Abstract This article focuses on the computation of costs for a combination reduction of activities will not always indicate the minimum cost for a specified duration even if the computation provides a plan for the exact time duration required. Dynamic programming provides a method of dealing with this type of problem. The objective is to find the minimum cost for a given time. This schedule is a complete list of least cost plans. If the desired time does not coincide with a plan on the list the next plan with a shorter time may be chosen in the knowledge that excess time is not being bought. All alternatives have been considered in the computation, and those which have been rejected are inferior to those appearing on the final schedule.
F. A. Bailey (Sat,) studied this question.