Towards testing a new first-order decision making model for the procurement of public sector major infrastructure

Given global demand for new infrastructure, governments face substantial challenges in funding new infrastructure and simultaneously delivering Value for Money (VfM). As background to this challenge, a brief review is given of current practice in the selection of major public sector infrastructure in Australia, along with a review of the related literature concerning the Multi-Attribute Utility Approach (MAUA) and the effect of MAUA on the role of risk management in procurement selection. To contribute towards addressing the key weaknesses of MAUA, a new first-order procurement decision making model is mentioned. A brief summary is also given of the research method and hypothesis used to test and develop the new procurement model and which uses competition as the dependent variable and as a proxy for VfM. The hypothesis is given as follows: When the actual procurement mode matches the theoretical/predicted procurement mode (informed by the new procurement model), then actual competition is expected to match optimum competition (based on actual prevailing capacity vis-à-vis the theoretical/predicted procurement mode) and subject to efficient tendering. The aim of this paper is to report on progress towards testing this hypothesis in terms of an analysis of two of the four data components in the hypothesis. That is, actual procurement and actual competition across 87 road and health major public sector projects in Australia. In conclusion, it is noted that the Global Financial Crisis (GFC) has seen a significant increase in competition in public sector major road and health infrastructure and if any imperfections in procurement and/or tendering are discernible, then this would create the opportunity, through the deployment of economic principles embedded in the new procurement model and/or adjustments in tendering, to maintain some of this higher level post-GFC competition throughout the next business cycle/upturn in demand including private sector demand. Finally, the paper previews the next steps in the research with regard to collection and analysis of data concerning theoretical/predicted procurement and optimum competition.

Delivering value for money in the procurement of public sector major infrastructure : a new first-order decision making model

The significant challenge faced by government in demonstrating value for money in the delivery of major infrastructure resolves around estimating costs and benefits of alternative modes of procurement. Faced with this challenge, one approach is to focus on a dominant performance outcome visible on the opening day of the asset, as the means to select the procurement approach. In this case, value for money becomes a largely nominal concept and determined by selected procurement mode delivering, or not delivering, the selected performance outcome, and notwithstanding possible under delivery on other desirable performance outcomes, as well as possibly incurring excessive transaction costs. This paper proposes a mind-set change in this particular practice, to an approach in which the analysis commences with the conditions pertaining to the project and proceeds to deploy transaction cost and production cost theory to indicate a procurement approach that can claim superior value for money relative to other competing procurement modes. This approach to delivering value for money in relative terms is developed in a first-order procurement decision making model outlined in this paper. The model developed could be complementary to the Public Sector Comparator (PSC) in terms of cross validation and the model more readily lends itself to public dissemination. As a possible alternative to the PSC, the model could save time and money in preparation of project details to lesser extent than that required in the reference project and may send a stronger signal to the market that may encourage more innovation and competition.

Developing a research method to test a new first-order decision making model for the procurement of public sector major infrastructure

Given global demand for new infrastructure, governments face substantial challenges in funding new infrastructure and simultaneously delivering Value for Money (VfM). The paper begins with an update on a key development in a new early/first-order procurement decision making model that deploys production cost/benefit theory and theories concerning transaction costs from the New Institutional Economics, in order to identify a procurement mode that is likely to deliver the best ratio of production costs and transaction costs to production benefits, and therefore deliver superior VfM relative to alternative procurement modes. In doing so, the new procurement model is also able to address the uncertainty concerning the relative merits of Public-Private Partnerships (PPP) and non-PPP procurement approaches. The main aim of the paper is to develop competition as a dependent variable/proxy for VfM and a hypothesis (overarching proposition), as well as developing a research method to test the new procurement model. Competition reflects both production costs and benefits (absolute level of competition) and transaction costs (level of realised competition) and is a key proxy for VfM. Using competition as a proxy for VfM, the overarching proposition is given as: When the actual procurement mode matches the predicted (theoretical) procurement mode (informed by the new procurement model), then actual competition is expected to match potential competition (based on actual capacity). To collect data to test this proposition, the research method that is developed in this paper combines a survey and case study approach. More specifically, data collection instruments for the surveys to collect data on actual procurement, actual competition and potential competition are outlined. Finally, plans for analysing this survey data are briefly mentioned, along with noting the planned use of analytical pattern matching in deploying the new procurement model and in order to develop the predicted (theoretical) procurement mode.

A new first-order decision-making model for the procurement of public sector infrastructure: Procedures and Testing

Given global demand for new infrastructure, governments face substantial challenges in funding new infrastructure and delivering Value for Money (VfM). As part of the background to this challenge, a critique is given of current practice in the selection of the approach to procure major public sector infrastructure in Australia and which is akin to the Multi-Attribute Utility Approach (MAUA). To contribute towards addressing the key weaknesses of MAUA, a new first-order procurement decision-making model is presented. The model addresses the make-or-buy decision (risk allocation); the bundling decision (property rights incentives), as well as the exchange relationship decision (relational to arms-length exchange) in its novel approach to articulating a procurement strategy designed to yield superior VfM across the whole life of the asset. The aim of this paper is report on the development of this decisionmaking model in terms of the procedural tasks to be followed and the method being used to test the model. The planned approach to testing the model uses a sample of 87 Australian major infrastructure projects in the sum of AUD32 billion and deploys a key proxy for VfM comprising expressions of interest, as an indicator of competition.

The renormalization group and the implicit function theorem for amplitude equations

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

Adaptive depth estimation in image based visual servo control of dynamic systems

This paper considers the question of designing a fully image based visual servo control for a dynamic system. The work is motivated by the ongoing development of image based visual servo control of small aerial robotic vehicles. The observed targets considered are coloured blobs on a flat surface to which the normal direction is known. The theoretical framework is directly applicable to the case of markings on a horizontal floor or landing field. The image features used are a first order spherical moment for position and an image flow measurement for velocity. A fully non-linear adaptive control design is provided that ensures global stability of the closed-loop system. © 2005 IEEE.

Testing second order cyclostationarity in the squared envelope spectrum of non-white vibration signals

Cyclostationary models for the diagnostic signals measured on faulty rotating machineries have proved to be successful in many laboratory tests and industrial applications. The squared envelope spectrum has been pointed out as the most efficient indicator for the assessment of second order cyclostationary symptoms of damages, which are typical, for instance, of rolling element bearing faults. In an attempt to foster the spread of rotating machinery diagnostics, the current trend in the field is to reach higher levels of automation of the condition monitoring systems. For this purpose, statistical tests for the presence of cyclostationarity have been proposed during the last years. The statistical thresholds proposed in the past for the identification of cyclostationary components have been obtained under the hypothesis of having a white noise signal when the component is healthy. This need, coupled with the non-white nature of the real signals implies the necessity of pre-whitening or filtering the signal in optimal narrow-bands, increasing the complexity of the algorithm and the risk of losing diagnostic information or introducing biases on the result. In this paper, the authors introduce an original analytical derivation of the statistical tests for cyclostationarity in the squared envelope spectrum, dropping the hypothesis of white noise from the beginning. The effect of first order and second order cyclostationary components on the distribution of the squared envelope spectrum will be quantified and the effectiveness of the newly proposed threshold verified, providing a sound theoretical basis and a practical starting point for efficient automated diagnostics of machine components such as rolling element bearings. The analytical results will be verified by means of numerical simulations and by using experimental vibration data of rolling element bearings.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Electron diffusion and back reaction in dye-sensitized solar cells : the effect of nonlinear recombination kinetics

The electron collection efficiency in dye-sensitized solar cells (DSCs) is usually related to the electron diffusion length, L = (Dτ)^1/2, where D is the diffusion coefficient of mobile electrons and τ is their lifetime, which is determined by electron transfer to the redox electrolyte. Analysis of incident photon-to-current efficiency (IPCE) spectra for front and rear illumination consistently gives smaller values of L than those derived from small amplitude methods. We show that the IPCE analysis is incorrect if recombination is not first-order in free electron concentration, and we demonstrate that the intensity dependence of the apparent L derived by first-order analysis of IPCE measurements and the voltage dependence of L derived from perturbation experiments can be fitted using the same reaction order, γ ≈ 0.8. The new analysis presented in this letter resolves the controversy over why L values derived from small amplitude methods are larger than those obtained from IPCE data.

Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy

Robust designs for Poisson regression models

We consider the problem of how to construct robust designs for Poisson regression models. An analytical expression is derived for robust designs for first-order Poisson regression models where uncertainty exists in the prior parameter estimates. Given certain constraints in the methodology, it may be necessary to extend the robust designs for implementation in practical experiments. With these extensions, our methodology constructs designs which perform similarly, in terms of estimation, to current techniques, and offers the solution in a more timely manner. We further apply this analytic result to cases where uncertainty exists in the linear predictor. The application of this methodology to practical design problems such as screening experiments is explored. Given the minimal prior knowledge that is usually available when conducting such experiments, it is recommended to derive designs robust across a variety of systems. However, incorporating such uncertainty into the design process can be a computationally intense exercise. Hence, our analytic approach is explored as an alternative.