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An innovative mathematical model and optimized solution approach for machine patterns in berth allocation problems

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  • Bruno Luís Hönigmann Cereser

  • Aurelio Ribeiro Leite de Oliveira

  • Antonio Carlos Moretti

Abstract

In this paper, we integrate two decision problems related to the management of port terminals, the berth allocation problem and the machine assignment problem. The berth allocation problem consists of assigning and scheduling incoming vessels to berthing positions, and the machine assignment problem consists of assigning a machine pattern/profile. The machines can be quay cranes, trucks, or any other machine. We present two MILP formulations, one with machine patterns for the quay and another for berths. The objective function aims to minimize the waiting time and the handling time of the vessels. To solve the problem, we developed a heuristic algorithm capable of solving a problem instance in seconds. To compare the results, we generate several instance problems based on real data and solve them with our MILP formulation, our heuristic, and a FIFO algorithm. We tested our heuristic with instances with more than 100 berths, 500 vessels, and 250 machines. The solver was unable at finding solutions for instances with more than 4 berths after three hours of processing. The heuristic was able to solve all the instances in less than 3 seconds. On average, the heuristic solution is 8\% worse than the optimal solution.

Suggested Citation

  • Bruno Luís Hönigmann Cereser & Aurelio Ribeiro Leite de Oliveira & Antonio Carlos Moretti, 2025. "An innovative mathematical model and optimized solution approach for machine patterns in berth allocation problems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 35(3), pages 29-49.
    • Handle: RePEc:wut:journl:v:35:y:2025:i:3:p:29-49:id:2
    DOI: 10.37190/ord250302
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