  This paper considers single-machine scheduling problems in which a given
solution, i.e. an ordered set of jobs, has to be improved as much as possible
by re-sequencing the jobs. The need for rescheduling may arise in different
contexts, e.g. due to changes in the job data or because of the local objective
in a stage of a supply chain \red{that is} not aligned with the given sequence.
A common production setting entails the movement of jobs (or parts) on a
conveyor. This is reflected in our model by facilitating the re-sequencing of
jobs via a buffer of limited capacity accessible by a LIFO policy. We consider
the classical objective functions of total weighted completion time, maximum
lateness and (weighted) number of late jobs and study their complexity. For
three of these problems we present strictly polynomial-time dynamic programming
algorithms, while for the case of minimizing the weighted number of late jobs
NP-hardness is proven and a pseudo-polynomial algorithm is given.
