Convex hull algorithms are well known. However, in my case, the goal is slightly modified:
Given $N$ points in a plane, construct convex polygon with minimal area so that it contains all points, and there is no point that is closer than given distance $d$ from polygon edges, and number of vertices of such polygon is the same as number of vertices of the convex hull of given points.
In other words, given $N$ sheep:
... find the fence:
(Sheep can be considered points, but $d$ is still greater than $0$.)
Maybe you can take some ideas from the following paper
RAPPAPORT, David. A convex hull algorithm for discs, and applications. Computational Geometry, 1992, 1.3: 171-187.
where you model each sheep with a circle of radius $d$.
However the paper does not directly solve your problem because the convex hull described in the paper is composed by line segments and arcs of a circle.