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Kantorovich–Rubinstein Distance Minimization: Application to Location Problems

In: Large Scale Optimization in Supply Chains and Smart Manufacturing

Author

Listed:
  • Viktor Kuzmenko

    (V.M. Glushkov Institute of Cybernetics)

  • Stan Uryasev

    (Stony Brook)

Abstract

The paper considers optimization algorithms for location planning, which specifies positions of facilities providing demanded services. Examples of facilities include hospitals, restaurants, ambulances, retail and grocery stores, schools, and fire stations. We reduced the initial problem to approximation of a discrete distribution with a large number of atoms by some other discrete distribution with a smaller number of atoms. The approximation is done by minimizing the Kantorovich–Rubinstein distance between distributions. Positions and probabilities of atoms of the approximating distribution are optimized. The algorithm solves a sequence of optimization problems reducing the distance between distributions. We conducted a case study using Portfolio Safeguard (PSG) optimization package in MATLAB environment.

Suggested Citation

  • Viktor Kuzmenko & Stan Uryasev, 2019. "Kantorovich–Rubinstein Distance Minimization: Application to Location Problems," Springer Optimization and Its Applications, in: Jesús M. Velásquez-Bermúdez & Marzieh Khakifirooz & Mahdi Fathi (ed.), Large Scale Optimization in Supply Chains and Smart Manufacturing, pages 59-68, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-22788-3_3
    DOI: 10.1007/978-3-030-22788-3_3
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