A multiprocessor architecture is proposed which is based on the Multics concept of having all on-line information processor-addressible. All memory management is done by an intelligent paged virtual memory system, and each processor deals only with those segments relevant to its single executing program. The processors are chosen to have different implementations of a single system-wide instruction set and the problem is to effectively schedule different categories of programs, called task groups, on the dissimilar processors. Average weighted instruction times for each task group on every processor are defined as task/processor suitability measures, and typical values are given for different groups of programs running on IBM 370 models. Through the use of linear programming techniques, an optimal schedule for any such multiprocessor is then defined for the static case where task group loads and task/processor suitability values are known in advance. A priority-based task management scheduling algorithm is then defined which uses the optimal schedule of the formal model as a parameter, and its performance is simulated.