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Linear programming has long been used in pig production to generate diets, subject to nutritional constraints, with minimum cost. More recently, the development of accurate animal growth models and the development of effective nonlinear optimisation techniques, in conjunction with linear programming, have allowed us to address the bigger problem of building feeding schedules that maximise profitability. A feeding schedule is defined as the number of diets fed, together with the energy and amino acid content, the quantity and the length of time each diet is fed. Profitability is measured as gross margin. This paper looks at the effects of three factors on such optimal feeding schedules for grower-finisher pig herds: pig type (genotype), feed costs and carcass payment scheme, and dietary restraints (ad libitum and restricted feeding). Our research has three findings. Firstly, optimal feeding schedules vary with pig type; the benefit of considering pig type, when developing feeding programs, is very substantial. Secondly, level changes in ingredient costs have a minor impact on optimal dietary nutrition and growing period while level changes in carcass payment schemes have a minor impact on optimal dietary nutrition but a major impact on the optimal growing period. Finally, feeding schedules that maximise lean growth do not necessarily result in maximised profit.

For many decades linear programming has been used to find minimum cost diets, notably in the chicken and pig meat industries. More recently, animal growth models together with nonlinear optimisation methods have been used to find feeding schedules which simultaneously minimise feed costs and maximise market return, so maximising gross margin. Genetic algorithms can handle these problems, albeit slowly. In this paper we study the particular nature of the objective function (for pig meat production) and develop a global optimisation algorithm tailored to its discontinuous structure. We also demonstrate the use of stochastic programming to cope with changing feed costs and changing price at slaughter.

Pig growth simulation models are used to determine feeding strategies that improve profitability on commercial farms. For a given farm, the number of diets fed, their energy, amino acid content, the quantity fed and the diet period can vary, thus giving a very large number of possible feeding strategies (F, as many as 1050). Adding nonlinear optimisation methods to a growth model allows us to find an Fyielding the maximum for a given objective function, usually the gross margin per pig or per pig place and year. Our simulation program links a linear program for a least-cost diet formulation, a stochastic pig growth model and a genetic algorithm (GA) to find the Fgiving a best solution. When finding Ffor maximum profitability, the gross margin obtained by the GA is higher than that found by random search or by feeding pigs to their maximal lean growth. In the growth model, pig genotypes are characterised by the maximal protein deposition potential (Pdmax), minimum lipid to protein ratio (MinLP) and the energy intake potential (p). In the model, variances and covariances of these quantities are used to grow a population of pigs instead of a single pig. A simulation study was conducted to investigate how different pig genotypes and different relative economic weightings for gross margin and nitrogen excretion affect the nitrogen retention and profitability. It was found that a large increase in nitrogen retention can be achieved through diet optimisation before profitability is compromised and that a lean genotype will have better nitrogen retention. Adding stochasticity to the model for a given population size showed that as the variances increase the variability in gross margin increases and with unchanging variances, the variability in gross margin decreases as the population size increases. Overall, using a feeding schedule which maximises gross margin for a single pig within a population of pigs results in a lower gross margin.