Manufacturers can meet the due dates of orders by using overtime, in which case, additional cost incurs for the amount of overtime. Although many studies have been reported on scheduling, only a few papers are founds on production scheduling using overtime. We consider the problem of production scheduling using overtime on a single machine, in which each job has a given due-date, a constant processing time. We assume that the daily overtime does not exceed the daily regular operation time. The objectives is to minimize the total overtimes, while meeting all due dates. We first present a mathematical model, and then suggest a heuristic algorithm for the problem.