In many automated manufacturing environments, particularly flowlines and flexible manufacturing systems (FMSs), machines are arranged along a straight material-handling track with a material-handling device moving jobs from one machine to another. These layouts are referred to as row machine layouts. In this paper we study the row layout problem (RLP) under the design objective of minimizing the total backtracking distance of the material-handling device, which is an NP-complete problem. We propose the use of a dynamic programming algorithm for its solution. A special case of the problem, usually encountered in flexible manufacturing cells and which can be solved with a polynomial procedure, is also discussed. For the equidistance case (i.e., successive candidate locations are in equal distances), we formulate the problem as an integer linear program. The use of standard mathematical programming codes can efficiently solve this formulation.