  In this paper we consider a combination of the joint replenishment problem
(JRP) and single machine scheduling with release dates. There is a single
machine and one or more item types. Each job has a release date, a positive
processing time, and it requires a subset of items. A job can be started at
time $t$ only if all the required item types were replenished between the
release date of the job and time point $t$. The ordering of item types for
distinct jobs can be combined. The objective is to minimize the total ordering
cost plus a scheduling criterion, such as total weighted completion time or
maximum flow time, where the cost of ordering a subset of items simultaneously
is the sum of a joint ordering cost, and an additional item ordering cost for
each item type in the subset. We provide several complexity results for the
offline problem, and competitive analysis for online variants with min-sum and
min-max criteria, respectively.
