Stochastic Two Stage Model with Probabilistic Constraints for Optimal Rescue Ship Dispatching in Maritime Incidents

We propose a mathematical model to minimize the overall response time consisting of the current ship incident and future potential incident that might occur at some other site in the sea. Considering the uncertainties in both objective function and constraints, a two stage stochastic programming model having chance constraints for the number of rescue ships to be required at the potential incident site is formulated. Then, the model is transformed into equivalent programming model with deterministic constraints.In addition, we present as a variation of the deterministic constraints the expected value formulation where the expected number of rescue ships required is calculated. A numerical example is examined with sensitivity analysis which consequently shows the effects of changes in constraint parameters, i.e. quality of service, on the optimal solutions of the problem.