A Branch-and-Bound Algorithm for the Bi-Objective Quay Crane Scheduling Problem Based on Efficiency and Energy

Motivated by the call of the International Maritime Organization to meet the emission targets of 2030, this study considers two important practical aspects of quay crane scheduling: efficiency and energy consumption. More precisely, we introduce the bi-objective quay crane scheduling problem where the objective is to minimize the vessel's completion time and the crane's energy consumption. This is done by formulating a bi-objective mixed-integer programming model. A branch-and-bound algorithm was developed as the exact solution approach to find the full set of Pareto-optimal solutions. We consider (i) various lower bounds for both objectives, (ii) specific upper bounds, (iii) additional branching criteria, and (iv) fathoming criteria to detect Pareto-optimal solutions. Numerical experiments on benchmark instances show that the branch-and-bound algorithm can efficiently solve small- and medium-sized problems.

Automated summary

This study considers the practical aspects of efficiency and energy consumption in quay crane scheduling, motivated by the emission targets set by the International Maritime Organization for 2030. By formulating a bi-objective mixed-integer programming model and using a branch-and-bound algorithm, the study efficiently finds the full set of Pareto-optimal solutions for small- and medium-sized problems.