Integrating stochasticity into the objective function avoids Monte Carlo computation in the optimisation of beef feedlots D.G. Mayer a,b,⇑ , B.J. Walmsley a,c , M.J. McPhee a,c , V.H. Oddy a,d , J.F. Wilkins a,c , B.P. Kinghorn a,d , R.C. Dobos a,c , W.A. McKiernan a,c a Cooperative Research Centre for Beef Genetic Technologies, University of New England, Armidale, New South Wales, Australia b Department of Agriculture, Fisheries and Forestry, Ecosciences Precinct, Dutton Park, Queensland, Australia c Department of Primary Industries, Beef Industry Centre, Armidale, New South Wales, Australia d University of New England, Armidale, New South Wales, Australia article info Article history: Received 5 June 2012 Received in revised form 1 November 2012 Accepted 16 November 2012 Keywords: Beef cattle Model Market specifications Evolutionary algorithm Differential evolution abstract The real world contains many sources of natural variation. Useful simulation models of real-world prob- lems, 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 com- mercial 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 $20 for the second example where the animals had been allocated to pens on a more structured basis (by weights). This optimised allocation scheme appears to offer obvious improvements for feedlot operations, and is currently being trialed by a number of industry collaborators. Crown Copyright Ó 2012 Published by Elsevier B.V. All rights reserved. 1. Introduction Simulation models and optimisation are used by managers of a range of commercial operations (Fu, 1994), including beef produc- tion systems (Hochman et al., 1991; Machado et al., 2010), to re- main competitive and viable. Effective models must encompass the key features, states and pathways of the system being studied. Natural variation is an unavoidable feature of the real world, and useful simulation models need to incorporate it. When projecting the model into the future, under ‘what-if’ or formal optimisation investigations, the values of at least some of the driving variables (such as commodity prices, meteorological variables, soil parame- ters) are unknown, and variation exists in many of the biological processes such as pasture and animal growth rates. To account for these and other uncertainties, stochastic sampling methods are usually adopted to deal with such variability. Typically, the modeller estimates and assigns the respective de- grees of variation, usually with the Normal distribution, although other distributions can equally be incorporated. The expected behaviour is then estimated via Monte Carlo simulation (Fishman, 0168-1699/$ - see front matter Crown Copyright Ó 2012 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.compag.2012.11.006 ⇑ Corresponding author. Address: GPO Box 267, Brisbane 4001, Australia. Tel.: +61 7 3255 4287; fax: +61 7 3846 0935. E-mail address: david.mayer@qld.gov.au (D.G. Mayer). Computers and Electronics in Agriculture 91 (2013) 30–34 Contents lists available at SciVerse ScienceDirect Computers and Electronics in Agriculture journal homepage: www.elsevier.com/locate/compag