Resource Allocation in Activity Networks under Stochastic Conditions. A Geometric Programming-Sample Path Optimization Approach

We depart from the conventional ‘resource constrained project scheduling problem’, better known under the acronym RCPSP, by adding the element of randomness to the activities. In particular, we assume that each activity in the project has a work content that is exponentially distributed. The duration of an activity is then modeled as a function of the random work content and the allocated resources; the exact functional relationship can be arbitrarily defined. The stochastic optimization problem is approached by a method that is a ‘marriage’ between geometric programming (GP) and sample path optimization (SPO) that is flexible and can be implemented in a modular fashion.