Service-oriented operational decision optimization for dry bulk shipping fleet under stochastic demand

Dry bulk shipping plays a crucial role in intercontinental bulk cargo transport, with operators managing fleets to meet shippers’ transportation demand. A primary challenge for these operators is making optimal operational decisions about ship scheduling, routing, and sailing speed in the face of stochastic demand. We address this problem by developing a stochastic integer programming model designed to maximize revenue while maintaining high service levels for shippers. We quantify service levels for shippers using the probability of demand being fully satisfied. To solve this model, we introduce an innovative offline–online Lagrange relaxation framework. This framework leverages training data to determine the optimal Lagrange multiplier, which subsequently guides decision-making with test data. Numerical experiments show that our method closely matches the performance of Sampling Average Approximation (SAA) solutions while reducing computational time.