Resource allocation to minimize the makespan for jobs performed on a single machine

We consider a problem of optimal allocation of a continuous doubly-constrained resource to jobs performed on a single machine. The processing speed of a job depends on an amount of the continuous resource allotted to this job at a moment. This relation is expressed by a processing speed function characterizing each job. We propose a method of resource allocating for jobs which have to be performed sequentially (for example on a single machine) to minimize the schedule length. The problem for jobs with unique concave processing speed functions has not been considered so far.