Abstract
In this paper, we show how the Yule-Walker type difference equations for higher order moments and cumulants, recently derived for certain types of bilinear time series models, the BL(p,0,p,1) models, by Sesay and Subba Rao (1988, 1991), could be used for tentative identification of the order of the model. The technique we use for identification is canonical correlation analysis, carried out between the linear combination of the observations and linear combination of higher powers of the observations. The methods are illustrated with real and simulated examples.

Abstract

Abstract
In this paper, a fuzzy model for power system operation is presented. Uncertainties in loads and generations are modelled as fuzzy numbers. System behavior under known (while uncertain) injections is dealt with by a DC fuzzy power flow model. System optimal (while uncertain) operation is calculated with linear programming procedures where the problem nature and structure allows some efficient techniques such as Dantzig Wolfe decomposition and dual simplex to be used. Among the results, one obtains a fuzzy cost value for system operation and possibility distributions for branch power flows and power generations. Some risk analysis is possible, as system robustness and exposure indices can be derived and hedging policies can be investigated.

Abstract
The power flow is the fundamental tool for the study of power systems. The data for this problem are subject to uncertainty. This paper uses interval arithmetic to solve the power flow problem. Interval arithmetic takes into consideration the uncertainty of the nodal information, and is able to provide strict bounds for the solutions to the problem: all possible solutions are included within the bounds given by interval arithmetic. Results are compared with those obtainable by Monte Carlo simulations and by the use of stochastic power flows. Object oriented programming techniques make it possible to use interval arithmetic with minimal modifications to existing software. However, to reduce the conservatism inherent in all interval curtest computations, the paper describes an iterative method used to obtain the "hull" of the solution set.

Abstract

Abstract
We consider the formulation of non-preemptive single machine scheduling problems using time-indexed variables. This approach leads to very large models, but gives better lower bounds than other mixed integer programming formulations. We derive a variety of valid inequalities, and show the role of constraint aggregation and the knapsack problem with generalised upper bound constraints as a way of generating such inequalities. A cutting plane/branch-and-bound algorithm based on these inequalities has been implemented. Computational experience on small problems with 20/30 jobs and various constraints and objective functions is presented.