The Job Allocation/Assignment Problem has been a pivot of research for numerous well-known researchers around the world. However, as this problem is considered to be NP -complete, it is still not possible to find a deterministic number of steps that solves the said problem within a polynomial time. In this paradigm, the research community is focused to develop and design algorithms which produce results with minimum computational steps. As a result, without any doubt there is a great opportunity to examine the effectiveness of previously developed algorithms and compare them with solutions developed by other research scientists. In this paper, we have proposed a new variant of standard Genetic Algorithm (GA) referred to as Genetic Algorithm with Mutated-Crossover (GAMC) to solve this problem, implement it and analyze the results. The key point in this approach is to present the idea of Mutated-Crossover to avoid infeasible children generated by the crossover used in standard GA that has provided optimal results with lesser computational steps.