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A decomposition theory which includes Sidney's decomposition theory as a special case is constructed by using new fundamentals such as a dominance relation which solves a sequencing problem without precedence constraints, a unique interpretation rule which restricts application of the dominance relation and a composite job (for a sequence of jobs) which plays a central role in developing a new decomposition algorithm. It applies to all problems involved in Sidney's theory. Moreover, it involvesdoi:10.1016/0166-218x(87)90012-6 fatcat:sxpefwffafgxbjsn32h75jisia