Single machine resource allocation scheduling problems with deterioration effect and general positional effect.

This paper investigates single machine scheduling problems where the actual processing time of a job is dependent on its starting time, processing position and the amount of resource allocation. We present two unified models and provide a bicriteria analysis for the general scheduling criteria and the total weighted resource consumption. We consider two different versions for treating the two criteria and show that the unified models can be applied to solve scheduling problems under various due window assignment considerations. We prove that two different versions of the problems can be solved in polynomial time, respectively.