A need for an optimal solution for a given mathematical model is well known and many solution approaches have been developed to identify efficiently an optimal solution in a given situation. For example, one such class of mathematical models with industrial applications have been classified as mathematical programming models (MPM). The main idea behind these models is to find the optimal solution described by those models. However, the same is not true for a ‘K’ number of ranked optimal solutions, where K≥2. Mathematically, the K^th best solution, K≥2, deals with determination of the second, third, fourth or in general the K^th best solution. This K^th best solution K≥ 2, suddenly becomes much more demanding with respect to computational requirements, which increases with the increase in the value of K. This paper first identifies difficulties associated with determination of ranked solutions and later develops a random search method to find ranked optimal solutions in the case of an assignment problem. We test the efficiency of the proposed approach by executing the random search method on a number of different size assignment problems.
The paper has submitted to the Journal of the Operations Research Society of China.