A new method, namely, block-minima method is proposed for finding all efficient solutions to a bi-objective assignment problem (BOAP) which differs from goal programming approach, fuzzy programming approach and two phase approach. A new type of a reduced BOAP from the given BOAP, namely, minima BOAP is introduced and then, two theorems are derived which connect solutions of the minima BOAP and efficient solutions of BOAP.An illustrative example is presented to clarify the idea of the proposed method. This method provides the necessary decision support to decision makers when   they are handling various types of assignment problems involving two objectives.

bi-objective assignment problem, efficient solution, level of satisfaction, minima BOAP, block-minima method.