  There is intense effort into understanding the universal properties of
finite-time models of thermal machines---at optimal performance---such as
efficiency at maximum power, coefficient of performance at maximum cooling
power, and other such criteria. In this letter, a {\it global} principle
consistent with linear irreversible thermodynamics is proposed for the whole
cycle---without considering details of irreversibilities in the individual
steps of the cycle. This helps to express the total duration of the cycle as
$\tau \propto {\bar{Q}^2}/{\Delta_{\rm tot} S}$, where $\bar{Q}$ models the
effective heat transferred through the machine during the cycle, and
$\Delta_{\rm tot} S$ is the total entropy generated. By taking $\bar{Q}$ in the
form of simple algebraic means (such as arithmetic and geometric means) over
the heats exchanged by the reservoirs, the present approach is able to predict
various standard expressions for figures of merit at optimal performance, as
well as the bounds respected by them. It simplifies the optimization procedure
to a one-parameter optimization, and provides a fresh perspective on the issue
of universality at optimal performance, for small difference in reservoir
temperatures. As an illustration, we compare performance of a partially
optimized four-step endoreversible cycle with the present approach.
