  This paper approaches the integrated lot sizing and scheduling problem
(ILSSP), in which non-identical machines work in parallel with non-triangular
sequence-dependent setup costs and times, setup carry-over and capacity
limitation. The aim of the studied ILSSP, here called ILSSP-NT on parallel
machines, is to determine a production planning and tasks sequencing that meet
period demands without delay and in such a way that the total costs of
production, machine setup and inventory are minimized. The dearth of literature
on the ILSSP-NT, despite the increasing amount of applications in the
industrial sector, mainly in the food processing industry, motivated us to
conduct this study. In this paper, we propose efficient methods to solve the
ILSSP-NT on parallel machines. The methods virtually consist in the
hybridization of the relax-and-fix and fix-and-optimize methods with the
path-relinking and kernel search heuristics. To assess how well the heuristics
solve the ILSSP-NT on parallel machines, we compared their results with those
of the CPLEX solver with a fixed CPU time limit. The proposed matheuristics
significantly outperformed CPLEX in most of the tested instances.
