Given a set of available carriers under control, and a set of cargoes to be transported from origin to destination, a robust ship scheduling to minimize a mean-variance objective function with a required level of profit can be modeled as a quadratic programming problem. The Single index model is used to calculate the variance-covariance matrix efficiently. Computational experiments concerning relevant maritime transportation problems are performed on randomly generated configurations of tanker scheduling in bulk trade and some significant results are reported. The results of experiments confirm that the model is validated and its effectiveness is satisfactorily demonstrated.