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Dr. Vladimir Mahalec


Department of Chemical Engineering

Associate Director of Graduate Programs

W Booth School of Engineering Practice and Technology

Optimization of plant operations (production planning, scheduling, real-time optimization) and supply chain management; integration of planning, scheduling, RTO, and control; reduced size hybrid models for optimization; energy recovery from low temperature sources
Areas of Specialization:
Research Clusters:


Research Interests

Software engineering and application design, development, and implementation (advanced process control, process engineering and design, planning, scheduling, plant optimization, feedstock selection, trading and logistics). Expertise in value chain optimization in petroleum, petrochemicals, and other process industries.

Research Overview

            My research interests are driven by the desire to be able to solve real life problems, which often leads to the need to develop a new type of a model, a new computational procedure, or a new software required for large-scale numerical experimentation.  Until three years ago, most of our work used examples from petroleum refining.  The focus has now been shifted towards community energy systems.

            Research over the last 5 or 6 years can be divided in the following categories:

  1. Community energy systems.
  2. Optimal production planning and scheduling for continuous and discrete manufacturing plants
  3. Hybrid modelling
  4. Process monitoring and control
  5. Optimization algorithms

I. Community Energy Systems

Initial work in this area started three years ago as a feasibility study for district heating and cooling for a new development at Pier 7 and 8 in Hamilton (for Hamilton Community Energy).  This was followed by the work on enhancing efficiency of complex CCHP systems (Afzali  and Mahalec, 2017) and the work on simplifying procedures for determining the optimal operating conditions of CCHP system (Afzali and Mahalec, submitted

Over the next several years the plan is to work on the following questions:

  1. How much GHG reduction can be achieved in heating and cooling large buildings (e.g. a hospital or a shopping mall) by using best currently available technology under different level of carbon-pricing?
    1. At McMaster we (a team of several professors) have received a large grant to investigate over the next three years what are the best options for this. In the phase II (years 4-6) we plan to design and build such a system in partnership with one of the community energy companies.
  2. What improvements to the system designed in a) are needed to achieve 90% reduction in GHG emissions? What new technology is required?  What options are there to achieve this?
  3. What is the path to make existing district energy systems (e.g. Hamilton Community Energy) much less intensive in terms of GHG emissions? What structural changes correspond to different breakpoints in terms of GHG emissions and in terms of the level of investment?
  4. How to retrofit existing neighbourhoods to put them on the path towards 90% reduction in GHG emissions (combining the needs for building cooling and heating with the energy needed for personal transportation)?

II. Optimal production planning and scheduling for continuous and discrete manufacturing plants

Research in this area aims to enable optimal decision making for large scale plants.  Some of the solutions that we have proposed deal with:

  • Under what conditions less efficient competitor should upgrade its plant and how much time is available to implement such an upgrade in order to prevent being eliminated by the more efficient competitors?
  • How to ensure that the operating conditions for each period in a many-period production plan are optimal and as steady as possible (i.e. do not “bounce around” from period to period as a consequence of using a particular solver)?
  • How to optimize operating conditions, production plans and schedules for large models corresponding to the real-life plants?
  • How to account for uncertainty in production times of discrete multi-stage manufacturing processes?

As a part of the research, we have developed a GUI for plant model configuration in GAMS and have built a complete refinery model as an experimental workbench.  This has enabled us to examine our solution methods on large problems which are much bigger than typically considered by the researchers in the area.

III. Hybrid modelling

Since there are limits to the size of the nonlinear plant models which can be used for optimal planning or scheduling, industrial practice is to use linear approximations of the plant equipment.  This leads to errors in the production plans and schedules.  In other words, deemed optimum is not really an optimum.  Some published comparisons and our own work indicate that the errors introduced by the linearized model are on the order of 2% to 4% of the optimum (even with piecewise linearizations).

Our research has developed a new class of wide-boiling distillation models (hybrid models), comprised of rigorous mass balances, energy balances, and of approximate models representing the internal working of a particular piece of equipment.

This modelling approach has enabled us to model e.g. crude distillation units for use in real-time optimization (RTO) (Mahalec and Sanchez, 2012) and in scheduling and planning (Fu, Sanchez, and Mahalec, 2016). The accuracy of these models is within 1% of the rigorous models. The models are very small: about 150 to 200 equations (much smaller than 10,000 to 20,000 equations for the nonlinear rigorous model). Using these models in refinery planning, we have been able to demonstrate that even with the best current modelling industrial practices, there is a substantial portion of the profits which are not realized due to the using lower accuracy CDU unit models.

IV. Process monitoring and control

Numerous research studies have been published on identification of process faults based purely on measurements (e.g. by using PCA). Our work on fault identification (Mori et al, 2014) exploits knowledge of process model structure (network topology) to construct a causal network and novel Bayesian contribution indices within the probabilistic graphical network to identify the potential root-cause variables.   We demonstrate that the use of the probabilistic graphical network significantly improve fault detection capabilities when compared to methods based purely on data.          

Economic optimization of real time operation of an equipment can be approached either as an optimization of an economic model predictive controller or as a dynamic real-time optimization. Both of these approaches can be recast as solving NLP problems.    

Our recent work (Wang et al, 2017a) applies normalized parametric disaggregation (NMDT) to the economic optimization of NMPC. We demonstrate that a relatively simple algorithm, which can be implemented by advanced control engineers, ensures that globally optimal performance will be achieved. If performance needs to be optimized over a longer time horizon, the size of NMPC model becomes too large to solve it in real time.  D-RTO decomposes the economic real-time optimization in two layers. The top layer (D-RTO) computes optimal operating trajectories, while the lower level (MPC) guides the operation along these trajectories. State of the art research in the area uses different models in NMPC and D-RTO layers, leading to the mismatch between the models and consequently to the issues in real time performance.  The work we completed recently (Wang et al, 2017b) is the first work to use the same model in both layers, which improves the real-time performance and simplifies the implementation.   


V. Optimization

Research on algorithms for global optimization started several decades ago.  Limited computing power meant that relatively small problems were used for algorithm testing. Consequently, algorithm development proceeded along the paths which tried to exploit the problem structural characteristics and not necessarily the computing power. Our recent research (Castillo et al, 2017) explores construction of the algorithms which exploit the recent increases in the computing power to employ extensively OBBT. The results show that OBBT improves very significantly global optimization algorithm performance. We have solved large scale problems more accurately and faster than the commercial state-of-the-art solvers.


  • Dipl. Ing, U. of Zagreb (Zagreb, Croatia)
  • Ph.D., U. of Houston, (Houston, TX)
  • Post-Doctoral Associate, M.I.T. (Cambridge, MA)



 Publications (2012-2017)

  • Afzali, S. F., Mahalec, V. “Optimal design, operation and analytical criteria for determining optimal operating modes of a CCHP with fired HRSG, boiler, electric chiller and absorption chiller” Energy (2017) 139 1052-1065
  • Afzali, S. F., Mahalec, V. “Decision curves to determine optimal operation of CCHP systems” submitted (2017)
  • Castillo, C.P, Castro., P., Mahalec., V. “Global Optimization of MIQCPs with Dynamic Piecewise Relaxations” (2017) submitted
  • Tominac, P., Mahalec, V., “A dynamic game theoretic framework for process plant competitive upgrade and production planning”, AIChE J. (2017) DOI: 1002/aic.15995
  • Jalanko, M., Mahalec., V. “Inventory pinch based methodology for planning under uncertainty with application to gasoline blend Planning”, submitted (2017)
  • Fu, G., Castillo Castillo, P.A., Mahalec, V. “Impact of crude distillation unit distillation model accuracy on refinery production planning”, Eng. Manag. (2017) DOI 10.15302/J-FEM-2017052
  • Wang, X., Qian, F., Mahalec, V. “Globally optimal dynamic real-time optimization without model mismatch between optimization and control layer”, Chem. Eng. (2017) 104(Sept. 2) 64-75
  • Wang, X., Qian, F., Mahalec, V. “Globally optimal nonlinear model predictive control based on multi-parametric disaggregation”, of Process Control, (2017) 52(4) 1-13
  • Castillo, C.P, Castro., P., Mahalec., V. “Global optimization algorithm for large-scale refinery planning models with bilinear terms”, Eng. Chem. Res. (2017) 56(2) 530-548
  • Castillo, C.P, Castro., P., Mahalec., V., “Global optimization of nonlinear blend-scheduling problems”, Engineering (2017) 3 (2) 188-201
  • Tominac, P., Mahalec, V. “A Game Theoretic Framework for Petroleum Refinery Strategic Production Planning”, AIChE J. (2017) DOI: 1002/aic.15644
  • Mori, J., Mahalec, V., “Planning and Scheduling of Steel Plates Production. Part II: Scheduling of Continuous Casting”, Chem. Eng. (2017), 101 (9) 312-325
  • Castillo Castillo, P.A., Mahalec, V., “Improved continuous-time model for gasoline blend scheduling”, Chem. Eng. (2016) 84, 627-646
  • Castillo Castillo, P.A., Mahalec, V., “Inventory pinch gasoline blend scheduling algorithm combining discrete- and continuous-time models”, Chem. Eng. (2016) 84, 611-626
  • Fu, G., Y. Sanchez, Mahalec, V., ”Hybrid Model for Optimization of Crude Distillation Units”, AIChE J. (2016) 62(4) 1065-1078
  • Mori, J., Mahalec, V., “Planning and Scheduling of Steel Plates Production. Part I. Estimation of Production Times via Hybrid Bayesian Networks for Large Domain of Discrete Variables”, Chem. Eng. (2015), 79 , 113-134 ;
  • Mori, J, Mahalec, V., ‘Bayesian Inference in Hybrid Networks with Large Discrete and Continuous Domains”, Expert Sys. with App. (2016) 49, 1-19,
  • Fu, G. Mahalec, V., “Comparison of methods for computing crude distillation product properties in planning and scheduling”, Eng. Chem. Res. (2016), 54 (45), pp 11371–11382
  • Castillo Castillo, P., Castro, P., Mahalec, V., “Short-term crude mix and operating conditions optimization for oil refinery operations”  26th European Symposium on Computer Aided Process Engineering – ESCAPE 26 (2016)
  • Castillo Castillo, P.A., V. Mahalec, “Nonlinear blend scheduling via Inventory-pinch based Algorithm Using Discrete- and Continuous-time Models”, Chemical and Biochemical Engineering Quarterly, (2015) 28 (4) 425-436,
  • Chen, Y., Mahalec, V., Chen, Y., Liu, X., He, R., Sun, K., “Reconfiguration of satellite orbit for cooperative observation using variable-size multi-objective differential evolution”, European Journal of Operational Research, (2014) 242 (1) 10-20
  • Mori, J., Mahalec, V., Yu, J., “Identification of Probabilistic Graphical Network Model for Root-Cause Diagnosis in Industrial Processes”, Computers & Chemical Engineering, (2014) 71, 171-209
  • Castillo Castillo, P.A., Mahalec, V., “Inventory Pinch Based, Multi-scale Models for Integrated Planning and Scheduling: I. Gasoline Blend Planning” AIChEJ (2014), 60 (6), 2158-2178
  • Castillo Castillo, P.A., Mahalec, V., “Inventory Pinch Based, Multi-scale Models for Integrated Planning and Scheduling: II. Gasoline Blend Scheduling” AIChEJ (2014), 60 (7), 2475-2497
  • Castillo Castillo, P.A., Mahalec, V., “Inventory Pinch Based Multi-Scale Model for Refinery Production Planning” Proceedings of the 24th European Symposium on Computer Aided Process Engineering – ESCAPE 24 (2014), Klemes, J.J., Varbanov, P.S., Liew P.Y., (editors), 284-288
  • Chen, Y.,Mahalec, V., Chen, Y., He, R., and Liu, X. , “Optimal Satellite Orbit Design for Prioritized Multi-targets with Threshold Observation Time Using Self-Adaptive Differential Evolution”, Journal of Aerospace Engineering, (2013) DOI 1061/(ASCE)AS.1943-5525.0000393
  • Castillo Castillo, P.A., Kelly, J.D., Mahalec, V., “Inventory Pinch Algorithm for Gasoline Blend Planning”, AIChEJ 2013, 52 (10), 3748-3766
  • Thakral, A, Mahalec, V., “Composite Planning and Scheduling Algorithm Addressing Intra-Period Infeasibilities of Gasoline Blend Planning Models”, Canadian Journal of Chemical Engineering, (2013) 91 (7), 1244-1255
  • Kulkarni-Thaker, S., Mahalec, V., “Multiple Global Optima in Gasoline Blend Planning”, Eng. Chem. Res. (2013), 52 (31), 10707-10719
  • Ijaz, H., Ati, U.K., Mahalec, V., “Heat Exchanger Network Simulation, Data Reconciliation & Optimization”, Applied Thermal Eng., (2013) 52, 322-335
  • Mahalec, V., Sanchez, Y., “Inferential monitoring and optimization of crude separation units via hybrid models”, Computers and Chemical Eng., (2012), 45 (Oct. 12), 15-26


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Design of Software for Process Simulation, Design, Optimization and Plant Operations

  • Architecture for aspenONE (integrated solutions for plant operations) (2003-2006).
  • Design of a real-time optimization system, RT-OPT and equation-oriented ASPEN PLUS. (1991-1994)
  • Novel refinery-wide modeling. (1988-1991)
  • Design and implementation of refinery scheduling / simulation software (1982-1984)
  • Designed computational architecture for ASPEN PLUS. (1977-1978)

Design of Methods for Plant Control

  • Novel method for on-line calculation of distillation tower tray loading and control of tower operation close to the flooding operation.
  • Novel advanced multivariable control methods.
  • Design of a Control engineer’s interface for configuring multi-variable controllers