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Duality in constrained multi‐facility location models

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  • Halit Üster
  • Robert F. Love

Abstract

We consider the 𝓁p‐norm multi‐facility minisum location problem with linear and distance constraints, and develop the Lagrangian dual formulation for this problem. The model that we consider represents the most general location model in which the dual formulation is not found in the literature. We find that, because of its linear objective function and less number of variables, the Lagrangian dual is more useful. Additionally, the dual formulation eliminates the differentiability problem in the primal formulation. We also provide the Lagrangian dual formulation of the multi‐facility minisum location problem with the 𝓁pb‐norm. Finally, we provide a numerical example for solving the Lagrangian dual formulation and obtaining the optimum facility locations from the solution of the dual formulation. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 410–421, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10010

Suggested Citation

  • Halit Üster & Robert F. Love, 2002. "Duality in constrained multi‐facility location models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(4), pages 410-421, June.
    • Handle: RePEc:wly:navres:v:49:y:2002:i:4:p:410-421
    DOI: 10.1002/nav.10010
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    References listed on IDEAS

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    1. G. O. Wesolowsky & R. F. Love, 1972. "A Nonlinear Approximation Method for Solving a Generalized Rectangular Distance Weber Problem," Management Science, INFORMS, vol. 18(11), pages 656-663, July.
    2. Robert F. Love & Svend A. Kraemer, 1973. "A Dual Decomposition Method for Minimizing Transportation Costs in Multifacility Location Problems," Transportation Science, INFORMS, vol. 7(4), pages 297-316, November.
    3. Daniel Fylstra & Leon Lasdon & John Watson & Allan Waren, 1998. "Design and Use of the Microsoft Excel Solver," Interfaces, INFORMS, vol. 28(5), pages 29-55, October.
    4. James G. Morris & William A. Verdini, 1979. "Technical Note—Minisum I p Distance Location Problems Solved via a Perturbed Problem and Weiszfeld's Algorithm," Operations Research, INFORMS, vol. 27(6), pages 1180-1188, December.
    5. Henrik Juel & Robert F. Love, 1981. "On the Dual of the Linearly Constrained Multifacility Location Problem with Arbitrary Norms," Transportation Science, INFORMS, vol. 15(4), pages 329-337, November.
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