Carbon-efficient deployment of electric rubber-tyred gantry cranes in container terminals with workload uncertainty

Rubber-tyred gantry cranes are one of the major sources of carbon dioxide emissions in container terminals. In a move to green transportation, the traditional diesel powered cranes are being converted to electric ones. In this paper, we study the deployment of electric powered gantry cranes (ERTGs) in container terminal yards. Cranes always move in-between blocks to serve different workload. ERTGs use electricity for most movements but switch to diesel engines to allow inter-block transfers between unaligned blocks. We exploit this feature and propose to consider simultaneously the CO2 emissions and workload delays to develop carbon-efficient deployment strategies. Moreover, unlike previous works we consider the workload uncertainty, and model the problem as a two-stage stochastic program. A sample average approximation framework with Benders decomposition is employed to solve the problem. Multiple acceleration techniques are proposed, including a tailored regularised decomposition approach and valid inequalities. A case study with sample data from a major port in East China show that our proposal could reduce significantly CO2 emissions with only a marginal compromise in workload delays. Our numerical experiments also highlight the significance of the stochastic model and the efficiency of the Benders algorithms.