An Integer Programming Approach to the Multimode Resource-Constrained Multiproject Scheduling Problem

The project scheduling problem (PSP) is the subject of several studies in computer science, mathematics, and operations research because of the hardness of solving it and its practical importance. This work tackles an extended version of the problem known as the multimode resource-constrained multiproject scheduling problem. A solution to this problem consists of a schedule of jobs from various projects, so that the job allocations do not exceed the stipulated limits of renewable and nonrenewable resources. To accomplish this, a set of execution modes for the jobs must be chosen, as the jobs' duration and amount of needed resources vary depending on the mode selected. Finally, the schedule must also consider precedence constraints between jobs. This work proposes heuristic methods based on integer programming to solve the PSP considered in the Multidisciplinary International Scheduling Conference: Theory and Applications (MISTA) 2013 Challenge. The developed solver was ranked third in the competition, being able to find feasible and competitive solutions for all instances and improving best known solutions for some problems.