Dear Colleagues,

Advanced optimization algorithms and increased computational resources are opening new possibilities to integrate control and scheduling. Some of the most popular advanced control methods today were conceptualized decades ago. Over a time span of 30 years, computers have increased in speed by about 17,000 times and algorithms such as integer programming have a speedup of approximately 150,000 times on some benchmark problems. With the combined hardware and software improvements, benchmark problems can now be solved 2.5 billion times faster; i.e., applications that formerly required 120 years to solve are now completed in 5 seconds. New computing architectures and algorithms advance the frontier of solving larger scale and more complex integrated problems. Recent work demonstrates economic and operational incentives for merging scheduling and control.

There are many remaining areas for development. Improvement is needed with optimization algorithms that converge within a controller cycle time, improve scale-up with many discrete variables (especially in MINLP), exploit unique problem structures, and utilize strengths of emerging computing architectures. An example of a recent development is in scale-bridging models that serve as surrogates for the scheduler to encapsulate a simplified description of the control dynamics. Nonlinear relationships are needed where feedback linearization or linear dynamic models are not sufficient to capture the control dynamics. Further development towards unification of scheduling and control particularly needs industrial application with guidance on benefits and further development opportunities.

Suggested contributions to this Special Issue include approaches to formulating combined objective functions, multi-scale approaches to integration, mixed discrete and continuous formulations, estimation of uncertain control and scheduling states, mixed integer and nonlinear programming advances, benchmark development, comparison of centralized and decentralized methods, and software that facilitates creation of new applications and long-term sustainment of benefits. Contributions should acknowledge strengths, weaknesses and potential further advancements of their work, along with a demonstration of improvement over current industrial best-practice.

Additional information is available at http://www.mdpi.com/journal/processes/special_issues/Combined_Scheduling  Submissions are due Sept 30, 2017. We welcome your submission and request that you please let us know if you are planning to submit to this special issue.

Best regards,

John D. Hedengren
Logan Beal
Processes Guest Editors