An online joint replenishment problem combined with single machine scheduling

Abstract This paper considers a combination of the joint replenishment problem with single machine scheduling. There is resource, which required by all unit-time jobs, and job can be started at time point t on if only does not process another , resource replenished between its release date . Each has cost, independent amount replenished. The objective to minimize total cost plus maximum flow jobs. We consider online variant problem, where jobs are released over time, once inserted into schedule, starting cannot changed. propose deterministic 2-competitive algorithm for general input. Moreover, we show that certain class inputs (so-called p -bounded input), competitive ratio tends $$\sqrt{2}$$ 2 as number infinity. also derive several lower bounds best any under various assumptions.