R. L. Francis,et al.  Properties of a multifacility location problem involving euclidian distances , 1972 .

[52]  Richard C. Larson,et al.  On Insensitivities in Urban Redistricting and Facility Location , 1972, Oper. Res..

[53]  D. Hearn,et al.  The Minimum Covering Sphere Problem , 1972 .

[54]  D. Hearn,et al.  Geometrical Solutions for Some Minimax Location Problems , 1972 .

[55]  Richard E. Wendell,et al.  LOCATION AND PRODUCTION—A SPECIAL CASE , 1972 .

[56]  B. M. Khumawala An Efficient Branch and Bound Algorithm for the Warehouse Location Problem , 1972 .

[57]  The p-median problem , 1973 .

[58]  Abraham Warszawski,et al.  Multi-Dimensional Location Problems , 1973 .

[59]  James A. Fitzsimmons,et al.  A Methodology for Emergency Ambulance Deployment , 1973 .

[60]  A. M. El-Shaieb,et al.  A New Algorithm for Locating Sources Among Destinations , 1973 .

[61]  Richard L. Francis A Minimax Facility-Configuration Problem Involving Lattice Points , 1973, Oper. Res..

[62]  Richard E. Wendell,et al.  Location Theory, Dominance, and Convexity , 1973, Oper. Res..

[63]  Ilan Vertinsky,et al.  Ambulance Location: A Probabilistic Enumeration Approach , 1973 .

[64]  Warren Walker,et al.  Using the Set-Covering Problem to Assign Fire Companies to Fire Houses , 1974, Oper. Res..

[65]  M. Rao,et al.  An Algorithm for the M-Median Plant Location Problem , 1974 .

[66]  A. M. Geoffrion,et al.  Multicommodity Distribution System Design by Benders Decomposition , 1974 .

[67]  Richard M. Soland,et al.  Optimal Facility Location with Concave Costs , 1974, Oper. Res..

[68]  RICHARD C. LARSON,et al.  A hypercube queuing model for facility location and redistricting in urban emergency services , 1974, Comput. Oper. Res..

[69]  S. Halfin Letter to the Editor—On Finding the Absolute and Vertex Centers of a Tree with Distances , 1974 .

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

[71]  L. Cooper,et al.  An Always-Convergent Numerical Scheme for a Random Locational Equilibrium Problem , 1974 .

[72]  R. Love,et al.  A computation procedure for the exact solution of location-allocation problems with rectangular distances , 1975 .

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

[74]  James G. Morris A linear programming solution to the generalized rectangular distance weber problem , 1975 .

[75]  James P. Jarvis,et al.  Optimization in stochastic service systems with distinguishable servers , 1975 .

[76]  Timothy J. Lowe,et al.  Convex Location Problems on Tree Networks , 1976, Oper. Res..

[77]  Darwin Klingman,et al.  A Cotton Ginning Problem , 1976, Oper. Res..

[78]  Jonathan Halpern,et al.  THE LOCATION OF A CENTER-MEDIAN CONVEX COMBINATION ON AN UNDIRECTED TREE* , 1976 .

[79]  Robert F. Love,et al.  Note---One-Dimensional Facility Location-Allocation using Dynamic Programming , 1976 .

[80]  James V. Jucker,et al.  The Simple Plant-Location Problem under Uncertainty , 1976, Oper. Res..

[81]  J A White,et al.  TRAVELING SALESMAN LOCATION PROBLEM , 1976 .

[82]  D. Hearn,et al.  Minimax Multifacility Location with Euclidean Distances , 1976 .

[83]  C. M. Shetty,et al.  The rectilinear distance location-allocation problem , 1977 .

[84]  Donald R. Plane,et al.  Mathematical Programming and the Location of Fire Companies for the Denver Fire Department , 1977, Oper. Res..

[85]  Vedia Dokmeci A Quantitative Model to Plan Regional Health Facility Systems , 1977 .

[86]  G. Ross,et al.  Modeling Facility Location Problems as Generalized Assignment Problems , 1977 .

[87]  Edward Minieka,et al.  The Centers and Medians of a Graph , 1977, Oper. Res..

[88]  B. M. Khumawala,et al.  An Efficient Branch and Bound Algorithm for the Capacitated Warehouse Location Problem , 1977 .

[89]  D. Erlenkotter Facility Location with Price-Sensitive Demands: Private, Public, and Quasi-Public , 1977 .

[90]  M. Rao,et al.  The m-Center Problem: Minimax Facility Location , 1977 .

[91]  H. D. Ratliff,et al.  A Cut Approach to the Rectilinear Distance Facility Location Problem , 1978, Oper. Res..

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

[93]  Donald Erlenkotter,et al.  A Dual-Based Procedure for Uncapacitated Facility Location , 1978, Oper. Res..

[94]  T. Lowe Efficient Solutions in Multiobjective Tree Network Location Problems , 1978 .

[95]  Bruce L. Golden,et al.  Point estimation of a global optimum for large combinatorial problems , 1978 .

[96]  G. O. Wesolowsky,et al.  A New Method for the Multifacility Minimax Location Problem , 1978, The Journal of the Operational Research Society.

[97]  Zvi Drezner,et al.  A Trajectory Method for the Optimization of the Multi-Facility Location Problem With lp Distances , 1978 .

[98]  J. Halpern Finding Minimal Center-Median Convex Combination Cent-Dian of a Graph , 1978 .

[99]  Gabriel Y. Handler,et al.  Finding Two-Centers of a Tree: The Continuous Case , 1978 .

[100]  L. McGinnis,et al.  A Single Facility Rectilinear Location Problem with Multiple Criteria , 1978 .

[101]  A. Odoni,et al.  Locations of Medians on Stochastic Networks , 1979 .

[102]  George L. Nemhauser,et al.  Note--On "Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms" , 1979 .

[103]  George L. Nemhauser,et al.  Easy and hard bottleneck location problems , 1979, Discret. Appl. Math..

[104]  Lazaros P. Mavrides An Indirect Method for the Generalized k-Median Problem Applied to Lock-Box Location , 1979 .

[105]  Monique Guignard-Spielberg,et al.  A direct dual method for the mixed plant location problem with some side constraints , 1979, Math. Program..

[106]  J. Krarup,et al.  Selected Families of Location Problems , 1979 .

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

[108]  Lee J. White,et al.  A Maxmin Location Problem , 1980, Oper. Res..

[109]  Laurence A. Wolsey,et al.  Worst-Case and Probabilistic Analysis of Algorithms for a Location Problem , 1980, Oper. Res..

[110]  Robert P. Cerveny An Application of Warehouse Location Techniques to Bloodmobile Operations , 1980 .

[111]  Jonathan Halpern Duality in the Cent-Dian of a Graph , 1980, Oper. Res..

[112]  Richard M. Soland,et al.  A multicriteria approach to the location of public facilities , 1980 .

[113]  Henrik Juel BOUNDS IN THE LOCATION‐ALLOCATION PROBLEM , 1981 .

[114]  Basheer M. Khumawala,et al.  An Improved Algorithm for the Multi-commodity Location Problem , 1981 .

[115]  T. B. Boffey,et al.  The Multi-Commodity Facilities Location Problem , 1981 .

[116]  Zvi Drezner,et al.  Optimum Location Probabilities in the lp Distance Weber Problem , 1981 .

[117]  R. Chandrasekaran,et al.  Location on Tree Networks: P-Centre and n-Dispersion Problems , 1981, Math. Oper. Res..

[118]  John Baxter,et al.  Local Optima Avoidance in Depot Location , 1981 .

[119]  Jacques-François Thisse,et al.  Outcomes of voting and planning: Condorcet, Weber and Rawls locations , 1981 .

[120]  G. Laporte,et al.  An exact algorithm for minimizing routing and operating costs in depot location , 1981 .

[121]  S. M. Hedetniemi,et al.  Linear Algorithms for Finding the Jordan Center and Path Center of a Tree , 1981 .

[122]  Mark S. Daskin,et al.  A Hierarchical Objective Set Covering Model for Emergency Medical Service Vehicle Deployment , 1981 .

[123]  A. Bachem,et al.  A product positioning model with costs and prices , 1981 .

[124]  R. E. Wendell,et al.  New perspectives in competitive location theory , 1981 .

[125]  Ludo Gelders,et al.  A large scale location-allocation problem in the natural rubber industry , 1981 .

[126]  Tony J. Van Roy,et al.  A Dual-Based Procedure for Dynamic Facility Location , 1982 .

[127]  R. L. Francis,et al.  A Biobjective Multifacility Minimax Location Problem on a Tree Network , 1982 .

[128]  Charles ReVelle,et al.  The Hierarchical Service Location Problem , 1982 .

[129]  R. Love,et al.  Properties and Solution Methods for Large Location—Allocation Problems , 1982 .

[130]  Dorit S. Hochbaum,et al.  Heuristics for the fixed cost median problem , 1982, Math. Program..

[131]  Z. Drezner Competitive location strategies for two facilities , 1982 .

[132]  Oded Berman,et al.  Locating mobile servers on a network with markovian properties , 1982, Networks.

[133]  Arthur M. Farley Vertex Centers of Trees , 1982 .

[134]  Timothy J. Lowe,et al.  Duality and Distance Constraints for the Nonlinear p-Center Problem and Covering Problem on a Tree Network , 1982, Oper. Res..

[135]  Yves Smeers,et al.  On the optimal location of wastewater treatment plants , 1983 .

[136]  S. Hakimi On locating new facilities in a competitive environment , 1983 .

[137]  N. Megiddo,et al.  The Maximum Coverage Location Problem , 1983 .

[138]  R. L. Francis,et al.  State of the Art-Location on Networks: A Survey. Part II: Exploiting Tree Network Structure , 1983 .

[139]  R. Church,et al.  Computational Procedures for Location Problems on Stochastic Networks , 1983 .

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

[141]  J. Krarup,et al.  The simple plant location problem: Survey and synthesis , 1983 .

[142]  Douglas R. Shier,et al.  Optimal Locations for a Class of Nonlinear, Single-Facility Location Problems on a Network , 1983, Oper. Res..

[143]  A. Kolen Solving covering problems and the uncapacitated plant location problem on trees , 1983 .

[144]  G. Laporte,et al.  Hamiltonian location problems , 1983 .

[145]  James A. Fitzsimmons,et al.  A Warehouse Location Model Helps Texas Comptroller Select Out-of-State Audit Offices , 1983 .

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

[147]  Bernard Jurion,et al.  A Theory of Public Services with Distance-Sensitive Utility , 1983 .

[148]  Nimrod Megiddo,et al.  The Weighted Euclidean 1-Center Problem , 1983, Math. Oper. Res..

[149]  Reuven Chen Solution of minisum and minimax location–allocation problems with Euclidean distances , 1983 .

[150]  Dan Horsky,et al.  An Approach to the Optimal Positioning of a New Product , 1983 .

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

[152]  Hanif D. Sherali,et al.  A Decomposition Algorithm for a Discrete Location-Allocation Problem , 1984, Oper. Res..

[153]  Joseph S. Martinich,et al.  Network production-location problems under price uncertainty , 1984 .

[154]  O. Berman,et al.  Location-Relocation of Mobile Facilities on a Stochastic Network , 1984, Transp. Sci..

[155]  James E. Ward,et al.  A Partial Covering Approach to Siting Response Resources for Major Maritime Oil Spills , 1984 .

[156]  James E. Hodder Technical Note - Financial Market Approaches to Facility Location under Uncertainty , 1984, Oper. Res..

[157]  James E. Ward,et al.  Some Properties of Location Problems with Block and Round Norms , 1984, Oper. Res..

[158]  A methodological note on location-allocation models. , 1984, American journal of public health.

[159]  Martine Labbé,et al.  Outcomes of voting and planning in single facility location problems , 1985 .

[160]  R. T. Wong,et al.  `Multidimensional' extensions and a nested dual approach for the m-median problem , 1985 .

[161]  W. Domschke,et al.  Location and layout planning , 1997 .

[162]  Gabriel Y. Handler,et al.  Medi-Centers of a Tree , 1985, Transp. Sci..

[163]  Oded Berman,et al.  Optimal 2-Facility Network Districting in the Presence of Queuing , 1985, Transp. Sci..

[164]  Gabriel Y. Handler,et al.  The continuous m-center problem on a network , 1985, Networks.

[165]  Oded Berman,et al.  Locating a Mobile Server Queueing Facility on a Tree Network , 1985 .

[166]  Richard C. Larson,et al.  Locating an n-server facility in a stochastic environment , 1985, Comput. Oper. Res..

[167]  G. O. Wesolowsky,et al.  One‐facility location with rectilinear tour distances , 1985 .

[168]  David J. Eaton,et al.  Determining Emergency Medical Service Vehicle Deployment in Austin, Texas , 1985 .

[169]  Zvi Drezner,et al.  Location of Multiple Obnoxious Facilities , 1985, Transp. Sci..

[170]  Robert F. Love,et al.  The facility location problem for hyper-rectilinear distances , 1985 .

[171]  Oded Berman,et al.  Optimal Server Location on a Network Operating as an M/G/1 Queue , 1985, Oper. Res..

[172]  Timothy J. Lowe,et al.  Block-vertex duality and the one-median problem , 1985, Networks.

[173]  Francesco Mason,et al.  Properties of the k-centra in a tree network , 1985, Networks.

[174]  C. H. Aikens,et al.  Facility location models for distribution planning , 1985 .

[175]  R. Laundy A tree search algorithm for the multi-commodity location problem , 1985 .

[176]  S. Ratick,et al.  Evaluating dredging and offshore loading locations for U.S. coal exports using the local logistics system , 1986 .

[177]  W. L. Price,et al.  Locating a Blood Bank , 1986 .

[178]  Morton E. O'Kelly,et al.  The Location of Interacting Hub Facilities , 1986, Transp. Sci..

[179]  L. Mattsson Residential location and school planning in a tightening urban economy , 1986 .

[180]  David Simchi-Levi,et al.  Minisum location of a traveling salesman , 1986, Networks.

[181]  John Hooker Solving Nonlinear Single-Facility Network Location Problems , 1986, Oper. Res..

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

[183]  Margaret L. Brandeau,et al.  Locating the two-median of a tree network with continuous link demands , 1986 .

[184]  Samuel S. Chiu Optimal M/G/1 server location on a tree network with continuous link demands , 1986, Comput. Oper. Res..

[185]  Harilaos N. Psaraftis,et al.  Optimal Response to Oil Spills: The Strategic Decision Case , 1986, Oper. Res..

[186]  Anton C.M. Hopmans,et al.  A spatial interaction model for branch bank accounts , 1986 .

[187]  S. C. Wirasinghe,et al.  Location of bus garages , 1986 .

[188]  Hanif D. Sherali,et al.  Network location problems with continuous link demands: p-medians on a chain and 2-medians on a tree , 1986 .

[189]  T. Friesz,et al.  Spatial competition facility location models: Definition, formulation and solution approach , 1986 .

[190]  Samuel S. Chiu,et al.  The minisum location problem on an undirected network with continuous link demands , 1987, Comput. Oper. Res..

[191]  Uday S. Karmarkar,et al.  Competitive Location on a Network , 1987, Oper. Res..

[192]  G. Y. Handler,et al.  Relaxation method for the solution of the minimax location-allocation problem in Euclidean space , 1987 .

[193]  David Simchi-Levi,et al.  Minisum location of a travelling salesman on simple networks , 1988 .

[194]  Amedeo R. Odoni,et al.  A single-server priority queueing-location model , 1988, Networks.

[195]  Margaret L. Brandeau,et al.  Parametric Facility Location on a Tree Network with an Lp-Norm Cost Function , 1988, Transp. Sci..

[196]  Rajan Batta,et al.  Single Server Queueing-Location Models with Rejection , 1988, Transp. Sci..

[197]  New product pricing and positioning in an oligopolistic market , 1988 .

[198]  Rajan Batta,et al.  Locating Facilities on the Manhattan Metric with Arbitrarily Shaped Barriers and Convex Forbidden Regions , 1989, Transp. Sci..