This paper considers an order scheduling model to minimize the total weighted tardiness of orders. Each order requires different types of products. Each type of product is manufactured on its dedicated machine specified in advance. The completion time of each order is represented by the time when all the products belonging to the order are completed. The objective of this paper is to find the optimal production schedule minimizing the total weighted tardiness of a finite number of orders. In the problem analysis, we first derive a powerful solution property to determine the sequence of two consecutive orders. Moreover, two lower bounds of objective are derived and tested along with the derived property within a branch-and-bound scheme. Two efficient heuristic algorithms are also developed. The overall performances of the proposed property, branch-and-bound and heuristic algorithms are evaluated through various numerical experiments.