Integrated stockyard allocation and handling scheduling in dry bulk ports with mixed storage

Efficient dry bulk terminal operations are essential to global supply chains for raw materials such as coal and ores, yet fugitive dust from open storage and handling remains an environmental challenge. Enclosed silos can reduce dust dispersion, yet prolonged silo storage may cause self-heating and spontaneous-combustion risks, requiring preventive silo-to-yard transfers before temperatures exceed safety thresholds. This paper studies an integrated stockyard allocation and handling scheduling problem in dry bulk ports with mixed storage, where open stockyards and a silo complex coexist. The problem jointly determines storage allocation, handling schedules, inventory evolution, silo temperature dynamics, and preventive transfer decisions to minimize total task dwell time and environmental protection costs from open stockyard storage. We propose a novel space–time–state network (STSN)-based mathematical formulation for this problem. By embedding temporal, spatial, and temperature-state transitions into feasible network paths, the formulation reduces reliance on auxiliary logical variables and big- M constraints, thereby improving computational tractability. Numerical experiments show that the proposed model reduces the objective value by 16.5% on average relative to the rule-based benchmark across the instance set. Compared with the MIP formulation, the STSN-based model proves optimality for all tested instances and reduces end-to-end runtime by 70.3% on average for the instances where both models reach optimality. The trade-off and capacity-sizing analyses further show that the model can quantify the balance between operational efficiency and open-storage environmental costs and support case-specific evaluations of open stockyard capacity under specified operational conditions.