- Resource allocation problems (RAPs)are naturally represented as constraint networks (CNs), with constraints of inequality among activities that compete for the same resources at the same time . A large variety of timetabling problems can be formulated as CNs with inequality constraints (representing time conflicts among classes of the same teacher, for example). A new algorithm for solving networks of RAPs is described and its detailed behavior is presented on a small example. The proposed algorithm delays assignments of resources to selected activities and processes the network during the assignment procedure, to select delays and values. The proposed algorithm is an enhancement to standard intelligent backtracking algorithms , is complete and performs better than two former approaches to solving CNs of resource allocation , , . Results of comparing the proposed resource assignment algorithm to other ordering heuristics, on randomly generated networks, are reported.