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All Journal Sigma&Mu: Journal of Mathematics, Statistics and Data Science
AKANNI, Saheed Busayo
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Education Mathematics

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Operations Research Techniques for Cost Minimization in Transportation AKANNI, Saheed Busayo; Garba, M.K.; Abogunrin, O.O.; Noah, R.O.
Sigma&Mu: Journal of Mathematics Education, Mathematics, Statistics and Data Science Vol. 4 No. 1 (2026): March
Publisher : Balai Publikasi Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.56566/sigmamu.v4i1.619

Abstract

Optimizing the distribution of goods from multiple suppliers to multiple customers is a key challenge in supply chain management. This study compares the suitability of three classical methods for solving a 10-supplier by 15-customer transportation problem. The data used for the study were extracted from the 2023 record of a fertilizer-producing company in Nigeria, which has 10 outlets and 15 major distributors. The results revealed that the North-West Corner Method, although simple to apply despite the fact that it is cost-inefficient. Though the Minimum Cost Method behaved better in terms of efficiency, resulting to its focus on selecting low-cost routes. However, Vogel’s Approximation Method improved the allocations by adding cost-penalty factors. This led to the lowest overall cost of the three methods. Findings from the study showed that Vogel’s Approximation Method is a practical and effective way to get close-to-best solutions in the transportation problem. Within the framework of the paper, operational guidelines regarding logistics management and cost management were provided. This provision indicates that the choice of method is significant in repetitive decision-making in supply chain systems. This study provided guidelines for logistics and cost management, because it stressed that choosing the right method is essential for making repeated decisions in supply chain systems. Hence, the study concluded that if minimizing the cost of transportation is desired Vogel’s Approximation Method is recommended for supply chain system.
On Instrumental Variable Regression Method for Estimating Econometric Model Perturbed with Endogenous Variable AKANNI, Saheed Busayo; Garba, Mohammed Kabir; Osobase, Angela Abidemi
Sigma&Mu: Journal of Mathematics Education, Mathematics, Statistics and Data Science Vol. 4 No. 1 (2026): March
Publisher : Balai Publikasi Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.56566/sigmamu.v4i1.621

Abstract

Regression techniques are essential tools utilized to formulate, describe and evaluate econometric models. These techniques rely on some assumptions which, if one or more are violated the naive approach of estimating econometric models will be characterized with one problem or the other. Most often in real life situations, one or more of these assumptions cannot go unfulfilled while modelling econometric data. This study therefore, focuses on the consequences of violation of the assumption that error terms are linearly independent of explanatory variables in classical linear econometric model. For the Ordinary Least Squares (OLS) estimator to be sufficient, the expected value of the error term given the explanatory variable should be zero. And for OLS estimator to be consistent, the covariance between the error term and any of the explanatory variables should be zero. Endogeneity is one of the major challenges of econometric analyses. The effect of endogeneity is bias in estimates and therefore inducing the likelihood of committing the Types I and II errors more rapidly. To examine the behaviours of OLS estimators in the presence of endogeneity and compare its performances with Two-Stage Least Squares (2-SLS) as an alternative method of estimation, data were simulated in the environment of R statistical package in which endogeneity problem was infused into the data. It was discovered that relative to OLS, 2-SLS is consistent and less biased when modelling econometric data that are perturbed with endogeneity problem. Although, the 2-SLS might not be more efficient than the OLS under certain condition, but when there is problem of endogeneity in the model, the choice between OLS and 2-SLS depends on whether the Analyst is willing to trade-off efficiency for biasedness or vice versa in finite sample and asymptotically.
Co-Authors Abogunrin, O.O. Garba, M.K. Garba, Mohammed Kabir Noah, R.O. Osobase, Angela Abidemi