Resource dependent scheduling with truncated learning effects

In this article, we investigate the single-machine scheduling problem with truncated learning effect and resource allocation, where the actual processing time of a job is a general function of its additional resources and position in a sequence. The goal is to determine the optimal resource allocation and optimal sequence such that a weighted sum of scheduling cost and resource consumption cost is minimized. We show that the problem can be solved in $ O(n^3) $ time by using an assignment formulation, where $ n $ is the number of jobs.