Exact algorithm for solving project scheduling problems under multiple resource constraints

This paper presents a new algorithm, called the enumerative branch-and-cut procedure (EBAC), for minimizing the total project duration of a construction project under multiple resource constraints based on an enumeration tree. The EBAC generates new branches to the tree corresponding to "better" feasible alternatives. It starts with all of the feasible schedule alternatives as the trial schedule alternatives at any node. The trial schedule alternatives are then evaluated to determine whether they are "worse" than any existing partial schedules in the tree by using the presented cut rules, and a worse alternative will be eliminated from the enumeration tree. In other words, the tree will contain only better feasible schedules. The presented algorithm has been coded in the VB6.0 language on a personal computer. It has been tested with the 110 scheduling problems, which have been widely used for validating a variety of schedule algorithms over the last 20 years. The EBAC can obtain the shortest project durations for all of the 110 problems.