Can We Solve Every Project Instance?

In this chapter, we take on the challenge of optimally solving the resource-constrained project scheduling problem for all existing projects from various well-known datasets. Armed with a powerful supercomputer and the various branch-and-bound procedures proposed in the literature, we conduct an intensive computer experiment in the hope of finally understanding how projects should be optimally scheduled. Despite demonstrating through this experiment why certain algorithms perform better than others, we also learned that this well-known project scheduling problem remains very difficult to solve, even with the incredible increase in computing power we have witnessed in recent decades. This chapter is based on the article “An exact composite lower bound strategy for the resource-constrained project scheduling problem,” published in Computers and Operations Research.