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Mathematical Programming Models for Determining the Optimal Location of Beehives

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Abstract

Farmers frequently decide where to locate the colonies of their domesticated eusocial bees, especially given the following mutually exclusive scenarios: (i) there are limited nectar and pollen sources within the vicinity of the apiary that cause competition among foragers; and (ii) there are fewer pollinators compared to the number of inflorescence that may lead to suboptimal pollination of crops. We hypothesize that optimally distributing the beehives in the apiary can help address the two scenarios stated above. In this paper, we develop quantitative models (specifically using linear programming) for addressing the two given scenarios. We formulate models involving the following factors: (i) fuzzy preference of the beekeeper; (ii) number of available colonies; (iii) unknown-but-bounded strength of colonies; (iv) probabilistic carrying capacity of the plant clusters; and (v) spatial orientation of the apiary.

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Authors and Affiliations

  1. Institute of Mathematical Sciences and Physics, University of the Philippines Los Baños, Laguna, 4031, Philippines

    Maica Krizna A. Gavina & Jomar F. Rabajante

  2. University of the Philippines Los Baños Bee Program, University of the Philippines Los Baños, Laguna, 4031, Philippines

    Jomar F. Rabajante & Cleofas R. Cervancia

  3. Institute of Biological Sciences, University of the Philippines Los Baños, Laguna, 4031, Philippines

    Cleofas R. Cervancia

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  1. Maica Krizna A. Gavina
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  2. Jomar F. Rabajante
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  3. Cleofas R. Cervancia
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Correspondence to Jomar F. Rabajante.

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Gavina, M.K.A., Rabajante, J.F. & Cervancia, C.R. Mathematical Programming Models for Determining the Optimal Location of Beehives. Bull Math Biol 76, 997–1016 (2014). https://doi.org/10.1007/s11538-014-9943-9

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