The objective of this paper is to find out important characteristics and basic theorems for overtimes, while meeting all due dates of orders. This problem is classified into three cases. The first case is when all orders are ready to be processed now; and the second case is that the orders have random ready time and that due-date`s sequences are identical with the sequences of ready time. The third case is the orders have random ready time and that due date sequences are not identical with the sequences of ready time. We do not consider· split production in the first and second case, but in the last case, split production is considered. We first present the mathematical models for three cases. In the first and second case, we prove that if orders are processed as ascending sequences of due-dates , testing feasibility and minimizing total amounts of overtime can be found out. In the third case, we suggest an efficient grouping method for testing feasibility and minimizing overtimes.