Research Overview

Process operations involving scheduling, planning and supply-chain management comprising of deterministic and stochastic approaches

Today's market dynamics with volatile customer demand and competition have made supply-chain planning and scheduling more challenging and complex, making the need for optimization even more imperative. Our research has offered a number of unique solutions that open new opportunities in this area. We have developed a novel continuous time model for the short-term scheduling of batch and continuous plants which has outperformed all other existing models. This is the result of achieving an orders of magnitude reduction of the computational requirements of the solution procedure, thus enabling the optimization of large-scale problems [1-3] . Our recent work addresses the limitations of this earlier approach by devising a decomposition-based methodology using the fundamental ideas of Lagrangean decomposition [4] . This approach makes feasible the solution of the integrated planning and scheduling problem [4, 5] , which has been a subject of increasing interest over the last decade. To move the boundaries from scheduling to planning and achieve the integration of these different time scales problems, we recently suggested a new iterative methodology based on hierarchical decision making structure where at the planning level the timing constraints are only considered through a single parameter value that is updated in the scheduling level to achieve convergence [6] . This work is of particular importance especially in view of uncertainty which is among the main interests in our research work.

1. Ierapetritou, M.G. and C.A. Floudas, Effective continuous-time formulation for short-term scheduling. 1. Multipurpose batch processes. Industrial & Engineering Chemistry Research, 1998. 37 (11): p. 4341-4359.
2. Ierapetritou, M.G. and C.A. Floudas, Effective continuous-time formulation for short-term scheduling. 2. Continuous and semicontinuous processes. Industrial & Engineering Chemistry Research, 1998. 37 (11): p. 4360-4374.
3. Ierapetritou, M.G., T.S. Hene, and C.A. Floudas, Effective continuous-time formulation for short-term scheduling. 3. Multiple intermediate due dates. Industrial & Engineering Chemistry Research, 1999. 38 (9): p. 3446-3461.
4. Wu, D. and M.G. Ierapetritou, Decomposition approaches for the efficient solution of short-term scheduling problems. Computers & Chemical Engineering, 2003. 27 (8-9): p. 1261-1276.
5. Wu, D. and M. Ierapetritou, Cyclic short-term scheduling of multiproduct batch plants using continuous-time representation. Computers & Chemical Engineering, 2004. 28 (11): p. 2271-2286.
6. Wu, D., and M.G. Ierapetritou, Hierarchical Approach for Production Planning and Scheduling Under Uncertainty Using Continuous-Time Formulation. Special Issue on Process Optimization and Control in Chemical Engineering and Processing, To appear 2006.

Design and synthesis of flexible manufacturing systems that includes uncertainty analysis, process synthesis, and optimization algorithmic development

Uncertainty has long been recognized as one of the main parameters in decision making, since optimization must balance profit and risk. A major contribution of our work is the incorporation of the effects of parameter variability in decision-making. Expanding my earlier PhD work [7] , we have proposed a number of unique ideas to determine the feasible region of a process based on computational geometry tools (simplicial approximation [8-10] , a -shape reconstruction [11] ) . The latter approach is the only available scheme that can be used to identify the feasible space independently of its characteristics (nonconvex, disjoint). We have expanded the boundaries of design optimization in order to incorporate, for the first time, data analysis in terms of market demand, which gives rise to an integrated framework for modular design and optimization under uncertainty [12, 13] .

Uncertainty in process operations can transform an optimal production schedule to an infeasible one, thus leading to major upsets in production and supply-chain management. Thus, it is of great significance to be able to predict uncertainty by generating robust schedules or to react to unpredicted events in an optimal way in order to guarantee smooth optimal plant operations. Our work addresses this problem by proposing a novel mathematical programming approach that guarantees the optimal rescheduling policy in the face of unpredicted events [14] . Increased robustness is guaranteed following the approach of [15] . Our work has focused on the fundamentals of sensitivity analysis of the Mixed Integer Linear Programming formulation of the scheduling problem as a tool to identify promising alternative schedules with larger robustness [16] . Most recently we worked on the development of a new efficient parametric MILP approach that will result in the ultimate solution of uncertainty in process operations since it results in the mapping of uncertainty space using alternative solutions [17] . This work addresses a fundamental operations research issue, and it will in the future have tremendous impact on a number of decision-making problems, since they typically include binary decisions.

For the cases where the model is not available or very complicated and computationally expensive our recent work targets the development of efficient techniques for optimization of black-box models [18] . We recently applied such an approach to an equation free model where the model is described by detailed molecular simulations [19] . This work has tremendous potential in many different fields involving optimization of industrial processes which are usually described by legacy codes for which analytical information is not available, analysis of biological systems for which only experimental data points can be provided, sensitivity investigation of environmental systems e.g. atmospheric models for which one simulation can last for a number of computational hours.

7. Ierapetritou, M.G. and E.N. Pistikopoulos, Novel Optimization Approach of Stochastic Planning-Models. Industrial & Engineering Chemistry Research, 1994. 33 (8): p. 1930-1942.
8. Ierapetritou, M.G., New approach for quantifying process feasibility: Convex and 1-D quasi-convex regions. Aiche Journal, 2001. 47 (6): p. 1407-1417.
9. Goyal, V. and M.G. Ierapetritou, Determination of operability limits using simplicial approximation. Aiche Journal, 2002. 48 (12): p. 2902-2909.
10. Goyal, V. and M.G. Ierapetritou, Framework for evaluating the feasibility/operability of nonconvex processes. Aiche Journal, 2003. 49 (5): p. 1233-1240.
11. Banerjee, I., M.G. Ierapetritou, Feasibility evaluation of non-convex systems using shape reconstruction techniques. Industrial & Engineering Chemistry Research, 2005: p. Accepted for publication.
12. Goyal, V. and M.G. Ierapetritou, Integration of data analysis and design optimization for the systematic generation of equipment portfolio. Industrial & Engineering Chemistry Research, 2003. 42 (21): p. 5204-5214.
13. Goyal, V. and M.G. Ierapetritou, Deterministic framework for robust modular design with integrated-demand data analysis. Industrial & Engineering Chemistry Research, 2004. 43 (21): p. 6813-6821.
14. Vin, J.P. and M.G. Ierapetritou, A new approach for efficient rescheduling of multiproduct batch plants. Industrial & Engineering Chemistry Research, 2000. 39 (11): p. 4228-4238.
15. Vin, J.P. and M.G. Ierapetritou, Robust short-term scheduling of multiproduct batch plants under demand uncertainty. Industrial & Engineering Chemistry Research, 2001. 40 (21): p. 4543-4554.
16. Jia, Z.Y. and M.G. Ierapetritou, Short-term scheduling under uncertainty using MILP sensitivity analysis. Industrial & Engineering Chemistry Research, 2004. 43 (14): p. 3782-3791.
17. Jia, Z.Y.a.M.G.I., Uncertainty Analysis on the RHS for MILP problems. Aiche Journal, 2006.
18. Davis, E., A Bindal, and M.G. Ierapetritou, Adaptive Optimization of Noisy Black-Box Functions Inherent In Microscopic Models. Computers & Chemical Engineering, To appear, 2006.
19. Bindal, A., M.G. Ierapetritou, S. Balakrishnan, A. Makeev, I. Kevrekidis and A. Armaou., Equation-free, coarse-grained computational optimization using timesteppers. Chemical Engineering Science, 2006. 61 : p. 279.

Modeling of reactive flow processes involving reduction of complex reaction systems appearing in combustion and environmental systems, and integration of detailed chemistry with complex flow simulations

We have also carried out pioneering work in the area of adaptive kinetic model reduction, for use in the modeling of complex reactive systems. Our work in this area is based on a unique integration of rigorous mathematical programming techniques and feasibility concepts in order to develop a library of reduced models with their associated range of validity. Based on the specific criteria established, the simulator can then select "on line" the appropriate reduced model that should be used at each integration point (in time and in space) [20] , [21] . The significance of this proposed adaptive chemistry mechanism lies in its ability to represent the characteristics of the detailed chemistry within a detailed flow field environment; to date, this has been an unresolved problem.

20. Banerjee, I. and M.G. Ierapetritou, Development of an adaptive chemistry model considering micromixing effects. Chemical Engineering Science, 2003. 58 (20): p. 4537-4555.
21. Banerjee, I. and M.G. Ierapetritou, An adaptive reduction scheme to model reactive flow. 2006. 144 (3): p. 619-633.

Metabolic engineering for optimizing liver-cell functionality

Our recent work in metabolic engineering represents an important new direction in her research career, and is also an illustration of the incredible potential range of the mathematical programming applications and techniques that she is developing to biological systems. Our current work in this area focuses on optimizing the function of liver cells in order to be utilized for bioartificial devices [22] . Recent directions of this work include the integration of metabolic and regulatory networks as well as the analysis of the toxic effects of a variety of different substances including drugs, and environmental pollutants. Our work in this area is in collaboration with Professors Yarmush, Roth and Androulakis that bring expertise in the area of liver physiology, molecular bioengineering and bioinformatics. Their partnership resulted in two NSF funded grants in Quantitative Systems Biology and Metabolic Engineering programs. We also collaborate in the area of environmental toxicology with Professors Georgopoulos and Welsh from UMDNJ that has been recently stemmed with the tremendous success of establishing the first national center (http://ccl.rutgers.edu/ebCTC/)in toxicogenomics at Rutgers University and UMDNJ.

22. Sharma, N., M.G. Ierapetritou and M.L. Yarmush., Novel Quantitative Tools for Engineering Analysis of Hepatocyte Cultures in Bioartificial Liver Systems. Biotechnology and Bioengineering, 2005. 92 (3): p. 321.

Modeling, Optimization and Control of Pharmaceutical processes

In this project the problem we are trying to solve is the optimization of process design for a variety of pharmaceutical manufacturing processing units. The project involves both experimental and computational components. Experiments are used to build the necessary knowledge database for the behavior of the process in a variety of different operating conditions as well as the effect of different design parameters in system's performance. Modeling endeavors target the development of predictive models to represent the system's performance using hybrid schemes involving first principle models and data based methodologies. This project is part of NSF funded ERC center of Organic Particulate Systems (http://solids.rutgers.edu/ERC/index.html).

The first stage of the project addresses single units, whereas at the second stage the interactions between processing units will be analyzed and considered in an integrative modeling framework in order to identify the additional bottlenecks that arise due to process connectivity. Finally the last stage will involve the optimization of the overall production plant alternatives. This will be of particular importance in the design of the optimal control scheme.

The first phase of this project concentrates on model building since this is the main limitation for process synthesis and design optimization. Concentrating on powder blending and feeding (as an integral part of blending) as one of the most important units in process pharmaceutical manufacturing two main challenges are addressed:
(a) For existing units (batch blenders, weight-loss feeders) there is currently no good predictive model that is reliable in terms of performance prediction but also efficient so that it can be used within an optimal control and optimization framework.
(b) For units currently under development (continuous mixing) the main problems we are trying to overcome in this project is the lack of understanding of process behavior and its response to operating conditions and design parameter changes.

The second phase of this project concentrates on process design optimization given the models developed in phase 1. The main challenge of this phase is that the process models are characterized by uncertainty. So rigorous approaches to deal with process model uncertainty have to be developed.

The third and most important phase of this project concentrates of the integration of different processing stages and the optimization of the overall production line. The main challenges are the following:
(a) generation of the plant superstructure based on available alternatives
(b) identification of major bottlenecks due to process interactions
(c) optimization of the overall process synthesis problem that gives rise to large scale Mixed Integer Nonlinear problem (MINLP) with possible dynamic models involved.

The target for the first phase is the development of predictive models for existing and developing units. As briefly outlined in the previous section existing models illustrate a number of limitations in terms of either their predictive capabilities or their computational complexity. For developing units such as the continuous blending units, experiments are contacted to characterize the effect of system parameters on unit mixing performance. The development of predictive models will follow empirical and rigorous methodologies following the corresponding alternatives for existing units. The developed models will be characterized by uncertainty. Thus the problem is to develop efficient and rigorous approaches to deal with uncertainty in process optimization.

23. Portillo, P.M., Ierapetritou, M.G. and Muzzio F.J., 2007, Characterization of Continuous Convective Powder Mixing Processes. Powder Technology. In press.
24. Portillo P.M., Muzzio F.J., Ierapetritou M.G., 2007, Hybrid DEM-compartment modeling approach for granular mixing, AICHE, 53, 1, 119-128.
25. Portillo P.M., Muzzio F.J., Ierapetritou M.G., 2006, Characterizing Powder Mixing Processes utilizing Compartment Models, International Journal of Pharmaceutics, 320, 14-22.