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Resource-constrained project scheduling problems (RCPSP) are at the heart ofmany production planning problems across a plethora of applications. Althoughthe problem has been studied since the early 1960s, most developments and testinstances are limited to problems with less than 300 jobs, far from thethousands present in real-life scenarios. Furthermore, the RCPSP withdiscounted cost (DC) is critical in many of these settings, which requiredecision makers to evaluate the net present value of the finished tasks, butthe non-linear cost function makes the problem harder to solve or analyze.  In this work, we propose a novel approximation algorithm for the RCPSP-DC.Our main contribution is that, through the use of geometrically increasingintervals, we can construct an approximation algorithm, keeping track ofprecedence constraints, usage of multiple resources, and time requirements. Toour knowledge, this is the first approximation algorithm for this problem.Finally, through experimental analysis over real instances, we report theempirical performance of our approach, showing that our technique allows us tosolve sizeable underground mining problems within reasonable time frames andgaps much smaller than the theoretically computed ones.

Approximation algorithm for resource-constrained project scheduling problems with net present value objective