We present a solution methodology to obtain near-optimal solutions for the problem of scheduling multiple products on a network of single-stage, unrelated parallel units using simulated annealing (SA) with a performance criterion based on tardiness minimization. The approach incorporates sequence dependent clean-up times, varying processing rates for different products on different units, and constraints on feasible product-to-unit assignments. Near-optimal solutions are obtained for problems with 20-100 products and 3-11 units. A comparison is made between solutions obtained by SA, solutions obtained by the heuristic improvement method of Musier and Evans for similar computational effort, and solutions obtained by a list scheduling algorithm.