Resource constrained scheduling simulation model for alternative stochastic network projects

The paper presents a heuristic for resource constrained network project scheduling. A network project comprising both alternative deterministic decision nodes and alternative branching nodes with probabilistic outcomes is considered. Several renewable activity related resources, such as machines and manpower, are imbedded in the model. Each type of resource is in limited supply with a resource limit that is fixed at the same level throughout the project duration. Each activity in the project requires resources of various types with fixed capacities. The activity duration is a random variable with given density function. The problem is to minimize the expected project duration by determining for each activity, which will be realized within the project's realization, its starting time (decision variable), i.e. the time of feeding-in resources. The resource delivery schedule is not calculated in advance and is based on decision-making in the course of monitoring the project. The suggested heuristic algorithm is performed in real time via simulation. Decision-making is carried out: at alternative deterministic decision nodes, to single out all the alternative sub-networks (joint variants) in order to choose the one with the minimal average duration; at other essential moments when at least one activity is ready to be operated but the available amount of resources is limited. A competition among those activities is carried out to determine the subset of activities which have to be operated first and can be supplied by available resources. Such a competition is realized by a combination of a knapsack resource reallocation model and a subsidiary simulation algorithm.A numerical example to illustrate the heuristic algorithm is presented.