Abstract
This paper develops new formulations for the Strategic Berth Template Problem, which combines strategic and operational decisions for medium-term berth planning of a given set of cyclically calling ships. The strategic decisions determine the ship calls that will be served, whereas the operational ones establish the berth template that will be applied in a cyclic fashion in the planning horizon. The proposed formulations use binary variables that classify served ships depending on whether or not their service starts in their arrival cycle or in the next one. This helps modeling the problem, since a closed linear expression can be obtained for the waiting times. Constraints imposing that the availability of the berths is respected at each time period can be derived by defining additional binary variables pointing to the starting service times of the served ships. Aggregating such variables over all berths leads to a relaxed formulation, which can be solved in remarkably small computing times. Furthermore, the solution of an auxiliary subproblem produces feasible solutions to the original problem as well as a simple optimality check. Disaggregating the initial service time variables for the different berths leads to a valid formulation. Numerical results from extensive computational tests over a set of benchmark instances from the literature are presented and analyzed. The obtained results assess the excellent performance of the proposed formulations, which outperform existing ones.
Highlights
In this paper we study the Strategic Berth Template Problem (SBTP)
In addition to the natural strategic binary variables associated with the acceptance/rejection of ship calls, all the proposed formulations use binary variables that classify served ships depending on whether or not their service starts during their arrival cycle or in the one. This helps modeling the STBP, since a closed linear expression can be obtained for the waiting times
We close this section by pointing out that even if the formulations we have introduced produce SBTP solutions, the obtained solutions may be not sufficiently explicit, in the sense that in some cases they do not give the specific allocations of served ships to berths, or they do not obtain the specific sequences of consecutive ships served in each berth
Summary
In this paper we study the Strategic Berth Template Problem (SBTP). The SBTP combines strategic and operational decisions for medium-term berth planning of a given set of cyclically calling ships. In addition to the natural strategic binary variables associated with the acceptance/rejection of ship calls, all the proposed formulations use binary variables that classify served ships depending on whether or not their service starts during their arrival cycle or in the one This helps modeling the STBP, since a closed linear expression can be obtained for the waiting times. The obtained results highlight the effectiveness of the two formulations based on the indicator variables for the time periods when service to accepted ships start Both the 2-phase solution algorithm based on the relaxed formulation with the aggregated variables, as well as the exact formulation using the disaggregated decision variables outperform the most efficient formulation proposed in Iris et al (2018).
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