A LazyConstraints Approach to ResourceConstrained Project Scheduling We study the complex combinatorial optimization problem to schedule the activities of a single project with the objective to complete the project within the shortestpossible amount of time such that the limited resource capacities as well as the prescribed precedence relations between pairs of the activities are taken into account. In addition to various specific solution algorithms, the related literature proposes several MixedInteger Linear Programming (MILP) models, but these models remain complex to solve even for smallsized instances. We present a novel approach based on an MILP model in which the resourcecapacity constraints are formulated for all inclusionminimal sets of activities which, due to the limited capacities of the resources, cannot be processed simultaneously. We propose to remove these constraints from the model and iteratively add those constraints back which are violated in the solutions obtained. For a set of test instances from the literature, our computational results indicate that with respect to both, the deviation of the project duration obtained from the lower bound devised from the criticalpath length and the number of instances solved to optimality, the novel lazyconstraints approach outperforms ten stateoftheart MILP models.

Efficient priority rules for project scheduling under dynamic environments: A heuristic approach Abstract   This paper aims to identify an efficient priority rule (PR) for resource constrained project scheduling problems under dynamic environments. Here, the dynamicity comes from the unstable resource availability, timevarying resource demands and stochastic activity durations for each of the project activities. This extended dynamic project scheduling problem is solved by using a proposed Variable Neighbourhood Search Based Local Search Heuristic (VNSLSH). Six PRs are then integrated with the proposed heuristic to identify the best rule. Standard sets of 5760 and 7200 generated test instances with 30 and 120 activities are considered for experimentation. The influence of the variation of activity durations and risk or uncertainty levels on the algorithmxe2x80x99s performance is analysed and discussed. After analysing several PRbased heuristics, this study concludes that no one of the taken PR is dominant over others under this dynamic project scheduling environment.