We solve a periodic supply vessel planning problem under demand and weather uncertainty, arising in offshore of oil and gas production. Our study is motivated by the case of the Norwegian energy operator Equinor which supplied us with data. The aim is to determine an optimal fleet composition and a least-cost vessel schedule under uncertain demand at the installations and uncertain weather conditions. We present a methodology incorporating a metaheuristic within a discrete-event simulation model which, applied iteratively for the increasing values of reliability level parameters, yields a vessel schedule of least expected cost.