• Richard L. Church
  • Alan Murray
Part of the Advances in Spatial Science book series (ADVSPATIAL)


The anti-covering location problem (ACLP) is a well-recognized coverage-based dispersion model. Admittedly, reaching this conclusion requires a little work, but in fact this problem is related to the node packing, vertex packing, stable/independent set and r-separation problems, with considerable attention being devoted to each of these related problems (see Padberg 1973; Erkut 1990; Nemhauser and Sigismondi 1992; Murray 1995; Erkut et al. 1996; Murray and Kim 2008; Niblett 2014; Niblett and Church 2015). The name anti-cover can be attributed to Moon and Chaudhry (1984) who attempted to distinguish it from other well-known coverage problems. The name, therefore, reflects a sort of opposing goal compared to the set covering problem. The anti-covering location problem seeks to maximize the total weighted benefit of facilities sited in a region, doing so in a manner that ensures at least a minimum pre-specified distance or travel time between facilities and demand is maintained. If the benefit is the same for each potential facility location, then this is equivalent to maximizing the number of facilities that can be sited while maintaining minimum separation restrictions between all facilities and demand or between a sited facility and all other sited facilities. Of course, the goal of the location set covering problem detailed in Chap.  2 is to minimize the number of facilities needed for complete coverage of all demand, assuming the costs for selecting facilities is the same for every potential site. In this sense, then, the two problems have contrasting intents.


  1. Berge C (1957) Two theorems in graph theory. Proc Natl Acad Sci 43(9):842–844CrossRefGoogle Scholar
  2. Berman O, Huang R (2008) The minimum weighted covering location problem with distance constraints. Comput Oper Res 35:356–372CrossRefGoogle Scholar
  3. Bron C, Kerbosch J (1973) Algorithm 457: finding all cliques of an undirected graph. Commun ACM 16:575–577CrossRefGoogle Scholar
  4. Cazals F, Karande C (2008) A note on the problem of reporting maximal cliques. Theor Comput Sci 407:564–568CrossRefGoogle Scholar
  5. Chaudhry SS (2006) A genetic algorithm approach to solving the anti-covering location problem. Expert Syst 23:251–257CrossRefGoogle Scholar
  6. Chaudhry SS, McCormick ST, Moon ID (1986) Locating independent facilities with maximum weight: greedy heuristics. Omega 14(5):383–389CrossRefGoogle Scholar
  7. Church RL, Cohon JL (1976). Multiobjective location analysis of regional energy facility siting problems. Brookhaven National Lab, United States Energy Research and Development Administration. Upton, NY (USA): US GovernmentGoogle Scholar
  8. Church RL, Murray AT (2009) Business site selection, location analysis and GIS. Wiley, New YorkGoogle Scholar
  9. Cohon J (1978) Multi-objective programming and planning. Academic Press, New YorkGoogle Scholar
  10. Cravo GL, Ribeiro GM, Nogueira Lorena LA (2008) A greedy randomized adaptive search procedure for the point-feature cartographic label placement. Comput Geosci 34:373–386CrossRefGoogle Scholar
  11. Downs JA, Gates RJ, Murray AT (2008) Estimating carrying capacity for sandhill cranes using habitat suitability and spatial optimization models. Ecol Model 214:284–292CrossRefGoogle Scholar
  12. Edmonds J (1962) Covers and packings in a family of sets. Bull Am Math Soc 68(5):494–499CrossRefGoogle Scholar
  13. Erkut E (1990) The discrete p-dispersion problem. Eur J Oper Res 40:48–60CrossRefGoogle Scholar
  14. Erkut E, ReVelle C, Ulkiisal Y (1996) Integer-friendly formulations for the r-separation problem. Eur J Oper Res 92:342–351CrossRefGoogle Scholar
  15. Francis RL, Lowe TJ, Ratliff HD (1978) Distance constraints for tree network multifacility location problems. Oper Res 26:570–596CrossRefGoogle Scholar
  16. Gamarnik D, Goldberg DA (2010) Randomized greedy algorithms for independent sets and matchings in regular graphs: exact results and finite girth corrections. Comb Prob Comput 19:61–85CrossRefGoogle Scholar
  17. Giandomenico M, Rossi F, Smriglio S (2013) Strong lift-and-project cutting planes for the stable set problem. Math Program 141(1–2):165–192CrossRefGoogle Scholar
  18. Goycoolea M, Murray AT, Barahona F, Epstein R, Weintraub A (2005) Harvest scheduling subject to maximum area restrictions: exploring exact approaches. Oper Res 53:490–500CrossRefGoogle Scholar
  19. Grubesic TH, Murray AT (2008) Sex offender residency and spatial equity. Appl Spat Anal Policy 1:175–192CrossRefGoogle Scholar
  20. Hochbaum DS, Pathria A (1997) Forest harvesting and minimum cuts: a new approach to handling spatial constraints. For Sci 43(4):544–554Google Scholar
  21. Jones JG, Meneghin BJ, Kirby MW (1991) Formulating adjacency constraints in linear optimization models for scheduling projects in tactical planning. For Sci 37:1283–1297Google Scholar
  22. Kirby M, Hager W, Wong P (1986) Simultaneous planning of wildland management and transportation alternatives. TIMS Stud Manag Sci 21:371–387Google Scholar
  23. Mauri GR, Ribeiro GM, Lorena LA (2010) A new mathematical model and a Lagrangean decomposition for the point-feature cartographic label placement problem. Comput Oper Res 37(12):2164–2172CrossRefGoogle Scholar
  24. Mealey SP, Lipscomb JF, Johnson KN (1982) Solving the habitat dispersion problem in forest planning. Trans N Am Wildl Natur Resour Conf 47:142–153Google Scholar
  25. Moon AD, Chaudhry S (1984) An analysis of network location problems with distance constraints. Manag Sci 30:290–307CrossRefGoogle Scholar
  26. Murray AT (1995) Modeling adjacency conditions in spatial optimization problems. PhD dissertation, UCSB, Santa Barbara, CAGoogle Scholar
  27. Murray AT (2007) Spatial environmental concerns. In: Weintraub A, Romero C, Bjorndal T, Epstein R (eds) Handbook of operations research in natural resources. Springer, New York, pp 419–429CrossRefGoogle Scholar
  28. Murray AT, Church RL (1995a) Heuristic solution approaches to operational forest planning problems. OR Spektrum 17:193–203CrossRefGoogle Scholar
  29. Murray AT, Church RL (1995b) Measuring the efficacy of adjacency constraint structure in forest planning. Can J For Res 25:1416–1424CrossRefGoogle Scholar
  30. Murray AT, Church RL (1996) Constructing and selecting adjacency constraints. INFOR 34:232–248Google Scholar
  31. Murray AT, Church RL (1997) Facets for node packing. Eur J Oper Res 101:598–608CrossRefGoogle Scholar
  32. Murray AT, Church RL (1999) Using proximity restriction for locating undesirable facilities. Stud Locat Anal 12:81–99Google Scholar
  33. Murray AT, Kim H (2008) Efficient identification of geographic restriction conditions in anti-covering location models using GIS. Lett Spat Resour Sci 1:159–169CrossRefGoogle Scholar
  34. Murray AT, Wei R, Grubesic TH (2014) An approach for examining alternatives attributable to locational uncertainty. Environ Plan B Plan Des 41(1):93–109CrossRefGoogle Scholar
  35. Nelson JN, Brodie JB (1990) Comparison of a random search algorithm and mixed integer programming for solving area-based forest plans. Can J For Res 20:934–942CrossRefGoogle Scholar
  36. Nemhauser G, Sigismondi G (1992) A strong cutting plane/branch-and-bound algorithm for node packing. Oper Res 43:443–457CrossRefGoogle Scholar
  37. Nemhauser GL, Trotter LE (1975) Vertex packings: structural properties and algorithms. Math Program 8:232–248CrossRefGoogle Scholar
  38. Nemhauser GL, Wolsey LA (1988) Integer and combinatorial optimization. Wiley, New YorkCrossRefGoogle Scholar
  39. Niblett MR (2014) The anti-covering location problem: new modeling perspectives and solution approaches. PhD dissertation, UCSB, Santa Barbara, CAGoogle Scholar
  40. Niblett MR, Church RL (2015) The disruptive anti-covering location problem. Eur J Oper Res 247(3):764–773CrossRefGoogle Scholar
  41. Padberg MW (1973) On the facial structure of set packing polyhedral. Math Program 5:199–215CrossRefGoogle Scholar
  42. Ratick S, Meacham B, Aoyama Y (2008) Locating backup facilities to enhance supply chain disaster resilience. Growth Chang 39:642–666CrossRefGoogle Scholar
  43. Ribeiro GM, Lorena LAN (2008) Lagrangean relaxation with clusters for point-feature cartographic label placement problems. Comput Oper Res 35(7):2129–2140CrossRefGoogle Scholar
  44. Thompson EF, Halterman BG, Lyon TJ, Miller RL (1973) Integrating timber and wildlife management planning. For Chron 49(6):247–250CrossRefGoogle Scholar
  45. Tomita E, Tanaka A, Takahashi H (2006) The worst-case time complexity for generating all maximal cliques and computational experiments. Theor Comput Sci 363:28–42CrossRefGoogle Scholar
  46. Torres-Rojo JM, Brodie JD (1990) Adjacency constraints in harvest scheduling: an aggregation heuristic. Can J For Res 20:978–986CrossRefGoogle Scholar
  47. Vielma JP, Murray AT, Ryan DM, Weintraub A (2007) Improving computational capabilities for addressing volume constraints in forest harvest scheduling problems. Eur J Oper Res 176:1246–1264CrossRefGoogle Scholar
  48. Warrier D, Wilhelm WE, Warren JS, Hicks IV (2005) A branch-and-price approach for the maximum weight independent set problem. Networks 46(4):198–209CrossRefGoogle Scholar
  49. Wei R, Murray AT (2012) An integrated approach for addressing geographic uncertainty in spatial optimization. Int J Geogr Inf Sci 26:1231–1249CrossRefGoogle Scholar
  50. Wei R, Murray AT (2015) Spatial uncertainty in harvest scheduling. Ann Oper Res 232(1):275–289Google Scholar
  51. Wei R, Murray AT (2017) Spatial uncertainty challenges in location modeling with dispersion requirements. In: Thill J-C (ed) Spatial analysis and location modeling in urban and regional systems. Springer, New YorkGoogle Scholar
  52. Williams JC (2008) Optimal reserve site selection with distance requirements. Comput Oper Res 35(2):488–498CrossRefGoogle Scholar
  53. Yoshimoto A, Brodie JD (1994) Comparative analysis of algorithms to generate adjacency constraints. Can J For Res 24:1277–1288CrossRefGoogle Scholar
  54. Zeller RE, Achabal DD, Brown LA (1980) Market penetration and locational conflict in franchise systems. Decis Sci 11:58–80CrossRefGoogle Scholar
  55. Zoraster S (1990) The solution of large 0–1 integer programming problems encountered in automated cartography. Oper Res 38(5):752–759CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Richard L. Church
    • 1
  • Alan Murray
    • 1
  1. 1.Department of GeographyUniversity of CaliforniaSanta BarbaraUSA

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