Job Shop Scheduling and Its Fuzzification Based on Operations and Disjunctive Graph Representations In this paper, several approaches to job shop scheduling problem are presented. A mixed integer programming model is derived and, based on this result, it is implemented in the GAMS optimisation software tool. Since the problem is NPhard, this approach may not be used for large instances, its reasonable bounds are indicated using benchmarks from ORLibrary. Here, strategies based on operations and disjunctive graph representations are applied and their time complexities are derived. These representations are also used to heuristically generate feasible solutions from their searching space. Finally, a modification is described of the problem using uncertain processing times of jobs based on fuzzy numbers. Methods for comparing fuzzy numbers are then discussed.

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.