An Integrated TwoStage Optimization Method for JobShop Bottleneck Planning and Scheduling In many literatures, planning and scheduling problems have been considered separately. Furthermore, resource constraints for scheduling are not only relevant for equipment, but are also strongly affected by second resources and set up conversions. This paper derives how constraint programming enables problemdependent specialization and increases planning and scheduling efficiency. Constraint programing based scheduling involves multiresources capacity limit, demand fulfill, precedence, initialization, down activities and sequencedependent set up. Then, we improve this model to address on more complex problems by introducing a twostage optimization method to decrease the computational burden. Finally, computational results are demonstrated to show the efficiency of the proposed method for a real time large scale planning and scheduling problem.

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.