A decomposition theory based on a dominance relation and composite jobs

Yasuki Sekiguchi
1987 Discrete Applied Mathematics  
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 involves
more » ... a problem which Sidney's theory does not involve, i.e., a class of problems equivalent to a one-machine minimum total weighted-completion time problem. The theory shows also that a variety of tie-breaking rules can be used in the decomposition algorithm, though it was uniquely determined in the previous theory. 0166-218X/87/$3.50 0 1987, Elsevier Science Publishers B.V. (North-Holland)
doi:10.1016/0166-218x(87)90012-6 fatcat:sxpefwffafgxbjsn32h75jisia