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 problemsý. ýInput 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 approachý. ýIn this wayý, ýsome researchers have used a whitening technique to solve the grey assignment problemý. ýSince the whitening technique only provides a crisp equivalent model and does not reflect the evolutionary characteristics of a grey setý, ýit cannot keep the uncertainty properties in an interval involving the optimal solutioný. ýBased on these shortcomingsý, ýin this paper a new direct approach is introduced to solve linear assignment problem in grey environmentsý. ýFor preparing the mentioned methodý, ýsome theoretical results are given to support the methodologyý. ýFinallyý, ýa numerical example will be solved to test the validity of the proposed methodý. ýBased on the suggested methodologyý, ýwe emphasize that the same approach can be used whenever any linear programming model is formulated in grey environments.