Robust integrated multi-mode scheduling of flexible loading and unloading operations with maintenance services in a port container terminal

This study proposes an unparalleled integrated scheduling model for simultaneous loading, unloading, and maintenance operations in a port container terminal, wherein several heterogeneous handling equipment serve inbound and outbound vessels. In this regard, a multi-mode loading approach and the possibility of multiple allocations are also considered, wherein outbound vessels can be loaded by containers belonging to inbound vessels or the storage area. In addition, the proposed model covers all cases of equality and inequality in the number of inbound and outbound containers. More importantly, a flexible loading approach based on a class-based stowage plan is considered to better utilize equipment and increase the efficiency of the loading process. Additionally, since the timing of maintenance operations undoubtedly affects scheduling and entails miscellaneous uncertainties, a two-phase data-driven method is presented to estimate robust maintenance operation times. The first phase involves a hybrid machine learning strategy that combines the Savitzky–Golay Filter (SGF), the Takagi–Sugeno–Kang (TSK) fuzzy system, and minibatch gradient descent with regularization, DropRule, and AdaBound (MBGD-RDA) for the estimation of maintenance operation times. The second phase employs the distributionally robust optimization (DRO) technique that leverages $\phi$-divergence to address the uncertainties associated with the estimated times. Finally, a case study is conducted to demonstrate the effectiveness and applicability of the proposed framework, accompanied by an examination of various simulation experiments. The results obtained indicate that the implementation of a flexible loading strategy can lead to a 24% reduction in the loading time of vessels.