Abstract
In this paper we address a piston delivery scheduling problem with time-window constraints. The feature of this problem is a piston delivery. In a piston delivery, total running cost (length) to deliver products to all customers doesn't change even if we use a lot of or a few trucks. But the number of trucks necessary to satisfy time-window constraints is varied by the delivery timing. One of main factors of the delivery cost is the number of trucks to be secured. The minimum (or near minimum) number of trucks necessary for a given delivery request is a matter of interest. We propose a new solution method using Lagrangian relaxation for this problem. Numerical experiments show that the proposed method produces solutions with 25-20% less trucks than those by simple heuristics.
