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Maritime transportation is the backbone of international trade but ships emit a large amount of air pollutants at ports. To encourage ships to use clean energy while berthing at port, subsidies are provided to ship operators that use clean energy and the subsidy amount is generally determined based on subjective judgment. We, therefore, examine the optimal subsidy design for government-operated ports, aiming at balancing the environmental benefits and subsidy expenses. Considering the uncertainty of energy requirements by ships, we build a stochastic optimization model. Taking advantage of the problem structure, we convert the model into a deterministic one by applying sample average approximation and a binomial distribution. The model is then linearized and solved by CPLEX. A series of numerical experiments with realistic parameters are conducted to validate the model and useful managerial insights are obtained.

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