Considerable recent theoretical and experimental effort has been devoted to the study of quantum criticality and novel phases of antiferromagnetic heavy-fermion metals. In particular, quantum phase transitions have been discovered in heavy-fermion compounds with geometrical frustration. These developments have motivated us to study the competition between the Ruderman-Kittel-Kasuya-Yosida and Kondo interactions on the Shastry-Sutherland lattice. We determine the zero-temperature phase diagram as a function of magnetic frustration and Kondo coupling within a slave-fermion approach. Pertinent phases include the valence bond solid and heavy Fermi liquid. In the presence of antiferromagnetic order, our zero-temperature phase diagram is remarkably similar to the global phase diagram proposed earlier based on general grounds. We discuss the implications of our results for the experiments on Yb2Pt2Pb and related compounds.