A Note on Livestock Breeding Policies in Stable and Development Situations

Abstract

Multi-stage linear programming is used to develop sheep repIacement policies in a number of different situations. Policies are developed for eight and sixteen year periods assuming, firstly a constant feed supply, and secondly, an increasing feed supply over the period. The results show the optimal flock composition together with the sheep sale activities for each year of the plan. The marginal value products indicate which constraints are the most important and whether any should be relaxed in order to make the model more realistic. It is concluded that it is not necessary to use a very long planning period in order to determine the activities for the early years. The results from the shorter planning period appear to be consistent with long-term goals. In froductionTwo recent studies have examined the relative profitability of different sheep replacement policies in a breeding fl0ck.l These studies suggested "optimal" flock structures under various assumptions. However, neither study allowed for stochastic influences nor was the best method of changing from the current to the suggested policy indicated. The major emphasis of this study is to examine the latter of these two aspects. It has been limited to the deterministic case and no attempt has been made to examine the effect of variability, of either prices or biological parameters. While the examples considered deal only with sheep, the method can be readily adapted to other types of livestock such as beef cattle, Scobie [2, p. 1371 prepared some budgets to indicate how a change in flock structure might be effected. Here we aim to determine the optimal means of making the change in a situation where the grazier, for some reason, does not wish to, or cannot purchase sheep. In addition we examine the case where feed supply is constant and where the feed supply is increasing over time-the typical situation with pasture improvement. MethodMulti-stage linear programming is used to determine the optimal breeding and culling policy. Townsley and Schroder [ 41 demonstrated the use of linear programming to determine the optimal breeding flock composition. Again this was a static solution to the problem and did not indicate how a change should be carried out. We extend that type of model to a multi-stage model. Basically it consists of a run and a sell activity for each age group of ewes and for each group of young sheep.* Mr Healy is now with WestraIian Farmers Co-operative Ltd., Perth.1See Byrne [ I ] and Scobie C21. The latter contains much of the relevant information that was originally presented in [3]. 154