Task assignment to any computing system is a most interesting and demandable research problem. Various methodologies and techniques are available in the literature to provide the solution of such problems. The assignment problems in distributed computing systems are one of major factor to determine the performance of such systems. The Assignment problem is one of the main problems while assigning jobs to the worker or machines to the worker to get an optimal solution. The problem mentioned in this paper suggests an exhaustive search approach to the unbalanced assignment problem through partial bound optimization. The bound is based on partial bound values. This paper contains the devised technique, computational algorithm of the approach and its implementation. This study is capable to deal all such real life situations where the Jobs (tasks) are more than the number of Machine (processors). The obtain solution is under consideration that all the jobs are allotted on the available machines in an optimum way. Finally numerical example and its algorithm have been given to show the efficiency of the proposed techniques.

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The recruitment process in any departments or organizations is usually decided by traditional criteria. Lacking of theoretical basis, it is often difficult to achieve the desired result. In this paper we use triangular fuzzy number in delegation of recruitment process with the help of modified approach of assignment. For finding the optimal assignment, we make the balanced assignment problem, if unbalanced is given, then it is transformed into crisp assignment problem in linear programming by using the Robust’s ranking method. Finally the solution is obtained by modified method of assignment. This method is easier than the existing technique i.e. easier than the Hungarian Method and by this approach the numbers of iterations are reduced so that time taken by this method is less than the Hungarian method

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