In flexible manufacturing systems the most important element in determining the proper course of technological processes, transport and storage is the control and planning subsystem. The key planning task is to determine the optimal sequence of production orders. This paper proposes a new method of determining the optimal sequence of production orders in view of the sum of the costs related to the delayed execution of orders. It takes into account the different unit costs of delays of individual orders and the amount of allowable delays of orders involving no delay costs. The optimum sequence of orders, in the single-machine problem, in view of the sum of the costs of delays may be significantly different from the optimal order, taking into account the sum of delay times.