Model predictive control (MPC) is a popular controller design technique in the process industry. Conventional MPC uses linear or non-linear discrete-time models. Recently, we have extended MPC to a class of discrete event systems that can be described by a model that is 'linear' in the (max, +) algebra. In our previous work we have only considered MPC for the perturbations-free case and for the case with bounded noise and/or modelling errors. In this paper we extend these results on MPC for max-plus-linear systems to a stochastic setting. We show that under quite general conditions the resulting optimization problems turn out to be convex and can thus be solved very efficiently.