A computational study on the number of iterations to solve the transportation problem

Abstract

The Transportation Problem is one of the classical problems in Operations Research. The development of more powerful personal computers in the past years made it possible to solve larger problems, creating huge opportunities of applications. The MODI method is the most cited method in the literature to solve the Transportation Problem. This method requires an initial basic feasible solution and for this purpose the literature often presents the Northwest Corner Rule, the Lest Cost Method and the Vogel Method. This paper aims to study these three different methods and analyze the number of iterations necessary to reach the optimal solution when they are used.

Mathematical Programming and Solution Approaches for Transportation Optimisation in Supply Network

“…The authors, by deliberately modifying the cost matrix before applying the northwest corner method, proved that the proposed solution positively influences the effectiveness of the method by reducing the number of iterations performed. In [27], an analysis was made of the number of steps necessary to determine the optimal transport problem using the northwest corner method, the minimum cost method, and the VAM method. The subject of the research were transport cost matrices with dimensions of 5 × 5, 10 × 10, 20 × 20, 40 × 40, 80 × 80, 160 × 160, 320 × 320, while the values of supply and demand were generated in a random way from a set of numbers from 5 to 50,000.…”

Decision-Making for the Bakery Product Transportation using Linear Programming

“…Gumuskaya et al [19] emphasize the significance of coordination and conflicting incentives in logistics operations, particularly concerning the emergence of congestion. Loch & Silva [20] examined the concept of degeneracy in initial simple feasible solutions for transportation issues. They discovered that the preliminary simple solutions obtained were not necessarily fundamental and required comparison with degenerated variables.…”