A high-performance exact method for the resource-constrained project scheduling problem

Abstract This paper describes an efficient exact algorithm for project scheduling with resource constraints. The procedure consists of creating partial schedules which are always feasible with respect to both precedence and resource constraints. These partial schedules are connected through a tree, and a lower bound on the completion of the uncompleted activities is associated with each partial schedule. The branching process takes place from a partial schedule with the minimum lower bound and continues until the optimal schedule is created. Despite branching from a partial schedule with the minimum lower bound, the algorithm does not need large memory for keeping partial schedules as independent data, and does not require large comparability time for selecting a partial schedule to branch from. These make it possible to solve test problems each involving up to 100 activities and six different resource types. The computational results of the performance of the algorithm are reported. Scope and purpose The resource-constrained project scheduling (RCPS) problem occurs in industrial organizations, and has been of a particular interest to industrial engineers. Current branch-and-bound procedures to find optimal solutions to this problem are based on either best-first or backtracking schemes. Best-first methods avoid redundant calculation but need a large amount of memory, which makes them impractical for solving large-sized problems. On the other hand, backtracking methods do not require a large amount of memory, but require extensive duplicating searching. This paper develops a procedure which integrates the positive features of both best-first and backtracking methods to solve the RCPS problem. The computational results show that the procedure has the advantages of being practical in the sense of memory requirements as well as ability to avoid a great deal of duplicating searching.