Dr. Christopher L. E. Swartz
Christopher Swartz
Dofasco Chair in Process Automation and Information Technology
Director, McMaster Advanced Control Consortium
Department of Chemical Engineering
1280 Main Street West,
Hamilton, ON, L8S 4L7, Canada
Driving directions and map

Office: JHE 360
Voice: +1 (905) 525 9140 extension 27945
email: swartzc@mcmaster.ca

operations optimization, integration of design and control, mathematical modeling, scheduling and supply chain optimization
  • BSc(Eng) Cape Town
  • PhD, Wisconsin
  • MAIChE, MCSChE, P. Eng. (Ontario)


Research Interests 

Current trends of competition in an increasingly global market place, rising costs, and tightening environmental constraints make it increasingly important for process plants to be operated efficiently and in an environmentally responsible manner in order to remain competitive. This includes operation of individual process units, process plants, as well as the supply chains of which they are part.  Mathematical optimization provides a tool for addressing this - as the basis of both decision-support and model-based control systems, and for optimal process design.  My research focus is on applied optimization and automation of process systems, with the goal of developing mathematical formulations and solutions to improve the economics of operations, subject to prevailing operational, safety and environmental constraints.  Key research thrusts are described below.



Design for Dynamic Performance

The design of a plant can have a significant impact on its ability to be satisfactorily controlled.  Our research group has been involved in the development of optimization-based computational strategies, both for assessing plant operability and for incorporating operability requirements into optimal design calculations.  A current application seeks to identify design limitations to transition speed in air separation plants, where rapid response to demand and electricity price changes is highly beneficial.  




Dynamic Optimization of Process Operations

We consider optimization of transient processes described by differential-algebraic equation (DAE) systems in several contexts, with a focus toward industrial applications.  (i) Electric arc furnaces (EAFs) are widely used in the steel industry for melting scrap, and are large consumers of electrical energy.  Our group has been involved in the development of modeling and computational strategies for dynamic optimization of industrial EAF systems.  (ii) Shutdowns in chemical processing plants are detrimental both to plant economics and critical product characteristics. We have developed formulation and computational strategies for determining optimal operating policies in the face of shutdowns in multi-unit operations, with application to a Kraft pulp mill. Current work extends the approach to include model discontinuities, handling of uncertainty through feedback, and optimal relaxation of specifications under abnormal operating conditions.  (iii) A further area of study within our group is the interaction between model predictive control (MPC) and a higher-level optimization layer. This includes analysis of the performance of LP-MPC cascade control systems - a common configuration in commercial MPC implementations, and the analysis and development of dynamic real-time optimization (D-RTO) systems that utilize a dynamic model at the supervisory optimization level. 




Computational Strategies for Large-Scale Dynamic Optimization

We are exploring the use of parallel computing approaches for the solution of large-scale dynamic optimization problems under uncertainty.  A multiple-shooting approach is utilized for solving the dynamic optimization problem, with the uncertain parameter space discretized into a finite number of scenarios.  The independent integration tasks are distributed among multiple processors for parallel solution.      




Optimal Scheduling and Planning

Our research in this field is driven primarily by industrial needs, and our studies typically involve close collaboration with industrial partners. Recent and current studies include optimal raw material purchasing and plant operation under uncertainty in steel manufacturing, the development of optimal scheduling and planning formulations for an industrial food processing application, and optimal scheduling of converter aisle operations in a nickel smelting plant.  In addition, we are exploring strategies for reactive scheduling, and systematic integration of planning and scheduling. 




Supply Chain Optimization

Key drivers in the process industry toward an increased focus on supply chain technologies are increasing pressure to reduce costs and inventories due to market competition, a shift from commodity products toward low-volume, demand-driven specialty products, globalization of operations, and more rapidly fluctuating demands. Within our group, we consider strategies for optimal supply chain operation and design, as well as the development of computational tools for supply chain performance analysis. 

Work in this area includes (i) a novel robust model predictive control formulation for application to process supply chain systems, (ii) a supply chain formulation that includes time-limited transportation contracts within an optimal supply

chain design, and (iii) development of a systematic framework for supply chain operability analysis, motivated by Canadian forest products industry transformation from commodity production to integrated biorefineries producing biofuels and specialty chemicals, where flexibility and responsiveness to accommodate market variation, feedstock variability and fluctuating customer demands is a key consideration.    




Industrial Collaboration
Our group collaborates with several industries through the McMaster Advanced Control Consortium (MACC), and the McMaster Steel Research Centre. MACC fosters industrially relevant research in process systems engineering and provides a community of academic researchers and industrial practitioners who share knowledge and experiences. Further information about MACC is available at the website:



McMaster Advanced Control Consortium


Selected Publications 

Washington, I.D. and Swartz, C.L.E. (2014).  Design under uncertainty using parallel multiperiod dynamic optimization.  AIChE J., in press DOI 10.1002/aic.14473.

Mastragostino, R. and Swartz, C.L.E. (2014).  Dynamic operability analysis of process supply chains for forest industry transformation. Ind. Eng. Chem. Res., 53, 9825-9840.

Hazaras, M., Swartz, C.L.E. and Marlin, T.E. (2014).  Industrial application of a continuous-time scheduling framework for process analysis and improvement.  Ind. Eng. Chem. Res., 53, 259-273.

Mastragostino, R., Patel, S. and Swartz, C.L.E. (2014).  Robust decision making for hybrid process supply chain systems via model predictive control.  Comp. Chem. Eng., 62, 37-55.

Chong, Z. and Swartz, C.L.E. (2013).  Optimal operation of process plants under partial shutdown conditions.  AIChE J., 59(11), 4151-4168.

Gerardi, D., Marlin, T.E. and Swartz, C.L.E. (2013).  Optimization of primary steelmaking purchasing and operation under raw material uncertainty.  Ind. Eng. Chem. Res., 52(35), 12383-12398.

Hazaras, M.J., Swartz, C.L.E. and Marlin, T.E. (2012).  Flexible maintenance within a continuous-time state-task network framework.  Comp. Chem. Eng., 46, 167-177.

Chong, Z. and Swartz, C.L.E. (2011). Discontinuous modeling formulations for the optimal control of partial shutdowns. Proc. 18th IFAC World Congress, Milan.

Cao, Y., Swartz, C.LE. and Baldea, M. (2011). Design for dynamic performance: Application to an air separation unit. Proc. American Control Conference, San Francisco.

Nikandrov, A. and Swartz, C.L.E. (2009).  Sensitivity analysis of LP-MPC cascade control systems, J. Process Control, 19, 16-24.

Baker, R. and Swartz, C.L.E. (2008).  Interior point solution of multilevel quadratic programming problems in constrained model predictive control applications.  Ind. Eng. Chem. Res., 47(1), 81-91.

MacRosty, R.D.M. and Swartz, C.L.E. (2007).  Dynamic optimization of electric arc furnace operation. AIChE J., 53(3), 640-653.

MacRosty, R.D.M. and Swartz, C.L.E. (2005). Dynamic modeling of an industrial electric arc furnace.  Ind. Eng. Chem. Res., 44, 8067-8083.