  We consider an NP-hard selective and periodic inventory routing problem
(SPIRP) in a waste vegetable oil collection environment. This SPIRP arises in
the context of reverse logistics where a biodiesel company has daily
requirements of oil to be used as raw material in its production process. These
requirements can be fulfilled by using the available inventory, collecting
waste vegetable oil or purchasing virgin oil. The problem consists in
determining a period (cyclic) planning for the collection and purchasing of oil
such that the total collection, inventory and purchasing costs are minimized,
while meeting the company's oil requirements and all the operational
constraints. We propose a MIP-based heuristic which solves a relaxed model
without routing, constructs routes taking into account the relaxation's
solution and then improves these routes by solving the capacitated vehicle
routing problem associated to each period. Following this approach, an a
posteriori performance guarantee is ensured, as the approach provides both a
lower bound and a feasible solution. The performed computational experiments
show that the MIP-based heuristic is very fast and effective as it is able to
encounter near optimal solutions with low gaps within seconds, improving
several of the best known results using just a fraction of the time spent by a
state-of-the-art heuristic. A remarkable fact is that the proposed MIP-based
heuristic improves over the best known results for all the large instances
available in the literature.
