Beyond the edge of feasibility: Analysis of bottlenecks The productivity of realworld systems is often limited by socalled bottlenecks. Hence, usually companies are not only interested in finding the best ways to schedule their current resources so that their benefits are maximized (optimization), but, in order to increase the productivity, they also conduct some analysis to find bottlenecks in their system and eliminate them in the most efficient way (e.g., with the lowest investment). We show that the current frequently used analysis (based on average shadow price) for identifying bottlenecks has some limitations: (1) it is limited to linear constraints, (2) it does not consider all potential sources for bottlenecks in a system, and (3) it does not provide adequate tools for decision makers to find the best way of investment to eliminate bottlenecks and maximize the profit they can gain. We propose a more comprehensive definition of bottlenecks that covers these limitations. Based on this new definition, we propose a multiobjective model for the benefit and investment. The solution for this model provides the best way of investment in resources to achieve maximum profit. As the proposed model is multiobjective and nonlinear, it opens an important opportunity for the application of evolutionary algorithms, which can subsequently have a significant impact on the decision making process of companies.

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.