# Tramp Ship Scheduling Problem with Berth Allocation Considerations and Time-dependent Constraints

## TL;DR

This paper introduces a mixed-integer linear programming model for tramp ship scheduling that incorporates berth allocation and time-dependent constraints, offering a practical approach for real-world maritime logistics.

## Contribution

It is the first to integrate spatial and temporal berth considerations into a comprehensive ship scheduling model with a heuristic solution method.

## Key findings

- The model effectively captures berth and time window constraints.
- The heuristic improves scheduling efficiency in complex scenarios.
- Numerical results demonstrate the approach's practical benefits.

## Abstract

This work presents a model for the Tramp Ship Scheduling problem including berth allocation considerations, motivated by a real case of a shipping company. The aim is to determine the travel schedule for each vessel considering multiple docking and multiple time windows at the berths. This work is innovative due to the consideration of both spatial and temporal attributes during the scheduling process. The resulting model is formulated as a mixed-integer linear programming problem, and a heuristic method to deal with multiple vessel schedules is also presented. Numerical experimentation is performed to highlight the benefits of the proposed approach and the applicability of the heuristic. Conclusions and recommendations for further research are provided.