Simplifying activity networks under generalized precedence relations to extended CPM networks

The critical path method (CPM) is a network planning technology with a simple and intuitive representation. However, it can only represent a special precedence relation–the finish‐to‐start minimum time lag. Currently, generalized precedence relations (GPRs) are represented by complex activity networks. We simplify complex activity networks under GPRs by representing the GPRs in a new way. This new extended CPM network is similar to the standard CPM network with the exception that arcs may have negative lengths and cycles. The extended CPM network facilitates problems with GPRs. Although many current models and algorithms are advanced and efficient for the CPM network problem, they are difficult or impossible to improve for GPRs applications. The extended CPM network, however, combats these problems and serves as an illustration of resource leveling with activity splitting. The current 0‐1 binary model formulation for the resource leveling with just finish‐to‐start minimum time lags is also applied to the problem with GPRs using the extended CPM network.