In this paper, we describe five solution strategies for scheduling CO2 shipments in a carbon capture and storage (CCS) maritime supply chain. Specifically, we consider an RTN-based MILP, a simplified timeslot-based MILP, discrete-event simulation (DES), an integrated DES and optimization approach, and a discrete-time constraint programming (CP) model. A key innovation in our methodology is the introduction of a DES model in a complex logistic problem that cannot be solved in a reasonable CPU time with a rigorous monolithic MILP optimization approach. This unique simulation tool, which is computationally very efficient but with strong limitations in terms of achieving global optimality, allows us to explore its effective integration with more rigorous optimization techniques. The integration of these two techniques involves using the optimization model to predefine major critical decisions that will be sequentially given to the DES model. Another highlight of this paper is applying constraint programming to reformulate the problem with a discrete-time representation, which offers a rigorous and flexible formulation. Using the powerful CP-SAT solver provided by OR-Tools, it is shown that the CP model can find feasible solutions faster than other discrete-time representation models. Several instances based on real data are solved by all five methodologies to compare their computational expense and the solutions obtained.
Xu et al. (2026) studied this question.