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Towards a stochastic programming modeling framework for districting

Author

Listed:
  • Antonio Diglio

    (Università degli Studi di Napoli Federico II)

  • Stefan Nickel

    (Karlsruhe Institute of Technology (KIT)
    Department of Logistics and Supply Chain Optimization, Research Center for Information Technology (FZI))

  • Francisco Saldanha-da-Gama

    (Faculdade de Ciências da Universidade de Lisboa
    Faculdade de Ciências da Universidade de Lisboa)

Abstract

In this paper a stochastic districting problem is investigated. Demand is assumed to be represented by a random vector with a given joint probability distribution function. A two-stage mixed-integer stochastic programming model is proposed. The first stage comprises the decision about the initial territory design: the districts are defined and all the territory units assigned to one and exactly one of them. In the second stage, i.e., after demand becomes known, balancing requirements are to be met. This is ensured by means of two recourse actions: outsourcing and reassignment of territory units. The objective function accounts for the total expected cost that includes the cost for the first-stage territory design plus the expected cost incurred at the second stage by outsourcing and reassignment. The (re)assignment costs are associated with the distances between territory units, i.e., the focus is put on the compactness of the solution. The model is then extended in different ways to account for aspects of practical relevance such as a maximum desirable dispersion, reallocation constraints, or similarity of the second-stage solution w.r.t. the first-stage one. The new modeling framework proposed is tested computationally using instances built using real geographical data.

Suggested Citation

  • Antonio Diglio & Stefan Nickel & Francisco Saldanha-da-Gama, 2020. "Towards a stochastic programming modeling framework for districting," Annals of Operations Research, Springer, vol. 292(1), pages 249-285, September.
    • Handle: RePEc:spr:annopr:v:292:y:2020:i:1:d:10.1007_s10479-020-03631-7
    DOI: 10.1007/s10479-020-03631-7
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    Cited by:

    1. Diglio, Antonio & Peiró, Juanjo & Piccolo, Carmela & Saldanha-da-Gama, Francisco, 2021. "Solutions for districting problems with chance-constrained balancing requirements," Omega, Elsevier, vol. 103(C).
    2. Diglio, Antonio & Peiró, Juanjo & Piccolo, Carmela & Saldanha-da-Gama, Francisco, 2023. "Approximation schemes for districting problems with probabilistic constraints," European Journal of Operational Research, Elsevier, vol. 307(1), pages 233-248.

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