Integrating stochasticity into the objective function avoids Monte Carlo computation in the optimisation of beef feedlots

• Authors: D. G. Mayer;B. J. Walmsley;M. J. Mcphee;V. H. Oddy;J. F. Wilkins;B. P. Kinghorn;R. C. Dobos;W. A. Mckiernan
• Venue: Computers and Electronics in Agriculture
• Year: 2013

The real world contains many sources of natural variation. Useful simulation models of real-world problems, such as the optimal allocation of beef cattle into feedlot pens, need to take this into account. Monte Carlo simulation is the usual method of achieving this, using multiple model runs, each with a different set of randomly generated variables. However, when the goal is system optimisation, this approach can make the computation extremely intensive, and difficult for the optimisation of even moderately-sized models. This problem was addressed in an industry model of feedlot operations, where animals are selected and drafted into separate pens, and grown to the optimal weight and fat ranges in the pricing grid. For each pen, it is planned that the majority of the animals achieve this targeted region of the price grid, so that the number of discounted carcasses will be minimal. The main problem is that animals which appear reasonably similar at intake then display variable growth and fattening rates. Hence deterministic predictions are unrealistic, and stochasticity needs to be factored in. However this interferes with the efficient optimisation of this feedlot operation, which ultimately needs to be done 'real-time' (at animal induction), and on-site at the feedlot. Our solution to this dilemma was to transfer all of the modelled stochastic processes onto the evaluation side of this problem, by integrating over Normal distributions applied to the expected prices for each animal. This allows the optimisation runs to directly estimate the expected economic outcome using just one model evaluation for each trial management strategy. This process is illustrated with two case-studies, based on separate past intakes of animals into a commercial feedlot. For both intakes, the simulated results as reflected by the carcass values for the actual times on feed matched well with the observed values. Simulated results indicate that increases in profitability can be obtained both by altering the days on feed, and by better allocation of the animals to the pens. The overall predicted increase in profit per animal was $34 for the first intake, where the actual allocation of animals to the pens was approximately random (the order they were offloaded), and $20 for the second example where the animals had been allocated to pens on a more structured basis (by weights). This optimised allocation scheme appears to offer obvious improvements for feedlot operations, and is currently being trialed by a number of industry collaborators.