Single-machine scheduling with simultaneous considerations of resource allocation and deteriorating jobs

This paper considers a single-machine scheduling problem with deteriorating jobs and convex resource allocation. We assume that the actual processing time of a job is a function of its convex resource allocation and its starting time. For the multi-objective single-machine scheduling problem, we show that the problem is polynomially solvable in O (n log n) time, where n is the total number of jobs.