Single machine scheduling problem with a common deadline and resource dependent release dates

This paper deals with an extension of the classical single machine scheduling problem with release dates. It is assumed that each job is available for processing at the moment (release date) which is a positive lienar decreasing function with respect to the amount of a common resource (e.g. gas, energy, catalyzer, financial outlay). The problem is to find a job schedule (processing order) and a resource allocation minimizing the total resource consumption under a given maximum schedule length. An exemplary application of the problem under consideration is given. It is shown that the decision form of the problem dealt with is NP-complete in the strong sense. It is NP-complete in the ordinary sense for the case of identical release date reduction rates. Some efficiently solvable cases of the problem and an approximate algorithm are shown. Some generalizations of the presented results are also outlined.