The assignment problem (AP) is a particular case of the transportation problem, in which the objective is to assign a number of resources to an equal number of activities at an overall minimum cost (or overall maximum profit). It has great implication in the real physical world. In 2012, Hadi Basirzadeh introduced a new approach to APs namely, Ones Assignment Method, for solving a wide range of such problems. This method is based on creating ones in the assignment matrix and then tries to find a complete assignment to these ones. In 2013, Ghadle K.P. and Muley Y.M. presented a new method namely, Revised Ones Assignment (ROA) method for solving wide range of APs, which is different from the preceding method. This method is also based on creating some ones in the assignment matrix and then tries to achieve exact optimal assignment, which is same as that of Hungarian method, in terms of ones. In 2014, M. Khalid et al. [7] introduced the New Improved Ones Assignment (NIOA) method, which overcomes the drawbacks of older algorithms and outperforms them by a considerable margin. In this paper, we have tried to reveal that the presented ROA method as well as the NIOA method for solving APs do not present optimal solution at all times. We give examples of the AP where the ROA and the NIOA methods fail to find their optimal solution. Also, a new set of rules, called ME rules, for covering all the 1s in a resultant assignment matrix by drawing minimum number of lines and also for testing the conditions for the achievement of a complete assignment are presented in this paper.
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