Bulletin of Mathematical Biology

, Volume 76, Issue 5, pp 997–1016

# Mathematical Programming Models for Determining the Optimal Location of Beehives

• Maica Krizna A. Gavina
• Jomar F. Rabajante
• Cleofas R. Cervancia
Original Article

DOI: 10.1007/s11538-014-9943-9

Gavina, M.K.A., Rabajante, J.F. & Cervancia, C.R. Bull Math Biol (2014) 76: 997. doi:10.1007/s11538-014-9943-9

## 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.

### Keywords

Beekeeping Pollination management Apis mellifera Stingless bees Bumblebees Crop pollination

© Society for Mathematical Biology 2014

## Authors and Affiliations

• Maica Krizna A. Gavina
• 1
• Jomar F. Rabajante
• 1
• 2
• Cleofas R. Cervancia
• 2
• 3
1. 1.Institute of Mathematical Sciences and PhysicsUniversity of the Philippines Los BañosLagunaPhilippines
2. 2.University of the Philippines Los Baños Bee ProgramUniversity of the Philippines Los BañosLagunaPhilippines
3. 3.Institute of Biological SciencesUniversity of the Philippines Los BañosLagunaPhilippines