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

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