# Farm planning for a typical crop-livestock integrated farm : an application of a mixed integer linear programming model

Ghebretsadik, Amanuel Habte (2004-12)

Assignment (MSc) -- University of Stellenbosch, 2004.

Thesis

ENGLISH ABSTRACT: In an integrated crop-livestock production farm, the profitability and sustainability of farm production is dependent on the crop rotation strategy applied. Crop rotations have historically been applied to maintain long-term profitability and sustainabiliry of farming production by exploiting the jointly beneficial interrelationships existing among different crop types and the animal production activity. Monocrop (specifically wheat) growers in the Swartland area of the Western Cape are struggling to maintain long-term profitability and sustainability of the crop production, challenging them to rethink about the introduction crop rotation in the production planning. By making proper assumptions, this paper develops a mixed integer linear programming model to suggest a decision planning for the farm planning problem faced by an integratedcrop- livestock production farmer. The mathematical model developed includes crop production, dairy production and wool sheep production activities, which permitted the consideration of five crop types within a crop rotation system. By assuming that a farmer uses a cycle of at most three years, the crop rotation model was incorporated in the composite mixed integer linear farm planning model. In order to demonstrate the application of the mathematical farm planning model formulated, a case study is presented. Relevant data from the Koeberg area of the Swartland region of the Western Cape was applied. For each planning period, the model assumed that the farm has the option of selecting from any of 15 cropping strategies. A land which is not allocated to any of the 15 crop rotation strategies due to risky production situation is left as grass land for roughage purposes of the animal production. Results of the mathematical model indicated that farm profit is dependent on the cropping strategy selected. Additionally, animal production level was also dependent on the crop strategy appl ied. Furthermore, study results suggest that the profit generated from the integrated crop-livestock farm production by adopting crop rotation was superior to profit generated 1'1'0111 the farm activities which are based on monocrop wheat strategy. Empirical results also indicated that the complex interrelationship involved in a mixed crop-livestock farm operation play a major role in determining optimal farm plans. This complex interrelationships favour the introduction of crop rotation in the crop production activities of the farm under investigation. Crop production risk is the major risk component of risk the farmer faces in the farm production. In this study, risk is incorporated in the mixed integer programrnmg farm planning model as a deviation from the expected values of an activity of returns. Model solution with risk indicated that crop rotation strategy and animal production level is sensitive to risk levels considered. The Results also showed that the incorporation of risk in the model greatly affects the level of acreage allocation, crop rotation and animal production level of the farm. Finally, to improve the profitability and sustainability of the farm activity, the study results suggest that the introduction of crop rotation which consist cereals, oil crops and leguminous forages is of paramount importance. Furthermore, the inclusion of forage crops such as medics in the integrated crop livestock production is beneficial for sustained profitability from year to year.

AFRIKAANSE OPSOMMING: Wisselbou is baie belangrik om volhoubare winsgewindheid te verseker in 'n geintegreerde lewendehawe I gewasverbouing boerdery in die Swartland gebied van Wes-Kaap. "n Monokultuur van veral koring produksie het ernstige problerne vir produsente veroorsaak. In hierdie studie word 'n gemengde heeltallige liniere prograrnmerings-model gebruik om te help met besluitneming in sulke boerderye.Die wiskundige model beskou die produksie van kontant- en voer-gewasse (5 verskillende soorte) asook suiwel- en wol/vleis-produksie (beeste en skape) .Daar word aanvaar dat die boer "n siklus van hoogstens 3 jaar in die wisselbou rotasie model gebruik .. 'n Gevallestudie word gedoen met behulp van toepaslike data van 'n plaas in die Koeberg gebied. Die model aanvaar dat die produsent 'n keuse het uit 16 wisselbou strategic .Resultate toon dat winsgewindheid afhanklik is van die strategie gekies en dat wisselbou beter resultate lewer as in die geval van "n monokultuur.Dit wys ook dat die wisselwerking tussen diereproduksie en gewasproduksie baie belangrik is in die keuse van 'n optimale strategie. Die risiko in gewasverbouing is die belangrikste risiko factor vir die produsent.In hierdie studie word risiko ook ingesluit in die gemengde heeltallige model, naamlik as 'n afwyking van die verwagte opbrengs-waardes .Die model toon duidelik dat gewasproduksie en lewendehawe-produksie baie sensitief is ten opsigte van die gekose risiko vlak. Die studie toon ook dat 'n wisselbou program wat die produksie van graan (veral koring) .oliesade asook voere insluit belangrik is vir volhoubare winsgewindheid Die insluiting van klawers (bv "medics") is veral belangrik hier.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/49965

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