An efficiency frontier is piecewise linear when the underlying production function is approximated through interconnected linear segments. The basic DEA models are all piecewise linear. See Chames et al (1981) for implications. [Chames A, Cooper W W and Rhodes E (1981), ‘Evaluating program and managerial efficiency: an application of data envelopment analysis to program follow through’, Mgmt. Sci., 6, pp 668-697.]