  We consider random walkers searching for a target in a bounded
one-dimensional heterogeneous environment, in the interval $[0,L]$, where
diffusion is described by a space-dependent diffusion coefficient $D(x)$.
Boundary conditions are absorbing at the position of the target (set at $x=0$)
and reflecting at the border $x=L$. We calculate and compare the estimates of
efficiency $\varepsilon_1=\langle 1/ t\rangle$ and $\varepsilon_2=1/\langle t
\rangle$. For the Stratonovich framework of the multiplicative random process,
both measures are analytically calculated for arbitrary $D(x)$. For other
interpretations of the stochastic integrals (e.g., It\^o and anti-It\^o), we
get general results for $\varepsilon_2$, while $\varepsilon_1$ is obtained for
particular forms of $D(x)$. The impact of the diffusivity profile on these
measures of efficiency is discussed. Symmetries and peculiar properties arise
when the search starts at the border ($x_0=L$), in particular, heterogeneity
spoils the efficiency of the search within the Stratonovich framework, while
for other interpretations the searcher can perform better in certain
heterogeneous diffusivity profiles.
