Influence maximisation has been an area of active research in recent years. This study aims to extend the fundamental influence maximisation problem (IMP) with respect to a set of target users on a social network. It is important to aim at the target users to speed up the rate of information diffusion and reduce the information diffusion cost. In doing so, the MITU algorithm was formulated and compared with state of the art algorithms. Publicly available datasets were used in validating the proposed algorithm. It was found that the MITU identified all target nodes while significantly lowering the information diffusion cost function (IDCF) by up to 79%. The influence overlap problem was equally identified in the heuristic algorithm where the seed set size was reduced by an average of six times. Furthermore, the random influencer selection identifies target nodes better than the betweenness and PageRank centralities. The findings could help organisations to reach target users on social media in the shortest cycle.