NILA – An Innovative Technique for Optimality Testing and Optimizing a Solution in Assignment Problems

Abstract

In this research article, we propose a very simple and innovative iterative technique named NILA (equivalent name for the MOON in the classical Tamil language) for optimality testing and also optimization of a solution obtained by a method in assignment problems. The NILA technique has been tested on a number of near optimal and optimal solutions obtained for many balanced and unbalanced assignment problems by several other available methods. Testing results validate that the proposed NILA technique is the ideal one for testing the optimality of an obtained solution and also optimizing that solution, if that's not optimal. Thereby, we obtain the 'tested optimal' solutions to assignment problems. Another added advantage of the proposed technique is that it also generates the possible numbers of alternative optimal solutions to a given assignment problem, it they exist to the problem. Howsoever, we have to accept the reality that for the assignment problems the solutions generated by the 'Hungarian' method and the 'Mantra' technique are 'optimal by default' (not necessary to test its optimality). It is the design (divine!) specialty of the two methods.

MODA Method - A Revised Version: For Optimality Testing and Optimizing a Solution in Transportation Problems

“…The readers are requested to refer the article [6] due to Murugesan R. for the detailed algorithm of the MODA method.…”

“…In 2022, Murugesan R. [6] proposed an innovative method named MODA (Modified Allocation) which tests the optimality of a solution and also optimizes the solution, if it is not optimal. By our further research we have identified the extra efforts made in the MODA method to trace and consider all possible loops starting and ending at an identified basic cell and passing through a non-basic cell.…”

“…For the assignment problems, the optimal solutions generated by the NILA technique [8] are 'tested optimal' and that of generated by the 'Hungarian' method and the 'Mantra' technique [8] are 'default optimal' by nature. The latter two are the 'direct' methods which produce 'default optimal' solutions to assignment problems.…”

Transportation Problems with Twin Optimal Solutions

“…In 2022, Murugesan R. [4] proposed an innovative method named MODA (Modified Allocation) which tests the optimality of a solution and also optimizes the solution, if it is not optimal. By our further research we have identified the extra efforts made in the MODA method to trace and consider all possible loops starting and ending at an identified basic cell and passing through a non-basic cell.…”

“…Consequently, we have simplified this difficulty by introducing the new idea of Solution Improvement Loops only to consider. This resulted in a revised version of the existing MODA method [5].…”