A study on Simulated Annealing method for reducing the transportation cost using the hybrid MODI method

Abstract

In this study, the goal is to reduce the transportation cost by integrating the MODI method with Simulated Annealing (SA). The process begins with a description of the procedure to produce an initial feasible solution by incorporating heuristic methods, such as Vogel's Approximation Method (VAM), thereby ensuring that these solutions follow supply, demand, and capacity constraints. The MODI method can now be implemented in refining this solution for verification purposes and to identify if it is optimal or not, using dual variables and opportunity costs. At this stage, Simulated Annealing is applied to further improve the solution with the generation and evaluation of neighbouring solutions iteratively so that the values of transportation flows are at their minimum values and there may be a need to minimize transportation costs to reduce them to their minimum values. In this way, the integrated approach effectively and efficiently optimizes tasks.