Finding the critical path in an activity network with time-switch constraints

An activity network is an acyclic graph with non-negative weights and with a unique source and destination. A project consisting of a set of activities and precedence relationships can be represented by an activity network and the mathematical analysis of the network provides useful information for managing the project. In a traditional activity network, it is assumed that an activity always begins after all of its preceding activities have been completed. This assumption may not be adequate enough to describe some practical applications where some forms of time constraints are attached to an activity. In this paper, we investigate one type of time constraint called time-switch constraint which assumes that an activity begins only in a specified time interval of a cycle with some pairs of exclusive components. Polynomial time algorithms are developed to find the critical path (or longest path) and analyze the float of each arc in this time-constrained activity network. The analysis shows that the critical path and float in this context differ from those of a traditional activity network in some management perspectives and thus, consideration of the time-switch constraint leads to enhanced project management through more effective use of budgets and resource allocation.