A new method namely, block-dripping method is proposed for finding a set of all efficient solutions to a bottleneck bi-criteria transportation problem which provides more efficient solutions than other existing methods [1, 14, 15] and the best compromise solution to the problem. Numerical example has been provided to illustrate the solution procedure. The proposed technique provides the necessary decision support to the decision makers, while they are handling time-oriented logistic problems having two objectives. Mathematics Subject Classification: 90C08, 90C90. © 2012 Springer-Verlag.