This paper presents a detailed description of a particular class of deterministic single product Maritime Inventory Routing Problems (MIRPs), which we call deep-sea MIRPs with inventory tracking at every port. This class involves vessel travel times between ports that are significantly longer than the time spent in port and require inventory levels at all ports to be monitored throughout the planning horizon. After providing a comprehensive literature survey of this class, we introduce a core model for it cast as a mixed-integer linear program. This formulation is quite general and incorporates assumptions and families of constraints that are most prevalent in practice. We also discuss other modeling features commonly found in the literature and how they can be incorporated into the core model. We then offer a unified discussion of some of the most common advanced techniques used for improving the bounds of these problems. Finally, we present a library, called MIRPLib, of publicly available test problem instances for MIRPs with inventory tracking at every port. Despite a growing interest in combined routing and inventory management problems in a maritime setting, no data sets are publicly available, which represents a significant “barrier to entry” for those interested in related research. Our main goal for MIRPLib is to help maritime inventory routing gain maturity as an important and interesting class of planning problems. As a means to this end, we (1) make available benchmark instances for this particular class of MIRPs; (2) provide the mixed-integer linear programming community with a set of optimization problem instances from the maritime transportation domain in LP and MPS format; and (3) provide a template for other researchers when specifying characteristics of MIRPs arising in other settings. Best known computational results are reported for each instance. 
MIRPLib – A library of maritime inventory routing problem instances: Survey, core model, and benchmark results