Resource Constrained Project Scheduling Models under Random Disturbances

In the chapter we consider two different scheduling models for stochastic network projects. Models of the first type consider several simultaneously realized stochastic network projects of PERT type. Resource scheduling models of the second type also cover PERT type projects, but with two different kinds of renewable resources: 1 extremely costly resources (A-resources) which have to be obtained for a short time within the project’s time span. Such resources have to be prepared and delivered externally at planned moments, 2 renewable resources (B-resources) which are at the company’s disposal. In all types of models each projects’ activity utilizes several non-consumable related resources with fixed capacities, e.g. machines or manpower. For each operation, its duration is a random variable with given density function. The first problem centers on determining: the earliest starting moment for each project’s realization, the limited resource levels for each type of resources to be stored during the projects’ realization, the moments when resources are fed in and projects’ activities start, in order to minimize the average total expenses of hiring and maintaining resources subject to the chance constraints. For the second class of developed models the problem boils down: to predetermine in advance, i.e., before each project starts to be realized, a deterministic delivery schedule for A-resources which are not at the project’s disposal, to determine both the starting times and the resource capacities to be utilized for activities which require limited renewable B-resources which are at the project’s disposal, to determine the starting moment of each project’s realization, in order to minimize average total projects’ expenses subject to the chance constraint. Problems of resource project scheduling are solved via simulation, in combination with a cyclic coordinate descent method and a knapsack resource reallocation model.