The Shilling Bottleneck heuristic decomposes the Job Shop problem into a series of One Machine Sequencing Problems (OMSPs) with release and due dates, precedence constraints and the minimization of maximum lateness objective. It is well known that delayed precedence constraints may exist between two operations to be performed on the same machine. We identify a new type of precedence constraint that may exist in an OMSP between the predecessor of an operation and the successor of another. The premise that an OMSP captures the sequencing relationships on other machines in the release and due date information is not valid when such precedence constraints exist. A modification of the OMSP representation is proposed based on a generalized lateness objective defined on a due window. The implications of such a representation for the OMSP solution procedure have been explored.