Recent debate about agricultural greenhouse gases (GHG) emissions mitigation highlights tradeoffs inherent in the way we produce and consume food, with increasing scrutiny on emissionsintensive livestock products 1-3. While most research has focussed on mitigation through improved productivity 4,5 , systemic interactions resulting from reduced beef production at regional level are still unexplored. A detailed optimisation model of beef production encompassing pasture degradation and recovery processes, animal and deforestation emissions, soil organic carbon (SOC) dynamics and upstream lifecycle inventory was developed and parameterized for the Brazilian Cerrado. Economic return was maximized considering two alternative scenarios: Decoupled Livestock Deforestation (DLD), assuming baseline deforestation rates controlled by effective policy; and Coupled Livestock Deforestation (CLD), where shifting beef demand alters deforestation rates. In DLD, reduced consumption actually leads to less productive beef systems, associated with higher emissions intensities and total emissions, while increased production leads to more efficient systems with boosted SOC stocks, reducing both per kg and total emissions. Under CLD, increased production leads to 60% higher emissions than in DLD. The results indicate the extent to which deforestation control contributes to sustainable intensification in Cerrado beef systems, and how alternative life-cycle analytical approaches 6 result in significantly different emission estimates.

This paper introduces the design and implementation of two parallel dual simplex solvers for general large scale sparse linear programming problems. One approach, called PAMI, extends a relatively unknown pivoting strategy called suboptimization and exploits parallelism across multiple iterations. The other, called SIP, exploits purely single iteration parallelism by overlapping computational components when possible. Computational results show that the performance of PAMI is superior to that of the leading open-source simplex solver, and that SIP complements PAMI in achieving speedup when PAMI results in slowdown. One of the authors has implemented the techniques underlying PAMI within the FICO Xpress simplex solver and this paper presents computational results demonstrating their value. In developing the first parallel revised simplex solver of general utility, this work represents a significant achievement in computational optimization.

We discuss the use of preconditioned conjugate gradients (CG) method for solving the reduced KKT systems arising in interior point algorithms for linear programming. The (indefinite) augmented system form of this linear system has a number of advantages, notably a higher degree of sparsity than the (positive definite) normal equations form. Therefore, we use the CG method to solve the augmented system and look for a suitable preconditioner.An explicit null space representation of linear constraints is constructed by using a nonsingular basis matrix identified from an estimate of the optimal partition in the linear program. This is achieved by means of recently developed efficient basis matrix factorisation techniques which exploit hyper-sparsity and are used in implementations of the revised simplex method.The approach has been implemented within the HOPDM interior point solver and applied to medium and large-scale problems from public domain test collections. Computational experience is encouraging.

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