IMPACT OF CAPITAL ON THE GROWTH PROCESS OF A SUGARCANE FARM IN MPUMALANGA

The research was conducted for a representative 50 ha farm in the Onderberg region in Mpumalanga province, where farmers use a combination of centre-pivot, drip, and dragline systems of different sizes to grow sugarcane. The main intention was to establish a multi-period linear programming model capable of economically evaluating a farm expansion decision making process for farmers faced with investment decisions in alternative irrigation systems, taking in to account the available initial capital of the farm. A linear programming (LP) model was used to assign a mainline for a total of twelve irrigation system combinations based on the assumption that the farmer wishes to start with a 30 ha centre-pivot investment. Generalized Algebraic Modelling System (GAMS) was used to formulate the farm growth model as mixed integer dynamic linear programming (MIDLP) for a 15 year planning horizon. Based on the results, farmers are initially forced to invest in lower cost irrigation systems when they lack capital to start a farm business due to the time value of money. They only consider lowering operating costs by investing in expensive irrigation systems when they have more own capital or borrowing capacity.Crop Production/Industries, Land Economics/Use, Research Methods/ Statistical Methods,

Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin

A Framework for Globally Optimizing Mixed-Integer Signomial Programs

Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener, Floudas in J. Glob. Optim., 2012. doi:10.1007/s10898-012-9874-7), this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to ε-global optimality. This framework generalizes the GloMIQO strategies of (1) reformulating user input, (2) detecting special mathematical structure, and (3) globally optimizing the mixed-integer nonconvex program. Novel contributions of this paper include: flattening an expression tree towards term-based data structures; introducing additional nonconvex terms to interlink expressions; integrating a dynamic implementation of the reformulation-linearization technique into the branch-and-cut tree; designing term-based underestimators that specialize relaxation strategies according to variable bounds in the current tree node. Computational results are presented along with comparison of the computational framework to several state-of-the-art solvers. © 2013 Springer Science+Business Media New York