A Probabilistic Framework for Evaluating Efficiency Gains in Vogel's Approximation Method

Transportation involves various uncertainties in determining the most efficient method for transporting goods. When a company has supply and destination points, or a supplier has specific demands, achieving an optimized balance becomes crucial. This task becomes more challenging when there is an imbalance between demand and supply, requiring an effective method to measure and address uncertainty. Probability theory provides a reliable framework for quantifying these uncertainties. Basic feasible solutions to transportation problems can be obtained using methods such as the North-West Corner Method, Least Cost Method, Row (Column) Minima Method, or Vogel’s Approximation Method. Among these, Vogel’s Approximation Method is widely recognized for its effectiveness in yielding superior results. This paper proposes a novel approach that integrates probability analysis into transportation problems, emphasizing the derivation of the probability distribution function (PDF) for Vogel's Approximation Method. The derived results not only enhance understanding but also offer valuable insights to improve decision-making processes within the transportation domain.