Given an n-vertex outerplanar graph G, we consider the problem of arranging the vertices of G on a line such that no two edges cross and various cost measures are minimized. We present efficient algorithms for generating layouts in which every edge (i,j) of G does not exceed a given bandwidth b(i,j), the total edge length and the cutwidth of the layout is minimized, respectively. We present characterizations of optimal layouts which are used by the algorithms. Our algorithms combine sublayouts by solving two processor scheduling problems. Although these scheduling problems are NP-complete in general, the instances generated by our algorithms are polynomial in n.