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Responsible for the subject: Bertók Botond, associate professor (

The subject assumes knowledge of the following subjects:

- Linear and non-linear programming

- Integer and mixed integer programming


1. Structural description of engineering systems (Graphs; Networks; P-graph; Process networks)
2. Structural analysis of engineering systems (Structural mappings; Combinatorial properties; Algorithmic enumeration of combinatorially feasible structures; Maximal structure generation)
3. Parametric model of process networks (Parameters of raw materials; Parameters of products; Parameters of intermediate materials; Parameters of operational units)
4. Mathematical programming model of process network synthesis (Lower and upper bound of variables related to operational units; Constraints for raw materials; Constraints for products; Constraints for intermediate materials; Parameterization of a linear cost function with a fixed part; Definition of an objective function; Relationships between continuous and integer variables )
5. Solution of the mathematical programming model of process network synthesis (Definition of decision variables; Estimation of the effects of decisions; Difference between estimated and real cost function; Branch and Bound algorithm; Branch and Bound in process synthesis; Subproblem selection rules; Decision variable selection rules; Measurement of the effectiveness of selection rules)
6. Synthesis of supply chains (Supply chain steps; Modeling multiple locations; Modeling multiple time periods; Evacuation planning; Modeling dedicated and shared markets; Regional factors affecting supply chain costs)
7. Synthesis of separation networks (Separation in engineering systems; Separation network elements; Types of separation networks; Mathematical models of multicomponent flows; Mathematical models of separation network elements; Mathematical models of separation networks; Synthesis of separation networks with mathematical programming; Synthesis of separation networks as process synthesis; Optimization of decision networks )
8. Multi-period production optimization (Multi-period systems in practice; Identification and grouping of periods; Relationships between periods; Decisions affecting investment and operation in case of several periods; Multi-period production optimization with process synthesis; Multi-period production optimization with mathematical programming; Cash-flow planning with multi-periodic optimization
9. Process optimization with uncertain parameters (Uncertain parameters in process optimization; Continuous and discrete distribution functions; Uncertainties affecting investment and operation; Multilevel decision models; Modeling management strategies; Optimization with uncertain parameters by process synthesis; Optimization with uncertain parameters by mathematical programming
10. Parametric model of continuous-time processes (Time parameters of raw materials; Time parameters of products; Time parameters of operational units)
11. Mathematical programming model of time-constrained process network synthesis (Lower and upper bounds of time variables related to operational units; Time variables assigned to materials; Constraints for raw materials; Constraints for products; Constraints for intermediate materials)


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Max Peters, Klaus Timmerhaus, Ronald West: Plant Design and Economics for Chemical Engineers 5th Edition, McGraw-Hill, 2003.

Urmila Diwekar: Introduction to Applied Optimization, Springer Optimization and Its Applications, Springer, 2010.

Jiri Klemes, Ferenc Friedler, Igor Bulatov, Petar Varbanov: Sustainability in the Process Industry: Integration and Optimization (Green Manufacturing & Systems Engineering), McGraw-Hill Professional, 2010.

Wilhelm Forst, Dieter Hoffmann: Optimization - Theory and Practice; Springer, 2010.

Bertók Botond, Kovács Zoltán: Gyártórendszerek modellezése, Typotex, 2011.

Ferenc Friedler, Ákos Orosz, Jean Pimentel Losada: P-graphs for Process Systems Engineering: Mathematical Models and Algorithms, Springer, 2022.