Implications of recent Australian wheat industry developments for overseas and domestic prices

This study is motivated by the proposition that the objectives of the AWB Ltd have changed since semi-privatisation of the Australian Wheat Board under the Wheat Marketing Act, 1989. Conceptualising this change of objectives as a shift from revenue maximization to profit maximization, this study examines the impact of such a change on the pricing policies of a multi-market price-setting firm. More specifically, this paper investigates, using two hypothetical objective functions, a risk averse AWB�s price-setting behaviour in an �overseas� and a �domestic� market in response to recent wheat industry developments. In the analysis these developments manifest themselves as differing price elasticities, differing transport costs and uncertain demand functions, and their implications particularly for the prices paid by domestic consumers are explored.

Modeling small-scale dairy farms in central Mexico using multi-criteria programming

Milk supply from Mexican dairy farms does not meet demand and small-scale farms can contribute toward closing the gap. Two multi-criteria programming techniques, goal programming and compromise programming, were used in a study of small-scale dairy farms in central Mexico. To build the goal and compromise programming models, 4 ordinary linear programming models were also developed, which had objective functions to maximize metabolizable energy for milk production, to maximize margin of income over feed costs, to maximize metabolizable protein for milk production, and to minimize purchased feedstuffs. Neither multicriteria approach was significantly better than the other; however, by applying both models it was possible to perform a more comprehensive analysis of these small-scale dairy systems. The multi-criteria programming models affirm findings from previous work and suggest that a forage strategy based on alfalfa, rye-grass, and corn silage would meet nutrient requirements of the herd. Both models suggested that there is an economic advantage in rescheduling the calving season to the second and third calendar quarters to better synchronize higher demand for nutrients with the period of high forage availability.

Entropy application to improve construction finance decisions

In financial decision-making processes, the adopted weights of the objective functions have significant impacts on the final decision outcome. However, conventional rating and weighting methods exhibit difficulty in deriving appropriate weights for complex decision-making problems with imprecise information. Entropy is a quantitative measure of uncertainty and has been useful in exploring weights of attributes in decision making. A fuzzy and entropy-based mathematical approach is employed to solve the weighting problem of the objective functions in an overall cash-flow model. The multiproject being undertaken by a medium-size construction firm in Hong Kong was used as a real case study to demonstrate the application of entropy. Its application in multiproject cash flow situations is demonstrated. The results indicate that the overall before-tax profit was HK$ 0.11 millions lower after the introduction of appropriate weights. In addition, the best time to invest in new projects arising from positive cash flow was identified to be two working months earlier than the nonweight system.

Application of the entropy technique and genetic algorithms to construction site layout planning of medium-size projects

Genetic algorithms (GAs) have been introduced into site layout planning as reported in a number of studies. In these studies, the objective functions were defined so as to employ the GAs in searching for the optimal site layout. However, few studies have been carried out to investigate the actual closeness of relationships between site facilities; it is these relationships that ultimately govern the site layout. This study has determined that the underlying factors of site layout planning for medium-size projects include work flow, personnel flow, safety and environment, and personal preferences. By finding the weightings on these factors and the corresponding closeness indices between each facility, a closeness relationship has been deduced. Two contemporary mathematical approaches - fuzzy logic theory and an entropy measure - were adopted in finding these results in order to minimize the uncertainty and vagueness of the collected data and improve the quality of the information. GAs were then applied to searching for the optimal site layout in a medium-size government project using the GeneHunter software. The objective function involved minimizing the total travel distance. An optimal layout was obtained within a short time. This reveals that the application of GA to site layout planning is highly promising and efficient.

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.