The aim of this paper is to combine the innovative concept of single valued neutrosophic sets and ordered semirings. It studies ordered semirings by the properties of their single valued neutrosphic subsets. In this regard, we define single valued neutrosophic $(m,n)$-ideals (SVN- $(m,n)$-ideals) of ordered semirings. First, we illustrate our new definition by non-trivial examples. Second, we study these SVN- $(m,n)$-ideals under different operations of SVNS. Finally, we find a relationship between the $(m,n)$-ideals of ordered semirings and level sets by finding a necessary and sufficient condition for an SVNS of an ordered semiring $R$ to be an SVN- $(m,n)$-ideal of $R$.