An approach for scheduling of a problem using a polynomial-time algorithm technique, was described. The elegant feasibility algorithm of Carlier is based on dynamic programming and it processes jobs from left to right on the time-axis. The objective of the algorithm is to find a non-preemptive schedule that maximizes the number of jobs completed by their deadlines. Computing the minimum time to complete k jobs reduces the running time, as the size of the dynamic programming table and the time needed to compute a single entry are both reduced.