The maritime inventory routing problem (MIRP) is a tactical and operational planning problem, that takes an integrated view on ship scheduling and inventory management for bulk products. Given production and consumption levels during a predetermined planning horizon, the problem aims at finding delivery schedules with minimal travel costs, such that the inventory bounds at both production and consumption ports are satisfied during the entire planning horizon. In this thesis, we consider instances of the MIRP with a heterogenous fleet and multiple products. We formulate both a mixed integer programming (MIP) and constraint programming (CP) model for these instances. These models are solved using commercially available dedicated solvers for both formalism. For small instance sizes and short planning periods, the MIP approach is prevalent in finding solutions quickly and of good quality. Due to the inventory constraints in the problem however, the MIP approach suffers from scalability issues more heavily than the CP approach. A rolling-horizon heuristic is proposed in order to find solutions of better quality in comparable running time.

In this thesis, the methods of Matrix Product States are examined. We give background in the origin of the methods and explain in detail how the method can be applied to a series of Josephson junctions. Numerical results are given for the ground state energy analysis of these series.