Abstract
Managing the limited resources of money, time and space poses a real problem in the livestock business in general and the poultry sector in particular. The stochastic linear programming with recourse will permit the formulation of a mathematical model that could easily be solved in order to attain the objective of maximizing profit but this will be hindered by the presence of some parameters like demand and supply which have no predetermined probability distributions. In an attempt to address the problem of unavailable probability distribution functions, this research is aimed at proposing a robust linear programming model which can handle problems and others in similar circumstances with the need of probability distributions.The robust model thus constructed is based on a modification of the stochastic model by Soyster. An application of this model on a real life data produced results showing an increase in profit made by a local poultry farmer from 241,485 FCFA to 362,580FCFA representing an increase in profit of more than 50% in over that obtained when using the ordinary Linear Programming Technique. The belief therefore is that, if models like this are implemented, not only would the livelihood of the poultry farmers be improved, but it will go a long way to better the economy and satisfy the ever increasing need of poultry products by the communities. Key words: Maximization, livestock, stochastic, robust, linear programming, optimization.
Highlights
Livestock systems occupy about 30% of the planet's icefree terrestrial surface area (Steinfeld et al, 2006) and are a significant global asset with a value of at least $1.4 trillion
As the number of species of type i and age a to pay for the deficit is a random variable, stochastic linear programming and the L-Shaped method requires calculating the mathematical expectation of profit for the recourse function
Stochastic Linear Programming and Robust Linear Programming are little known in the livestock sector despite their potential of optimising even in the presence of uncertainty in data
Summary
Livestock systems occupy about 30% of the planet's icefree terrestrial surface area (Steinfeld et al, 2006) and are a significant global asset with a value of at least $1.4 trillion. The AGA’s program on animal production focuses primarily on smallscale dairying, small-medium scale poultry and, to a lesser extent, on small ruminant systems which can make a significant contribution to improved livelihoods and local economic development This will be achieved through the provision of topical information, guidance and technical support to farmers. The objective of this research was to propose a robust linear programming (RLP) model that could be used to handle optimization problems in the livestock business sector in general and in poultry farming in particular in the absence of probability distribution of the uncertain parameters involved. In the case of the small-medium scale poultry farming, the main concern shall be to determine how many species of each type and age of birds to be kept at a particular period in order to maximize the benefit without violating the constraints of money, time, and available space while using the robust linear programming model
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