Abstract This chapter presents an extensive computational study of simple, but prominent matheuristics (i.e., heuristics that rely on mathematical programming models) to find high quality ship schedules and inventory policies for a class of maritime inventory routing problems. Our computational experiments are performed on a test bed of the publicly available MIRPLib instances. This class of inventory routing problems has few constraints relative to some operational problems, but is complicated by long planning horizons. We compare several variants of rolling horizon heuristics, K-opt heuristics, local branching, solution polishing, and hybrids thereof. Many of these matheuristics substantially outperform the commercial mixed-integer programming solvers CPLEX 12.6.2 and Gurobi 6.5 in their ability to quickly find high quality solutions. New best known incumbents are found for 26 out of 70 yet-to-be-proved-optimal instances and new best known bounds on 56 instances.


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