Ignacio Grossmann
Carnegie Mellon University, Chemical Engineering, Faculty Member
The evaluation and optimization of flexible chemical processes remains one of the most challenging problems in Process Systems Engineering. In this paper an overview of recent methods for quantifying the property of flexibility in... more
The evaluation and optimization of flexible chemical processes remains one of the most challenging problems in Process Systems Engineering. In this paper an overview of recent methods for quantifying the property of flexibility in chemical plants will be presented. As will he shown, these methods are gradually evolving from deterministic worst-case measures for feasible operation to stochastic measures that account for the distribution functions of the uncertain parameters. Another trend is the simultaneous handling of discrete and continuous uncertainties with the aim of developing measures for flexibility and reliability that can be integrated within a common framework. It will be then shown how some of these measures can be incorporated in the optimization of chemical processes. In particular, the problem of optimization of flexibility for multiproduct batch plants will be discussed.
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... Swaney RE and IE Grossmann, An index for oper-ational flexibility in chemical process design. ... By construction, SF5 as given by (3) and using the bounds computed in (2) will converge to the multiple integral in (I) within a small... more
... Swaney RE and IE Grossmann, An index for oper-ational flexibility in chemical process design. ... By construction, SF5 as given by (3) and using the bounds computed in (2) will converge to the multiple integral in (I) within a small error e if a large number of quadrature points ...
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Abstract This paper addresses the problem of developing a quantitative measure for the flexibility of a design to withstand uncertainties in the continuous parameters and discrete states. The metric is denoted as the expected stochastic... more
Abstract This paper addresses the problem of developing a quantitative measure for the flexibility of a design to withstand uncertainties in the continuous parameters and discrete states. The metric is denoted as the expected stochastic flexibility E(SF). For a given a linear model, a joint distribution for the parameters and probabilities of failure for the discrete states, the proposed metric predicts the probability of feasible operation for a design. A novel inequality reduction scheme is proposed to aid in performing the integration over the feasible region characterized by inequalities. A bounding scheme is also proposed to avoid the evaluation of the integrals over a large number of discrete states when determining the E(SF). An example problem is presented to demonstrate the fact that the proposed measure provides a framework for integrating flexibility and reliability in process design.
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In the last decade Mixed-Integer Programming solvers have evolved enormously contributing to the widespread application of optimization in real world problems in industry. Nonetheless, it is paramount for practitioners to have basic... more
In the last decade Mixed-Integer Programming solvers have evolved enormously contributing to the widespread application of optimization in real world problems in industry. Nonetheless, it is paramount for practitioners to have basic knowledge on how these solvers work and to be able to identify model structures, so one can take full advantage of the machinery at hand. In this paper we present a reformulation to a simple problem that appears as sub-problem in many supply chain models, and we show the advantage of using suitable mathematical structures in the form of cascading knapsack inequalities to solve it. Moreover, we introduce new reformulations to some special cases, producing tighter linear relaxation and faster solution times.
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This work addresses an integrated framework for deciding about the supplier selection for supply chains in the processed food industry. The relevance of including tactical production and distribution planning in this procurement decision... more
This work addresses an integrated framework for deciding about the supplier selection for supply chains in the processed food industry. The relevance of including tactical production and distribution planning in this procurement decision is assessed. The contribution of this paper is three-fold. Firstly, we propose a new two-stage stochastic mixed-integer programming model for the supplier selection in the process food industry that maximizes profit and minimizes risk of low customer service. Secondly, we reiterate the importance of considering main complexities of food supply chain management, such as: perishability of both raw materials and final products; uncertainty at both downstream and upstream parameters; and age dependent demand. Thirdly, we develop a solution method based on a multi-cut Benders decomposition and generalized disjunctive programming. Results indicate that sourcing and branding actions vary significantly between using an integrated and a decoupled approach. T...
This paper presents a tutorial on the state-of-the-art methodologies for the solution of two-stage (mixed-integer) linear stochastic programs and provides a list of software designed for this purpose. The methodologies are classified... more
This paper presents a tutorial on the state-of-the-art methodologies for the solution of two-stage (mixed-integer) linear stochastic programs and provides a list of software designed for this purpose. The methodologies are classified according to the decomposition alternatives and the types of the variables in the problem. We review the fundamentals of Benders Decomposition, Dual Decomposition and Progressive Hedging, as well as possible improvements and variants. We also present extensive numerical results to underline the properties and performance of each algorithm using software implementations including DECIS, FORTSP, PySP, and DSP. Finally, we discuss the strengths and weaknesses of each methodology and propose future research directions.
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Research Interests: Engineering, Computer Science, Chemistry, Integer Programming, CHEMICAL SCIENCES, and 12 moreMathematical Optimization, Branch and Bound, Net Present Value, Schedule, Infrastructure investment, Time Horizon, Industrial Chemistry/Chemical Engineering, Planning and Scheduling, Submarine Pipeline, Production Rate, Objective function, and Economic indicator
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Research Interests: Mechanical Engineering, Chemical Engineering, Mathematics, Computer Science, Fuzzy set theory, and 13 moreTabu Search, New Product Development, Probabilistic Logic, Production Scheduling, Interval arithmetic, Mathematical Optimization, Job shop scheduling, Fuzzy Set, Process Scheduling, Fuzzy Number, Probabilistic Model, Probabilistic Approach, and Probability Distribution Function
Abstract This paper addresses the problem of synthesizing heat exchanger networks that have the flexibility of coping with prespecified changes in flow rates, inlet temperatures and outlet temperatures in a finite sequence of time... more
Abstract This paper addresses the problem of synthesizing heat exchanger networks that have the flexibility of coping with prespecified changes in flow rates, inlet temperatures and outlet temperatures in a finite sequence of time periods. A multiperiod version of the mixed integer linear programming (MILP) trans-shipment model is presented which accounts for the changes in pinch points and utility requirement at each time period. With use of this model as a basis, a systematic procedure is proposed for synthesizing network configurations that require minimum utility cost for each period of operation and involve the fewest number of units. Application of this synthesis procedure is illustrated with two example problems.
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Research Interests: Engineering, Mechanical Engineering, Chemical Engineering, Computer Science, Process Systems Engineering, and 8 moreProduct Design, Life Cycle Assessment, Supply Chain, Product Lifecycle Management, SUPPLY CHAIN OPTIMIZATION, Life Cycle, Life Cycle Analysis, and Process and Product Design Optimization
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This work presents the synthesis of heat-integrated water networks (HIWNs) by using mathematical programming. A new superstructure is synthesised by combining a water network and a modified heat exchanger network. Based on the proposed... more
This work presents the synthesis of heat-integrated water networks (HIWNs) by using mathematical programming. A new superstructure is synthesised by combining a water network and a modified heat exchanger network. Based on the proposed superstructure, a mixed-integer nonlinear programming (MINLP) model is developed. The model is solved by using a one-step solution strategy enabling different initialisations and the generation of multiple solutions, from which the best one is chosen. The results show that the proposed model can be effectively used for solving HIWN problems of different complexities, including large-scale problems.
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Abstract In this paper the problem of obtaining the degree of flexibility that maximizes the total profit in an existing process flowsheet is addressed. Assuming a linear model for the process and given probability distribution functions... more
Abstract In this paper the problem of obtaining the degree of flexibility that maximizes the total profit in an existing process flowsheet is addressed. Assuming a linear model for the process and given probability distribution functions for the uncertain parameters, the curve ...
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In this paper the problem of optimally redesigning an existing process to increase its flexibility is addressed. Assuming a linear model for the process, a general strategy is proposed which determines first the optimal parametric changes... more
In this paper the problem of optimally redesigning an existing process to increase its flexibility is addressed. Assuming a linear model for the process, a general strategy is proposed which determines first the optimal parametric changes and then identifies the optimal structural ...
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In this work, we apply a decomposition technique to address the multiperiod heat exchanger network synthesis. Each period corresponds to changes in operating conditions, i.e. inlet temperatures and heat capacity flowrates. The problem... more
In this work, we apply a decomposition technique to address the multiperiod heat exchanger network synthesis. Each period corresponds to changes in operating conditions, i.e. inlet temperatures and heat capacity flowrates. The problem size grows quickly with the number of streams and the number of periods resulting in a large scale problem to solve. In order to reduce the problem to a manageable size, we propose a specialized heuristic algorithm that relies on the concept of Lagrangean decomposition. We present an iterative scheme where feasible solutions are postulated from the Lagrangean decomposition subproblems, and the Lagrangean multipliers are updated through a subgradient method. Numerical examples are used to illustrate the proposed approach and the solutions are compared with the full space solutions with no decomposition. In general, slightly better solutions are found but in the terms of computational effort, its use is only justified as the problem size is increased.
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In this work, we apply a decomposition technique to address the multiperiod heat exchanger network synthesis. Each period corresponds to changes in operating conditions, i.e. inlet temperatures and heat capacity flowrates. The problem... more
In this work, we apply a decomposition technique to address the multiperiod heat exchanger network synthesis. Each period corresponds to changes in operating conditions, i.e. inlet temperatures and heat capacity flowrates. The problem size grows quickly with the number of streams and the number of periods resulting in a large scale problem to solve. In order to reduce the problem to a manageable size, we propose a specialized heuristic algorithm that relies on the concept of Lagrangean decomposition. We present an iterative scheme where feasible solutions are postulated from the Lagrangean decomposition subproblems, and the Lagrangean multipliers are updated through a subgradient method. Numerical examples are used to illustrate the proposed approach and the solutions are compared with the full space solutions with no decomposition. In general, slightly better solutions are found but in the terms of computational effort, its use is only justified as the problem size is increased.