The problem of maximizing total early work in a two-machine flow-shop is known to be NP-hard, for which an O(n²d²) dynamic program and an O(n⁴⁄ε²) FPTAS exist in the literature. In this paper, we present new optimality properties, which pave the base for an O(nd²) time dynamic programming algorithm and an O(n³⁄ε²) time FPTAS. We further generalize the problem to a distributed flow shop consisting of m parallel two-machine flow-shops. We develop an O(mn(2d)³m) time dynamic programming algorithm and an O(mn(4n/∈)³m time FPTAS.