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Location with acceleration-deceleration distance

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  • Drezner, Zvi
  • Drezner, Tammy
  • Wesolowsky, George O.

Abstract

In this paper we investigate a model where travel time is not necessarily proportional to the distance. Every trip starts at speed zero, then the vehicle accelerates to a cruising speed, stays at the cruising speed for a portion of the trip and then decelerates back to a speed of zero. We define a time equivalent distance which is equal to the travel time multiplied by the cruising speed. This time equivalent distance is referred to as the acceleration-deceleration (A-D) distance. We prove that every demand point is a local minimum for the Weber problem defined by travel time rather than distance. We propose a heuristic approach employing the generalized Weiszfeld algorithm and an optimal approach applying the Big Triangle Small Triangle global optimization method. These two approaches are very efficient and problems of 10,000 demand points are solved in about 0.015seconds by the generalized Weiszfeld algorithm and in about 1minute by the BTST technique. When the generalized Weiszfeld algorithm was repeated 1000 times, the optimal solution was found at least once for all test problems.

Suggested Citation

  • Drezner, Zvi & Drezner, Tammy & Wesolowsky, George O., 2009. "Location with acceleration-deceleration distance," European Journal of Operational Research, Elsevier, vol. 198(1), pages 157-164, October.
  • Handle: RePEc:eee:ejores:v:198:y:2009:i:1:p:157-164
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    References listed on IDEAS

    as
    1. Zvi Drezner & Atsuo Suzuki, 2004. "The Big Triangle Small Triangle Method for the Solution of Nonconvex Facility Location Problems," Operations Research, INFORMS, vol. 52(1), pages 128-135, February.
    2. Tammy Drezner & Zvi Drezner, 2004. "Finding the optimal solution to the Huff based competitive location model," Computational Management Science, Springer, vol. 1(2), pages 193-208, July.
    3. Plastria, Frank, 1992. "GBSSS: The generalized big square small square method for planar single-facility location," European Journal of Operational Research, Elsevier, vol. 62(2), pages 163-174, October.
    4. James G. Morris, 1981. "Convergence of the Weiszfeld Algorithm for Weber Problems Using a Generalized “Distance” Function," Operations Research, INFORMS, vol. 29(1), pages 37-48, February.
    5. Peter Kolesar, 1975. "A Model for Predicting Average Fire Engine Travel Times," Operations Research, INFORMS, vol. 23(4), pages 603-613, August.
    6. Jack Brimberg & Robert F. Love, 1992. "A New Distance Function for Modeling Travel Distances in a Transportation Network," Transportation Science, INFORMS, vol. 26(2), pages 129-137, May.
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    Cited by:

    1. Hugo M. Repolho & António P. Antunes & Richard L. Church, 2013. "Optimal Location of Railway Stations: The Lisbon-Porto High-Speed Rail Line," Transportation Science, INFORMS, vol. 47(3), pages 330-343, August.
    2. Emilio Carrizosa & Jonas Harbering & Anita Schöbel, 2016. "Minimizing the passengers’ traveling time in the stop location problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(10), pages 1325-1337, October.
    3. M. Hakan Akyüz & Temel Öncan & İ. Kuban Altınel, 2019. "Branch and bound algorithms for solving the multi-commodity capacitated multi-facility Weber problem," Annals of Operations Research, Springer, vol. 279(1), pages 1-42, August.
    4. Zvi Drezner & Vladimir Marianov & George O. Wesolowsky, 2016. "Maximizing the minimum cover probability by emergency facilities," Annals of Operations Research, Springer, vol. 246(1), pages 349-362, November.
    5. Burkey, M.L. & Bhadury, J. & Eiselt, H.A., 2012. "A location-based comparison of health care services in four U.S. states with efficiency and equity," Socio-Economic Planning Sciences, Elsevier, vol. 46(2), pages 157-163.
    6. Frank Plastria & Mohamed Elosmani, 2013. "Continuous location of an assembly station," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 323-340, July.
    7. M. Akyüz & İ. Altınel & Temel Öncan, 2014. "Location and allocation based branch and bound algorithms for the capacitated multi-facility Weber problem," Annals of Operations Research, Springer, vol. 222(1), pages 45-71, November.

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    Keywords

    Location Global optimization;

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