Skip to main content

Layout Problems with Reachability Constraint

  • Conference paper
  • First Online:
  • 1467 Accesses

Part of the book series: Operations Research Proceedings ((ORP))

Abstract

Many design/layout processes of warehouses, depots or parking lots are subject to reachability constraints, i.e., each individual storage/parking space must be directly reachable without moving any other item/car. Since every storage/parking space must be adjacent to a corridor/street one can alternatively consider this type of layout problem as a network design problem of the corridors/streets.

More specifically, we consider the problem of placing quadratic parking spaces on a rectangular shaped parking lot such that each of it is connected to the exit by a street. We investigate the optimal design of parking lot as a combinatorial puzzle, which has—as it turns out—many relations to classical combinatorial optimization problems.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight 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

  1. Bingle, R., Meindertsma, D., Oostendorp, W., Klaasen, G.: Designing the optimal placement of spaces in a parking lot. Math. Modell. 9(10), 765–776 (1987)

    Article  Google Scholar 

  2. Abdelfatah, A.S., Taha, M.A.: Parking capacity optimization using linear programming. J. Traffic Logist. Eng., 2(3), 2014.

    Google Scholar 

  3. Verhulst, F., Walcher, S. (eds.): Das Zebra-Buch zur Geometrie. Springer, Berlin (2010)

    Google Scholar 

  4. Kleinhans, J.: Ganzzahlige Optimierung zur Bestimmung optimaler Parkplatz-Layouts. Bachelor Thesis, Bergische Universität Wuppertal (2013)

    Google Scholar 

  5. Du, D.-Z., Wan, P.-J.: Connected Dominating Set: Theory and Applications, vol. 77. Springer Optimization and Its Applications. Springer, Berlin (2013)

    Google Scholar 

  6. Douglas, R.J.: NP-completeness and degree restricted spanning trees. Discret. Math. 105(1), 41–47 (1992)

    Article  Google Scholar 

  7. Reis, M.F., Lee, O., Usberti, F.L.: Flow-based formulation for the maximum leaf spanning tree problem. Electron Notes Discrete Math. 50, 205–210 (2015). LAGOS’15 – VIII Latin-American Algorithms, Graphs and Optimization Symposium

    Google Scholar 

  8. Fujie, T.: The maximum-leaf spanning tree problem: Formulations and facets. Networks 43(4), 212–223 (2004)

    Article  Google Scholar 

  9. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, San Francisco (1979)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michael Stiglmayr .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Stiglmayr, M. (2020). Layout Problems with Reachability Constraint. In: Neufeld, J.S., Buscher, U., Lasch, R., Möst, D., Schönberger, J. (eds) Operations Research Proceedings 2019. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-030-48439-2_22

Download citation

Publish with us

Policies and ethics