A scheduling problem in a real production line with uncertain sequence-dependent set-up times and a random yield is considered. The production line can produce multiple product types as production lots, each of which is composed of a number of products of the same product type. To changeover product types, a sequence-dependent set-up operation should be performed, and only the lower and upper bounds are known for the sequence-dependent set-up times. Moreover, the processing time to produce the required number of product for each production lot is uncertain due to the random yield. For the objective of minimising the average tardy probability of given production lots, a systematic approximation scheme to estimate tardy probabilities of lots in any given production sequence is developed by taking not only the uncertainties but also the computational efficiency into account. As practical solution approaches, a simulated annealing and a discrete particle swarm optimisation algorithms using the approximation scheme are developed, and their performance are evaluated by computational experiments. Since there has been no research on the scheduling problems with uncertain sequence-dependent set-up times and random yield, the authors expect this research will make an excellent contribution to develop practical scheduling methodologies in uncertain scheduling environments.