Discrete-event systems with only synchronization and no concurrency, also known as timed event graphs or (max, +)-linear systems, have been studied by several authors. The synchronization constraints that arise in these discrete-event systems are hard, i.e. they cannot be broken under any circumstances. In this paper we consider a more extended class of discrete-event systems with both hard and soft synchronization constraints, i.e. if necessary, some synchronization conditions may be broken, but then a penalty is incurred. We show how the model predictive control (MPC) framework, which is a very popular controller design method in the process industry, can be extended to this class of discrete-event systems. In general, the MPC control design problem for discrete-event systems with soft and hard synchronization constraints leads to a non-linear non-convex optimization problem. We show that the optimal MPC strategy can also be computed using an extended linear complementary problem.