Machine scheduling with deliveries to multiple customer locations

One important issue in production and logistics management is the coordination of activities between production and delivery. In this paper, we develop a single-machine scheduling model that incorporates routing decisions of a delivery vehicle which serves customers at different locations. The objective is to minimize the sum of job arrival times. The problem is NP-hard in the strong sense in general. We develop a polynomial time algorithm for the case when the number of customers is fixed. More efficient algorithms are developed for several special cases of the problem. In particular, an algorithm is developed for the single-customer case with a complexity lower than the existing ones.