International Journal For Multidisciplinary Research

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Linear Programming Approaches to Transportation Problems: An Application of Gomory's Cutting Plane Method

Author(s) Dr. RAJESH SHRIVASTAVA, Mr. DHIRAJ DWIVEDI, Anita Mandloi, Jyoti Panthi
Country India
Abstract This study investigates the optimization of a transportation problem involving three supply points and four demand centers by transforming it into a linear programming problem. The primary focus is to apply Gomory’s Cutting Plane Method to obtain an optimal integer solution and compare it with the solution derived using the Vogel Approximation Method (VAM). The research begins by formulating the transportation problem in a linear programming framework, followed by the application of Gomory’s method, which is particularly useful for integer programming problems where fractional solutions are not feasible. The Vogel Approximation Method, a widely used heuristic for generating good initial feasible solutions in transportation problems, serves as the comparative benchmark. Results indicate that while VAM provides quick and reasonably effective solutions, Gomory’s Cutting Plane Method achieves an exact optimal integer solution. The comparative analysis highlights the strengths and limitations of each method in terms of solution quality and computational effort. The study provides valuable insights for decision-makers in logistics and supply chain management seeking efficient and accurate optimization techniques for distribution problems.
Keywords Linear Programming Problem, Transportation Problem, Gomory's Cutting Plane Method, Vogel Approximation Method
Field Mathematics
Published In Volume 7, Issue 6, November-December 2025
Published On 2025-11-12
DOI https://doi.org/10.36948/ijfmr.2025.v07i06.60211
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