A novel robust exact decomposition algorithm for berth and quay crane allocation and scheduling problem considering uncertainty and energy efficiency

 In container terminals, electricity price variation has a tangible impact on the operating cost of port equipment, especially the quay crane (QC). Accordingly, significant operational cost savings could be realized via careful planning. This study addresses, for the first time, berth allocation and QC assignment and scheduling problem (BACASP) considering energy price variations. A novel mathematical model is developed to minimize both energy costs and vessel tardiness. Furthermore, we consider the uncertainty in QC processing time and vessel arrival time, based on which we propose a robust formulation that optimizes the worst-case scenario. This study also highlights why robustness is essential for cost-cutting considering the energy prices in the BACASP. The model is unable to achieve optimality using CPLEX, even for small instances. Thus, a novel exact decomposition algorithm is proposed to solve the problem over a reasonable computational time. Its novelty lies in four proposed strengthening procedures designed and embedded within the algorithm. To test the algorithm, several instances are generated based on the literature and real data of a port partner. Then, several experiments are conducted to highlight the impact of implementing the four strengthening procedures and demonstrate how considering energy constraints within the BACASP leads to significant cost savings.