This paper studies a tugboat–barge scheduling problem in inland waterways where tugboats tow multiple barges and perform multiple trips under a drop-and-pull (DP) mode. We formulate a mixed-integer programming model that determines tug routes, barge assignments, and service times under time-window and capacity constraints, and propose an Adaptive Large Neighborhood Search (ALNS) algorithm with simulated annealing to solve practical-scale instances. A case study based on the middle–lower Yangtze trunk network and a short-distance regional network around Shanghai shows that long-distance DP transport exhibits a clear three-stage demand–cost pattern with route structures remaining stable up to a critical demand threshold, whereas short-distance transport on a compact network experiences frequent route reconfigurations and highly fluctuating cost elasticity. Sensitivity analyses further reveal a cost-driven switch between integrated trunk routing and more dispersed end-routing when barge unit costs become sufficiently higher than tugboat costs, offering guidance for fleet deployment and pricing in DP systems.
Xiao et al. (Wed,) studied this question.