Hybrid Time-Based Framework for Maritime Inventory Routing Problem

The choice of a suitable time representation
plays a major role
in designing a computationally efficient planning/scheduling framework.
For the time representation to be effective, it needs to capture the
nuances of the actual process, while ensuring that the resultant model
is tractable and computationally efficient. In this paper, a novel
time representation scheme, titled hybrid time discretization, which
combines both continuous- and discrete-time representations in a single
framework, is proposed and used to solve a complex multiproduct maritime
inventory routing problem (MIRP) with undedicated compartments. Several
continuous- and discrete-time-based frameworks have been proposed
to solve the MIRP over the years. While single-/multigrid discretized
frameworks do efficiently capture the time-sensitive nuances of the
problem (such as active/inactive jetty hours and hourly/daily variations
in the demands), they struggle to solve larger problem instances to
the required optimality gap in a reasonable time. This is primarily
due to the large disparities among the timings of different task components
in the model. On the other hand, continuous-time representation can
significantly reduce the problem size and computational effort; however,
modeling the entire problem using the continuous-time-based framework
could have problems in representing some time-sensitive intricacies
in the demands and jetty/port activities. To allay the above-mentioned
drawbacks, in this paper, a novel hybrid time representation is proposed,
which combines a continuous-time representation with a multigrid discrete-time
framework. The proposed novel framework is cast in a rolling horizon
strategy and tested on various scenarios generated for the above-mentioned
maritime transportation problem, which are shown to be significantly
more complex than those presented in the literature. The proposed
MILP framework is able to solve most of the test cases to the required
optimality in a reasonable time without the need for heuristic or
meta-heuristic assists. The proposed hybrid time representation could
find significant utility in other lateral applications such as batch
scheduling and inventory routing problems.