https://ir.unisa.ac.za/handle/10500/21068 2026-05-12T21:08:12Z 2026-05-12T21:08:12Z Tshuma, Sikhulile https://ir.unisa.ac.za/handle/10500/32292 2026-04-13T19:59:40Z 2025-12-31T00:00:00Z

Analysis of the monthly loadshedding and unplanned power outages in South Africa: mean and quantile regression count time series models Tshuma, Sikhulile Various nations within sub-Saharan Africa are currently facing different stages of loadshedding, with South Africa being of no exception to this trend. Loadshedding has been implemented as a strategy to manage electricity consumption during peak demand periods while allowing for increased usage during off-peak times. This study examines the monthly trends of loadshedding and unplanned power outages in South Africa, utilizing mean and quantile regression count time series models. Unplanned outages can arise from multiple factors, including maintenance activities on power lines, equipment malfunctions, adverse weather events, cable theft or emergencies such as accidents. Recurrent outages impede business activities, leading to a decrease in productivity and an increase in operational expenditures. Given the profound impact of power interruptions on economic stability and social welfare, this research aims to quantify and analyze the temporal trends and seasonal patterns of outages. By leveraging a comprehensive dataset, we first apply Poisson and negative binomial regression models to assess the average frequency and duration of outages, revealing significant trends and seasonal fluctuations. Following this, we employ quantile regression techniques to explore the distributional impacts of various factors, including socioeconomic variables and weather conditions, on the occurrence of outages. The analysis considers five quantiles—10th, 25th, 50th, 75th, and 90th. While negative binomial regression adequately captures average loadshedding dynamics, quantile regression proves superior in modelling extreme outage conditions that are most relevant for electricity system risk management and policy planning. The data was diagnosed to be highly correlated. Therefore penalised models were also employed. Our findings indicate that an increase in contracted demand, along with both planned and unplanned outages, correlates with a rise in the frequency of loadshedding. This suggests that loadshedding is influenced not only by heightened demand but also by failures in generation and distribution infrastructure. The thorough methodology adopted in this research deepens our understanding of the challenges surrounding power supply in South Africa, offering critical insights for policymakers and stakeholders to formulate targeted strategies aimed at mitigating the effects of loadshedding and enhancing energy resilience. Tackling these challenges necessitates substantial investment in infrastructure, a diversification of energy sources, and enhanced management of the electricity supply chain.

2025-12-31T00:00:00Z Okonta, Simon Dumbiri https://ir.unisa.ac.za/handle/10500/31436 2024-08-12T09:56:09Z 2023-02-01T00:00:00Z

Multi-objective stochastic programming for a multi-commodity multi-modal network flow model for flood disaster relief operations Okonta, Simon Dumbiri Abstract The increasing and alarming occurrence of disaster caused by flooding in Nigeria has necessitated this research work. There abound publications just describing the problem and calling for urgent help to reduce the effects on the citizenry but there appear no scientific/mathematical solutions offered to tackle the rescue operations. We therefore proposed a Mathematical Programming Model for disaster rescue operations. Our work is a Multi-Objective Stochastic Programming problem that seeks to minimize: (i) proportion of unmet demand satisfaction, (ii) total cost, and (iii) total shipping time. The study has root in practical problems facing the community. An empirical illustration of 2012 flood disaster was used as a case study. We considered four type of supply depots: National centre depot (NCD), Three Local Distribution Centres (LDC) and six points of Distribution (POD). The model comprised of vehicle types (a) air – helicopters and (b) land – trucks. Three basic types of emergency supply (item (l)): food, water and medical facilities were considered as relief materials. In the process, three basic scenarios: mild, medium, and severe situations were considered with associated probabilities: 0.25, 0.5 and 0.25 respectively. The work provided an adequate and efficient, mathematical model for quick response under emergency. This model proved effective and efficient in meeting the urgent needs of the devastated citizens who were involved in the disaster. It was efficient as there was a thin line between demand and demand met. The study equally proved that a minimized cost of about $1,016,673.37 could be used to carryout rescue operations. This figure becomes very necessary for the government, research agencies and other developmental agencies for the purpose of planning. The model by using the air and road transport modes and allowing direct and indirect transporting to the PODs saved time, resulting to many lives being saved.

2023-02-01T00:00:00Z Mudhombo, Innocent https://ir.unisa.ac.za/handle/10500/30398 2023-08-16T08:46:39Z 2022-01-01T00:00:00Z

Some variable selection and regularization methodological approaches in quantile regression with applications Mudhombo, Innocent The importance of robust variable selection and regularization as solutions to the collinearity influential high leverage points’ adverse effects in a quantile regression (QR) setting cannot be overemphasized, just as the diagnostic tools that identify these high leverage points. In the literature, researchers have dealt with variable selection and regularization quite extensively for penalized QR that generalizes the well-known least absolute deviation (LAD) procedure to all quantile levels. Unlike the least squares (LS) procedures, which are unreliable when deviations from the Gaussian assumptions (outliers) exist, the QR procedure is robust to Y-space outliers. Although QR is robust to response variable outliers, it is vulnerable to predictor space data aberrations (high leverage points and collinearity adverse effects), which may alter the eigen-structure of the predictor matrix. Therefore, in the literature, it is recommended that the problems of collinearity and high leverage points be dealt with simultaneously. In this thesis, we propose applying the ridge regression procedure (RIDGE), LASSO, elastic net (E-NET), adaptive LASSO, and adaptive elastic net (AE-NET) penalties to weighted QR (WQR) to mitigate the effects of collinearity and collinearity influential points in the QR setting. The new procedures are the penalized WQR procedures i.e., the RIDGE penalizedWQR (WQR-RIDGE), the LASSO penalizedWQR (WQR-LASSO), the E-NET penalized WQR (WQR-E-NET) and the adaptive penalized QR procedures (the adaptive LASSO penalized QR (QR-ALASSO) and adaptive E-NET penalized QR (QR-AE-NET procedures and their weighted versions). The penalized WQR procedures are based on the computationally intensive high-breakdown minimum covariance determinant (MCD) determined weights and the adaptive penalized QR procedures are based on the RIDGE penalized WQR (WQR-RIDGE) estimator based adaptive weights. Under regularity conditions, the adaptive penalized procedures satisfy oracle properties. Although adaptive weights are commonly based on the RIDGE regression (RR) estimator in the LS setting when regressors are collinear, this estimator may be plausible for the symmetrical distributions at the ℓ1-estimator (RQ at τ = 0.50) rather than at extreme quantile levels. We carried out simulations and applications to well-known data sets from the literature to assess the finite sample performance of these procedures in variable selection and regularization due to the robust weighting formulation and adaptive weighting construction. In the collinearityenhancing point scenario under the t-distribution, the WQR penalized versions outperformed the unweighted procedures with respect to average shrunken zero coefficients and correctly fitted models. Under the Gaussian and t-distributions, at predictor matrices with collinearity-reducing points, the weighted regularized procedures dominate the prediction performance (WQR-LASSO forms best). In the collinearity-inducing and collinearity-reducing points scenarios under the Gaussian distribution, the adaptive penalized procedures outperformed the non-adaptive versions in prediction. Under the t-distribution, a similar performance pattern is depicted as in the Gaussian scenario, although the performance of all models is adversely affected by outliers. Under the t-distribution, the QR-ALASSO andWQR-ALASSO procedures performed better in their respective categories.

2022-01-01T00:00:00Z Molebatsi, Malebo Tshegofatso https://ir.unisa.ac.za/handle/10500/29846 2024-05-22T12:31:48Z 2023-01-25T00:00:00Z

Handling of multicollinearity problem in modelling non-performing loans in Africa's portfolio data Molebatsi, Malebo Tshegofatso Non-performing loans (NPLs) are detrimental to profits in the banking sector. Predicting the level of NPLs using macroeconomic variables is vital in order to build mitigating actions for such scenarios to safeguard the profitability of the institution. Macroeconomic variables are susceptible to high correlations amongst each other, bringing about the problem of multicollinearity. Predicting in the presence of multicollinearity brings about unreliable and inefficient results. This study aims to find an optimal and efficient way of forecasting NPLs using Ordinary Least Squares (OLS), Ridge Regression (RR) and Principal Component Analysis (PCA) while correcting for multicollinearity. To do this, NPL data from bank X was attained, along with multiple macroeconomic variables, specifically for Kenya and Nigeria. It is critical to assess the determinants of NPLs so that effective and efficient policies can be deployed to prevent the rising trajectory of NPLs. To minimize the risks of using expert judgement, it is necessary to consider effective statistical methods for predicting NPLs. The benefits accrued from such methods include (1) minimum collection costs incurred when a loan defaults, such as less phone calls urging the customers to pay, less litigation costs when trying to recover the assets, less shortfalls incurred when disposing off the assets that have been repossessed and less auction sales if the assets have to be auctioned, to mention a few; (2) correct pricing for the risk; (3) be able to differentiate between high-risk and low-risk accounts based on the macroeconomic factors; and (4) be more prudent in granting credit to minimize losses and maximise profits. This study considers the OLS, RR and PCA in modeling the NPLs data from bank X. The results showed that multicollinearity exists for most variables. Some of the variables did not conform to the assumptions of the OLS. The models for OLS for both countries were significant, while some of the variables displayed illogical outcomes, possibly due to multicollinearity among the predictor variables. RR method solved for multicollinearity and had a relatively predictive power for Nigeria data and not Kenya, whereas PCA solved for multicollinearity and introduced a positive factor in data reduction and had a relatively better predictive power. The mean square errors (MSEs) for PCA and RR were lower than that of OLS. A key limitation was inadequate data from the banking sector due to sensitivity issue. We conclude that the data can be expanded, and the number of variables reduced so that prediction can be more precise. Further work using other methods such as GARCH can be explored to improve the prediction of the NPLs in the midst of multicollinearity.

2023-01-25T00:00:00Z