Abstract

This study presents the development of mathematical model for determining the potential number of sheep and lambs in a ten-year period. The  model enables prediction of the number of female sheep and lambs, plans for future feeding, care and breeding costs. Two types of sheep breeding (traditional and intensive) were considered, assuming the following: 1) the initial herd contained S pregnant ewes; 2) new ewes or female lambs were not bought; 3) female lambs obtained by reproduction of the livestock unit were not sold; 4) male and female lambs and ewes which did not satisfy the selection and health criteria for further reproduction, were sold. Considering the reproductive cycles of Württemberg, Ile d’ France, Suffolk and domestic Tsigai (from Serbia) sheep breeds, we established the number of ewes and lambs for sale, after n years from the herd establishment. It depends on the following parameters: the initial size of herd S, average percentage p of new, two year old ewes reproduced from the herd, and average percentage r of non culled sheep. A recursive formula for the number of ewes is given as well as the number of lambs for sale after n years. Proposed formulas could be used for numerous additional financial analyses of sheep breeding. General  model for evaluation of yearly and cumulative income for both types of sheep breeding has been presented. The obtained results represent the first step in deciding which breed and which type of breeding should be accepted in order to gain the highest possible profit.

Key words: Culling and reproductive, mathematical model, sheep breeding.