Abstract— Beekeepers are faced with q u i t e a number of challenges such as selection of fields and enhancement of honey production. In this paper crisp deterministic honey bee production model was formulated in an attempt to optimize the distribution of beehives in the apiary in order to maximize production of honey and minimize unhealthy competition among foraging bees which often arises as a result of overcrowding. The model was characterized u s i n g Weighted sum model (WSM) and Analytic Hierarchical Model (AHM). Finally the validity of the model was tested with the real life data and the results obtained shows that proper distribution of the bee hives in the apiary is important to maximize production and minimize unpleasant fields. Keywords—Beehive, Field, Honey bee production, Mathematical Model, Optimization, Optimal spatial distribution. I INTRODUCTION Honey bees are social insects that belong to the family of Apidae, Apis and Apis melifera and are considered to be one of the most highly developed social insects among the invertebrate animals due to their social life which involves exhibiting very well adapted collective behaviors. These social insects visit approximately t wo million flowers to make one pound of honey for human use, [5]. Honey bees live in colonies made of only one queen, some few drones and thousands of workers. The strength of the bee colonies basically depends on the availability of nectar and pollen which are the major needs of honey bees. Honey bee production (honey beekeeping) is the rearing of honey bee for honey and other by-products. It is the maintenance of honey bee colonies, commonly in hives, by humans which provides great potential for development in almost all countries of the world, [12], [5]. T raditional beekeeping in trees is practiced by climbing the tree. The climbing involves the use of ladder and ropes. In some parts of Southern and Central States of Nigeria, pots are kept on the ground as a means of hives in bee-keeping,[1]. In Eastern Nigeria, palm wine is used to attract bees to traditional hives. In Southern Bauchi, clay or mud hives are used to keep bees. The modern and/or scientific method of beekeeping is called Apiculture, it is the practice of honey bee rearing that combines the knowledge of the social behavior and biology of the bees with that of the environment and the use of apiary equipment to maximize honey production and output of other bee hives production,[3]. Bees play significant roles in agricultural sector as honey bees are highly needed in crop pollination leading to increase i n national food production and regeneration of plant species. Honey not only tasted good but also provides important food nutrients, protein, energy and sugar which accounts for 95-99 percent of honey dry matter, [8]. A colony of honey bee is a biological unit or family that consist of three different t ypes of bees. The Queen or mother bee which is a fertile, egg laying female, the worker bees are infertile female. The drones which are male bees are always present in the reproductive season, but may be kicked out by worker bees during dearth or food scarcity. The composition is usually one queen to 60,000 workers and about 100 drones in an average colony,[1 2 ], [ 1 5 ] . Bee keeping has significant role in ensuring food securit y because honey bee pollination cultivated crop and vegetable and enhance productivity (such as fruits, vegetable and dairy products, including ice cream),[3]. Optimization of production of honey bees is at moment paramount in the nation’s economy. Mathematical model is the general characterization of a process, object or concept in term of mathematics in order to determine behaviors in different situations,[4]. Optimization algorithm known as Honey Bee Algorithm are search methods where the goal is to find an optimal solution to a problem, in order to satisfy one or more objective functions, possibly subject to a set of constraints. Studies of social animals and social insects have resulted in a number of mathematical models and computational models of swarm intelligence. A good number of researches have been carried out on honey bee algorithm and mathematical Optimization of Honey Bee Production Y.O. Aderinto, A. Azagbaekwue, O. M. Bamigbola Department of Mathematics, Faculty of Physical Sciences, University of Ilorin, Ilorin, Nigeria M. O. Oke, A. A. Obayomi Department of Mathematics, Ekiti State University, Ado-Ekiti, Nigeria L. O. Salaudeen Department of Mathematics, Federal University Oye-Ekiti, Nigeria T. O. Aliu Department of Mathematics and Statistics, Kwara State University, Molete, Nigeria. Corresponding Email: aderinto@unilorin.edu.ng INTERNATIONAL JOURNAL OF MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES DOI: 10.46300/9101.2020.14.13 Volume 14, 2020 ISSN: 1998-0140 54