Customer order scheduling to minimize total weighted completion time

In this paper we study the scheduling problem in which each customer order consists of several jobs of different types, which are to be processed on m facilities. Each facility is dedicated to the processing of only one type of jobs. All jobs of an order have to be delivered to the customer at the same time. The objective is to schedule all the orders to minimize the total weighted order completion time. While the problem has been shown to be unary NP-hard, we develop a heuristics to tackle the problem and analyze its worst-case performance.