Branch and Bound Algorithms for Resource Constrained Project Scheduling Problem Subject to Nonrenewable Resources with Prescheduled Procurement

A lot of projects in real life are subject to some kinds of nonrenewable resources that are not exactly similar to the type defined in the project scheduling literature. The difference stems from the fact that, in those projects, contrary to the common assumption in the project scheduling literature, nonrenewable resources are not available in full amount at the beginning of the project, but they are procured along the project horizon. In this paper, we study this different type of nonrenewable resources. To that end, we extend the resource constrained project scheduling problem (RCPSP) by this resource type (RCPSP-NR) and customize four basic branch and bound algorithms of RCPSP for it, including precedence tree, extension alternatives, minimal delaying alternatives, and minimal forbidden sets. Several bounding and fathoming rules are introduced to the algorithms to shorten the enumeration process. We perform comprehensive experimental analysis using the four customized algorithms and also CPLEX solver.