Minimizing total tardiness for the order scheduling problem

This paper considers the order scheduling problem to minimize total tardiness. The system is composed of multiple machines, and each order consists of multiple components, with each component being manufactured on a dedicated machine (specified in advance). The completion time of each order is represented by the time at which all the components comprising the order are completed. The tardiness minimization is the performance objective of this paper. In the problem analysis, this paper first derives some dominance properties to determine the sequence of some orders, and then analyzes problem complexities for some special cases. Three heuristic algorithms are derived with a performance bound. Moreover, three lower bounds of objective are derived and tested along with the derived properties in a branch-and-bound scheme. The overall performances of the proposed property, branch-and-bound and heuristic algorithms are evaluated via numerical experiments.