Modeling assignment of quay cranes using queueing theory for minimizing CO2 emission at a container terminal

Quay cranes (QCs) play a significant role in CO2 emission of the operations of global supply chains, since huge global container traffic requires a considerable number of handing operations of QCs. The traditional studies of QC assignment mainly aim to investigate the scheduling efficiency of QCs and seldom touch on CO2 emission or other green transportation objectives and the resulting models are normally mixed-integer programming (MIP) problems and solved by heuristic algorithms. In this paper, a convex mathematical programming model is proposed for the QC assignment problem, in which the queueing theory is used to model the queueing behavior of automatic guided vehicles (AGVs). The objective of the proposed model is to minimize CO2 emission during an unloading process of containers from QCs to AGVs by optimizing the number of QCs. The analytical solution of the number of QCs is obtained to the proposed model. It is found that the optimal number of QCs increases with the expected arrival rate of AGVs and the mean fuel consumption per AGV per hour but it decreases with the mean queue service rate of QCs and the electricity consumption per QC per hour.