Subroutine ARSME solves a resource constrained, network scheduling problem for the case in which activities may be arbitrarily interrupted and restarted later with no increase in activity duration. The number of resource types is not a limiting factor in our procedure. The amount of any one resource available a t any moment is constant. We shall use the "activity-on-arc" network representation, under the commonly imposed assumption that the network contains no directed cycles and has only one "beginning" and only one "terminal" node (event) . I t is further assumed that the network nodes (events) are ordered in such a way tha t node i precedes node j, if i < j . Such an ordering is always possible and it induces an ordering among the arcs (activities). Optimal approaches to resource constrained, network scheduling problems where activities can require more than one resource type are presented in [1, 4]. Both methods assume integer durations of activities, and the method presented in [1] divides activity durations into unit intervals. Both methods can handle networks with up to about 30 activities and 3 resource types. Subroutine ARSME is constructed in such a way tha t its storage requirements are minimal, a fact which permits the solution of problems for very large networks with many resource types. Moreover, an optimal solution can be obtained in a shorter time when relatively smaller amounts of the resources are available than when resources are less limited. Let the number of activities be equal to M and the number of resource types be equal to RT. For ac t iv i ty j ( j = 1, 2 , . . . , M) and resource k (k = 1, 2 , . . . , RT)