Skip to main content
SpringerLink
Log in
Book cover

Foundations of Location Analysis pp 109–135Cite as

Covering Problems

  • Chapter
  • First Online:

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 155))

Abstract

The mail-order DVD rental company Netflix chooses distribution center locations so that most of its customers receive their DVDs within one business day via first-class U.S. Mail. Similarly, many municipalities aim to have fire crews reach 911 callers within a specified time, such as four minutes. Both of these are examples of the notion of coverage, a concept central to several classes of facility location models; it indicates whether a demand location is within a pre-specified radius (measured by distance, travel time, cost, or another metric) of its assigned facility. Homeowners are covered if they are within four minutes of the nearest fire station, and Netflix customers are covered if they are within one mailing day of a distribution center. Note that in the fire-station example, municipalities typically want to cover all residents (while minimizing the number of service stations to open), whereas Netflix wants to cover as many customers as possible (subject to a limit on the number of warehouses it may operate at any time, as specified by its capital budget). The fire-station problem is an example of the set covering location problem (SCLP), while Netflix’s problem is an example of the maximal covering location problem (MCLP). This chapter discusses both problems.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Aytug H, Saydam C (2002) Solving large-scale maximum expected covering location problems by genetic algorithms: a comparative study. Eur J Oper Res 141:480–494

    Google Scholar 

  • Batta R, Dolan JM, Krishnamurthy NN (1989) The maximal expected covering location problem revisited. Transp Sci 23:277–287

    Google Scholar 

  • Berman O, Krass D (2002) Facility location problems with stochastic demands and congestion. In: Drezner Z, Hamacher HW (eds) Facility location: applications and theory. Springer, New York (Chapter 11)

    Google Scholar 

  • Bramel J, Simchi-Levi D (1997) On the effectiveness of set covering formulations for the vehicle routing problem with time windows. Oper Res 45:295–301

    Google Scholar 

  • Church R (1974) Synthesis of a class of public facilities location models. PhD thesis, The Johns Hopkins University, Baltimore

    Google Scholar 

  • Church R, ReVelle C (1974) The maximal covering location problem. Pap Reg Sci Assoc 32:101–118

    Google Scholar 

  • Church RL, Meadows B (1979) Location modelling using maximum service distance criteria. Geogr Anal 11:358–373

    Google Scholar 

  • Church RL, Roberts KL (1983) Generalized coverage models and public facility location. Pap Reg Sci 53:117–135

    Google Scholar 

  • Church RL, Stoms DM, Davis FW (1996) Reserve selection as a maximal covering location problem. Biol Conserv 76:105–112

    Google Scholar 

  • Current J, Daskin MS, Schilling D (2002) Discrete network location models. In: Drezner Z, Hamacher HW (eds) Facility location: applications and theory. Springer, New York (Chapter 3)

    Google Scholar 

  • Daskin MS (1982) Application of an expected covering model to emergency medical service system design. Decis Sci 13:416–439

    Google Scholar 

  • Daskin MS (1983) A maximum expected covering location model: formulation, properties and heuristic solution. Transp Sci 17:48–70

    Google Scholar 

  • Daskin MS (1995) Network and discrete location: models, algorithms, and applications. Wiley, New York

    Google Scholar 

  • Daskin MS, Stern EH (1981) A hierarchical objective set covering model for emergency medical service vehicle deployment. Transp Sci 15:137–152

    Google Scholar 

  • Daskin MS, Hogan K, ReVelle C (1988) Integration of multiple, excess, backup, and expected covering models. Environ Plan B 15:15–35

    Google Scholar 

  • Daskin MS, Haghani AE, Khanal M, Malandraki C (1989) Aggregation effects in maximum covering models. Ann Oper Res 18:115–140

    Google Scholar 

  • Eaton DJ, Daskin MS, Simmons D, Bulloch B, Jansma G (1985) Determining emergency medical service vehicle deployment in Austin, Texas. Interfaces 15:96–108

    Google Scholar 

  • Eiselt HA, Sandblom C-L (2004) Decision analysis, location models, and scheduling problems. Springer, New York

    Google Scholar 

  • Fisher ML (1981) The Lagrangian relaxation method for solving integer programming problems. Manag Sci 27:1–18

    Google Scholar 

  • Fisher ML (1985) An applications oriented guide to Lagrangian relaxation. Interfaces 15:10–21

    Google Scholar 

  • Flynn J, Ratick S (1988) A multiobjective hierarchical covering model for the essential air services program. Transp Sci 22:139–147

    Google Scholar 

  • Galvão RD, Chiyoshi FY, Morabito R (2005) Towards unified formulations and extensions of two classical probabilistic location models. Comput Oper Res 32:15–33

    Google Scholar 

  • Galvão RD, ReVelle C (1996) A Lagrangean heuristic for the maximal covering location problem. Eur J Oper Res 88:114–123

    Google Scholar 

  • Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, New York

    Google Scholar 

  • Gleason JM (1975) A set covering approach to bus stop location. Omega 3:605–608

    Google Scholar 

  • Hakimi SL (1964) Optimum locations of switching centers and the absolute centers and medians of a graph. Oper Res 12:450–459

    Google Scholar 

  • Hakimi SL (1965) Optimum distribution of switching centers in a communication network and some related graph theoretic problems. Oper Res 13:462–475

    Google Scholar 

  • Larson RC (1974) A hypercube queuing model for facility location and redistricting in urban emergency services. Comput Oper Res 1:67–95

    Google Scholar 

  • Larson RC (1975) Approximating the performance of urban emergency service systems. Oper Res 23:845–868

    Google Scholar 

  • Marianov V, ReVelle C (1996) The queueing maximal availability location problem: a model for the siting of emergency vehicles. Eur J Oper Res 93:110–120

    Google Scholar 

  • Megiddo N, Zemel E, Hakimi SL (1983) The maximum coverage location problem. SIAM J Algebra Discrete Method 4:253–261

    Google Scholar 

  • Nozick LK, Turnquist MA (2001) Inventory, transportation, service quality and the location of distribution centers. Eur J Oper Res 129:362–371

    Google Scholar 

  • Rajagopalan HK, Vergara FE, Saydam C, Xiao J (2007) Developing effective meta-heuristics for a probabilistic location model via experimental design. Eur J Oper Res 177:83–101

    Google Scholar 

  • Rao A (1974) Counterexamples for the location of emergency service facilities. Oper Res 22:1259–1261

    Google Scholar 

  • ReVelle C (1993) Facility siting and integer-friendly programming. Eur J Oper Res 65:147–158

    Google Scholar 

  • ReVelle C, Hogan K (1989) The maximum availability location problem. Transp Sci 23:192–200

    Google Scholar 

  • ReVelle C, Marks D, Liebman JC (1970) An analysis of private and public sector location models. Manag Sci 16:692–707

    Google Scholar 

  • Schilling DA, ReVelle C, Cohon J, Elzinga DJ (1980) Some models for fire protection locational decisions. Eur J Oper Res 5:1–7

    Google Scholar 

  • Snyder LV (2006) Facility location under uncertainty: a review. IIE Transactions 38:537–554

    Google Scholar 

  • Storbeck JE (1982) Slack, natural slack and location covering. Socioecon Plan Sci 16:99–105

    Google Scholar 

  • Toregas C, ReVelle C (1972) Optimal location under time or distance constraints. Pap Reg Sci Assoc 28:133–143

    Google Scholar 

  • Toregas C, Swain R, ReVelle C, Bergman L (1971) The location of emergency service facilities. Oper Res 19:1363–1373

    Google Scholar 

  • Toregas C, ReVelle C, Swain R (1974) Reply to Rao’s note on the location of emergency service facilities. Oper Res 22:1262–1267

    Google Scholar 

  • White J, Case K (1973) On covering problems and the central facilities location problem. Unpublished paper, Virginia Polytechnic Institute and State University, Blacksburg

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial and Systems Engineering, Lehigh University, 200 West Packer Ave., Mohler Lab, 18015, Bethlehem, PA, USA

    Lawrence V. Snyder

Authors
  1. Lawrence V. Snyder
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lawrence V. Snyder .

Editor information

Editors and Affiliations

  1. Faculty of Business Administration, University of New Brunswick, Fredericton,, New Brunswick, Canada

    H. A. Eiselt

  2. Depto. Ingenieria Electrica, Pontificia Universidad Católica de Chile, Av. Vicuna Mackenna 4860, Macul, Santiago, Chile

    Vladimir Marianov

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Snyder, L.V. (2011). Covering Problems. In: Eiselt, H., Marianov, V. (eds) Foundations of Location Analysis. International Series in Operations Research & Management Science, vol 155. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7572-0_6

Download citation

Publish with us

Policies and ethics

Search

Navigation