This thesis considers the scheduling challenges encountered at a particular facility in the nuclear industry. The scheduling problem is modelled as a variant of the job shop scheduling problem. Important aspects of the considered problem include the scheduling of jobs with both soft and hard due dates, and the integration of maintenance planning with job scheduling. Two variants of the scheduling problem are considered: The first variant makes the classic job shop assumption of infinite queueing capacity at each machine, while such queueing capacity is non-existent in the second variant. Without queueing capacity, the scheduling problem is a variant of the blocking job shop problem. For the non-blocking variant of the problem, it is shown that good solutions can be obtained quickly by hybridising a novel Ant Colony Optimisation method with a novel Branch and Bound method. For the blocking variant of the problem, it is shown that a novel Branch and Bound method can rapidly find optimal solutions. This Branch and Bound method is shown to provide good performance due to, amongst other things, a novel search strategy and a novel branching strategy.