A New Approach for Solving Grey Assignment Problems

Linear assignment problem is one of the most important practical models in the literature of linear programming problems‎. ‎Input data in the cost matrix of the linear assignment problem are not always crisp and sometimes in the practical situations is formulated by the grey systems theory approach‎. ‎In this way‎, ‎some researchers have used a whitening technique to solve the grey assignment problem‎. ‎Since the whitening technique only provides a crisp equivalent model and does not reflect the evolutionary characteristics of a grey set‎, ‎it cannot keep the uncertainty properties in an interval involving the optimal solution‎. ‎Based on these shortcomings‎, ‎in this paper a new direct approach is introduced to solve linear assignment problem in grey environments‎. ‎For preparing the mentioned method‎, ‎some theoretical results are given to support the methodology‎. ‎Finally‎, ‎a numerical example will be solved to test the validity of the proposed method‎. ‎Based on the suggested methodology‎, ‎we emphasize that the same approach can be used whenever any linear programming model is formulated in grey environments.