Abstract:
The Assignment problem represents a specific type of linear programming
transportation problem. The goal is to allocate a specific number of resources to an
equal number of activities while minimizing costs or maximizing profits. It’s crucial to
address this topic in real life situations for example production planning, particular job
tasks, economic etc. In our analysis, we have examined both the conventional method
(Hungarian method) and the past proposed methods. After thoroughly examining these
methods, I have put forward a novel alternative approach for directly determining an
optimal solution for an Assignment problem. We tested the newly proposed method
using several numerical examples and compared the results with the standard method.
The first and second step row reduction and column reduction in the proposed method
are similar to the Hungarian method beginning steps. After that I introduced some new
steps different from the Hungarian method to solve Assignment problems in Linear
Programming. The comparison results indicate that both methods produce the same
optimal solution. However, the alternative method achieved the optimal solution in
fewer steps, results time saving. The best thing about this approach is that it only
involves basic arithmetic and logical computations. The data was analyzed and resolved
using statistical software “TORA”, yielding comparable results. The numerical
examples clearly demonstrate the effectiveness of the new method. This new method
ensures that the solution adheres to the constraints of linear programming while offering
enhanced scalability and applicability to a wider range of real-world problems, such as
job scheduling and transportation logistics. This novel method not only improves
computational efficiency but also enhances flexibility, making it applicable to both
balanced and unbalanced assignment problems.
