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This work considers the optimal production planning and scheduling problem in beer production facilities. The underlying optimization problem is characterized by significant complexity, including multiple production stages, several processing units, shared resources, tight design and operating constraints and intermediate and final products. Breweries are mainly differentiated to the rest of the beverage industries in terms of long lead times required for the fermentation/maturation process of beer. Therefore, synchronizing the production stages is an extremely challenging task, while the long time horizon leads to larger and more difficult optimization problems. In this work we present a new MILP model, using a mixed discrete-continuous time representation and the immediate precedence framework in order to minimize total production costs. A number of test cases are used to illustrate the superiority of the proposed model in terms of computational efficiency and solution quality compared with approaches developed in other research contributions. The proposed model provides consistently better solutions and improvements of up to 50% are reported. In order to address large-scale problem instances and satisfy the computation limitations imposed by the industry, a novel MILP-based solution strategy is developed, that consists of a constructive and an improvement step. As a result, near-optimal solutions for extremely large cases consisting of up to 30 fermentation tanks, 5 filling lines and 40 products are generated in less than two hours. Finally, the proposed method is successfully applied to a real-life case study provided by a Greek brewery and near-optimal schedules are generated in relatively short CPU times.

This work presents a Mixed Integer Programing (MIP) formulation for a new complex NP-hard combinatorial optimization problem, the Location Inventory Routing with Distribution Outsourcing (LIRPDO). Due to its computational complexity, only small problem instances can be solved by exact solvers. Therefore, a General Variable Neighborhood Search (GVNS)-based metaheuristic algorithm for solving large LIRPDO instances is presented. The proposed approach has been tested on 20 new randomly generated LIRPDO instances, 20 existing benchmark LIRP instances from the literature and 30 new large-scale random generated LIRP instances. An extended numerical analysis illustrates the efficiency of the underlying method, leading to acceptable solutions requiring limited computational effort.

This paper presents an optimization-based approach to address the problem of the optimal daily energy scheduling of interconnected power systems in electricity markets. More specifically, a Mixed Integer Linear Programming model (MILP) has been developed to address the specific challenges of the underlying problem. The main focus of the proposed framework is to examine the importance and the impacts of electricity interconnections and cross-border electricity trade on the scheduling of power systems, both at a technical and economic level. The applicability of the proposed approach has been tested on an illustrative case study including five power systems which can be interconnected (with a certain interconnection structure) or not. The proposed model determines in a detailed and analytical way the optimal power generation mix, the electricity trade among the systems, the electricity flows (in case of interconnection options), the marginal price of each system, as well as it investigates through a sensitivity analysis the effects of the available interconnection capacity on the resulting power production mix. The work demonstrates that the proposed optimization approach is able to provide important insights into the appropriate energy strategies followed by the market participants, as well as on the strategic long-term decisions to be implemented by investors and/or policy makers at a national and/or regional level, underlining potential risks and providing appropriate price signals on critical energy infrastructure projects under real market operating conditions.

This work presents a Mixed Integer Linear Programming (MILP) model for the optimal interconnected power systems planning over a time horizon of one year. The power generation units include thermal units, hydroelectric units and renewable units (wind and solar power plants). Each system can produce power in order to satisfy its demand and/or supply energy to another system via interconnections. The time horizon of interest, consists of a representative day for each month of the year. The model considers the possibility of building new units selected from a set of proposed ones, as well as expanding the capacity of existing renewable energy units (generation expansion planning), stressing the flexibility that electricity trade provides to power systems. The possibility of expanding the existing interconnection capacity between systems is also considered (transmission expansion planning). The proposed optimization model relies on balance, design, operational and logical constraints. Environmental-related con...

This work presents a mathematical modeling framework for the simulation and optimization of pressure/vacuum swing adsorption (P/VSA) processes for post-combustion CO 2 capture. A single-stage P/VSA process for CO 2 capture from dry flue gas is considered using new zeolite 13X-based adsorbents resulting from perturbation on the 13X zeolite isotherm. A two-bed six-step P/VSA cycle configuration with light product pressurization is employed in systematic simulation and optimization studies. First a zeolite 13X, the current benchmark commercial adsorbent for CO 2 capture, is considered. Accordingly, the model is used to study and evaluate new zeolite 13X-based adsorbents for more efficient CO 2 capture. The results from systematic comparative simulation studies demonstrate that a modified zeolite 13X-based adsorbent appears to have better process performance compared with the original zeolite 13X. Furthermore, process optimization studies employing the above potential adsorbents are performed to minimize energy consumption for specified minimum requirements in CO 2 purity and recovery. The optimization results indicate that the minimum target of 95% in CO 2 purity and 90% in CO 2 recovery is easily met for the P/VSA process under consideration for both potential adsorbents under different operating conditions resulting in different energy requirements and CO 2 productivity.

This paper presents an optimization-based approach to address the problem of the optimal daily energy scheduling of interconnected power systems in electricity markets. More specifically, a Mixed Integer Linear Programming model (MILP) has been developed to address the specific challenges of the underlying problem. The main focus of the proposed framework is to examine the importance and the impacts of electricity interconnections and cross-border electricity trade on the scheduling of power systems, both at a technical and economic level. The applicability of the proposed approach has been tested on an illustrative case study including five power systems which can be interconnected (with a certain interconnection structure) or not. The proposed model determines in a detailed and analytical way the optimal power generation mix, the electricity trade among the systems, the electricity flows (in case of interconnection options), the marginal price of each system, as well as it investigates through a sensitivity analysis the effects of the available interconnection capacity on the resulting power production mix. The work demonstrates that the proposed optimization approach is able to provide important insights into the appropriate energy strategies followed by the market participants, as well as on the strategic long-term decisions to be implemented by investors and/or policy makers at a national and/or regional level, underlining potential risks and providing appropriate price signals on critical energy infrastructure projects under real market operating conditions.

This work presents a generic optimization framework to address the problem of the optimal design and operational scheduling of energy microgrids. The problem to be solved is formulated as a mixed-integer linear programming (MILP) model whose objective function concerns the total cost minimization of the energy microgrid. The energy generating units to be installed consist of technologies using fuel (natural gas) as a raw material (microturbines, fuel cells etc.), and renewable energy sources (wind and solar). The microgrid is divided into a certain number of zones, each of which is characterized by a given amount of electricity demand to be satisfied, while the system can exchange electrical energy with the main power grid by acquiring from and selling energy to the grid. The efficiency and applicability of the proposed model is illustrated using three case studies. The maximum allowable level of CO2 emissions, the price of electricity purchased from the main grid, and the price of electricity sold to the main grid constitute the parameters whose influences on the economic variables of the microgrid, on the quantities and the capacities of the installed technologies, as well as on the energy balance of the microgrid are investigated. The proposed model provides a systematic and analytical methodological framework for a detailed planning and scheduling of energy microgrids, highlighting potential risks and appropriate price signals on critical energy projects undertaken by investors and/or designed by policy makers at a national and/or regional level under realistic operating conditions.

The aim of this work is to demonstrate the response of advanced model-based predictive control (MPC) strategies for Polymer Electrolyte Membrane Fuel cell (PEMFC) systems. PEMFC are considered as an interesting alternative to conventional power generation and can be used in a wide range of stationary and mobile applications. An integrated and modular computer-aided Energy Management Framework (EMF) is developed and deployed online to an industrial automation system for monitoring and operation of a PEMFC testing unit at CERTH/CPERI. The operation objectives are to deliver the demanded power while operating at a safe region, avoiding starvation, and concurrently minimize the fuel consumption at stable temperature conditions. A dynamic model is utilized and different MPC strategies are online deployed (Nonlinear MPC, multiparametric MPC and explicit Nonlinear MPC). The response of the MPC strategies is assessed through a set of comparative experimental studies, illustrating that the control objectives are achieved and the fuel cell system operates economically and at a stable environment regardless of the varying operating conditions.

Flexibility in supply chain networks dealing with uncertainty, has become a research challenge over the past years. This work proposes a flexible supply chain network design (SCND) model that uses generalized production/warehousing nodes instead of individual production plants and warehouses while conquers with demand uncertainty using a scenario-based approach. It also deals with inventory management and decisions on strategical and tactical level (facility location, production rate, warehouse capacity, demand allocation between generalized nodes, inventory levels, product flows, suppliers’ product availability and links between all facilities). The proposed Mixed-Integer Linear Programming (MILP) model allows intra-layer flows between generalized nodes and aims at minimizing total network cost. A case study is formed to test the applicability of the model for a medium sized European company. A comparison was made between a classic supply chain network and generalized network that deals with uncertainty. Results have revealed cost benefits for this model, making it not only applicable, but also cost effective for the company that will apply it. This decision support system, can help managers in taking strategic decisions such as facility location, with a higher level of accuracy.

The production scheduling problem of a real-life food industry is addressed in this work. An efficient MILP-based solution strategy is developed to optimize weekly schedules for a Spanish canned fish production plant. The multi-stage, multi-product facility under study consists of both continuous and batch operations resulting in an extremely complex scheduling problem. In order to reduce its computational complexity, an aggregated approach is cleverly proposed, in which the continuous processes are explicitly modeled, while valid feasibility constraints are introduced for the batch stage. Based on this approach, two MILP models are developed, using a mixed discrete-continuous time representation. All technical, operating and design constraints of the facility are considered, while salient characteristics of the canned-food industry, such as assurance of the end products’ microbiological integrity, are aptly modeled. Both the minimization of makespan and changeovers is studied. In order to meet the computational limits imposed by the industry, an order-based decomposition algorithm is further investigated. The method is successfully applied to real-life case studies, generating near-optimal solutions in short CPU times. The suggested solution strategy can be easily extended to consider other real-life scheduling problems from the process industries sector that share similar production characteristics.

An integrated two-stage pressure/vacuum swing adsorption (P/VSA) process for postcombustion CO2 capture from dry flue gas has been simulated and optimized. In the first stage CO2 is concentrated to 40–60% at almost atmospheric pressure, and in the second stage it is further concentrated to 95%. A two-bed six-step cycle configuration was employed in the first stage, while a two-bed five-step cycle configuration was used in the second stage. All possible combinations of two different types of adsorbents (zeolite 13X and Mg-MOF-74) have been employed to study the effect of adsorbent type on key process performance indicators of the process under consideration. The results from systematic comparative simulations demonstrate that the combination of adsorbents zeolite 13X–Mg-MOF-74 has the best process performance, in terms of CO2 purity and CO2 recovery, followed by the use of zeolite 13X at both stages of the process. Furthermore, process optimization studies employing the above combinations of adsorbents hav...

Multistage population balances provide a more detailed mathematical description of cellular growth than lumped growth models, and can therefore describe better the physics of cell evolution through cycles. These balances can be formulated in terms of cell age, mass, size or cell protein content and they can be univariate or multivariate. A specific three stage population balance model based on cell protein content has been derived and used recently to simulate evolution of cell cultures for several applications. The behavior of the particular mathematical model is studied in detail here. A one equation analog of the multistage model is formulated and it is solved analytically in the self-similarity domain. The effect of the initial condition on the approach to self-similarity is studied numerically. The three equations model is examined then by using asymptotic and numerical techniques. It is shown that in the case of sharp interstage transition the discontinuities of the initial condition are preserved during cell growth leading to oscillating solutions whereas for distributed transition, the cell distribution converges to a self-similar (long time asymptote) shape. The closer is the initial condition to the self similar distribution the faster is the convergence to the self-similarity and the smaller the amplitude of oscillations of the total cell number. The findings of the present work lead to a better understanding of the multistage population balance model and to its more efficient use for description of experimental data by employing the expected solution behavior.

This work presents a new modelling framework and an efficient solution approach for the optimization of supply chain for CAR T-cell therapies. The proposed supply chain structure is patient-centric, as the administration of CAR T-cell therapies is performed in local treatment facilities located close to patients’ sites. Cells are re-engineered in a set of available manufacturing centres, the selection of which is to be decided. A limited number of specialized hospitals operate as coordinators of the overall therapy process. Mobile medical units are considered for delivering therapies from manufacturing centres to local treatment facilities. The underlying problem is formulated as a mixed-integer linear programming model. However, due to the computational complexity, solutions using state-of-the-art solvers such as CPLEX, are obtained only for small and rather unrealistic problem cases. To tackle more realistic-sized problem cases, a General Variable Neighborhood Search (GVNS) algorithm is proposed. The algorithm is tested on 20 new, randomly generated, large problem instances. Solutions were compared with those obtained by CPLEX. Finally, extensive numerical analyses were performed to derive useful insights for the key factors affecting design and operation of CAR T-cell therapies supply chains.

Currently, there is an increasing clinical demand for bone implants for several orthopedic and maxillofacial surgical procedures. Meeting these demands can be achieved with stem cells differentiate...

This work considers the production scheduling of a real-life, consumer goods industry. The production facility consists of multiple continuous stages, and the packing stage constitutes the main pro...

This paper introduces a general mathematical programming framework that employs an innovative generalized supply chain network (SCN) composition coupled with forward and reverse logistics activities. Generalized echelon will have the ability to produce/distribute all forward materials/products and recover/redistribute simultaneously all the returned which are categorized with respect to their quality zone. The work addresses a multi-product, multi-echelon and multi-period Mixed-Integer Linear Programming (MILP) problem in a closed-loop supply chain network design solved to global optimality using standard branch-and-bound techniques. Further, the model aims to find the optimal structure of the network in order to satisfy market demand with the minimum overall capital and operational cost. Applicability and robustness of the proposed model are illustrated by using a medium real case study from a European consumer goods company whereas its benefits are valued through a comparison with a counterpart model that utilizes the mainstream fixed echelon network structure.

Supply chain network (SCN) design and operation is a strategic and value adding process for all synchronous companies. In the face of globalization, several issues should be contemplated and incorp...

This work considers a strategic producer whose generation portfolio consists of conventional and wind power production. Based on the single leader-follower game, a bi-level complementarity model is constructed to derive optimal capacity withholding strategies for this portfolio in a pool-based market. The upper level of the model represents the maximization of the strategic producer’s expected profits while the lower level represents the security-constrained economic dispatch conducted by the independent system operator. The market clearing scheme refers to energy-only markets optimizing jointly scheduled energy and reserves through a two-stage stochastic programming. The first stage illustrates the day-ahead market clearing and the second stage illustrates the balancing market clearing taking into consideration the wind generation uncertainty. With the use of the Karush-Kuhn-Tacker optimality conditions the initial bi-level model is recast into a mathematical programming with equilibrium constraints model which is then reduced into an equivalent mixed integer linear programming using the strong duality theorem and disjunctive constraints. The proposed algorithm derives optimal scheduled thermal and wind energy as well as reserve deployments. It also provides optimal offers based on the endogenous formation of local marginal prices under network constraints and different wind energy penetration levels.

Two binary integer programming discrete-time models and two precedence-based mixed integer programming continuous-time formulations are developed for the resource-constrained project scheduling problem. The discrete-time models are based on the definition of binary variables that describe the processing state of every activity between two consecutive time points, while the continuous-time models are based on the concept of overlapping of activities, and the definition of a number of newly introduced sets. Our four mathematical formulations are compared with six representative literature models in 3240 benchmark problem instances. A detailed computational comparison assesses the performance of the mathematical models considered.

This work proposes a mathematical modeling framework for the design of supply chain networks by providing flexibility on facilities’ location and operation. The proposed model addresses the design of a multiproduct and multiechelon network consisting of generalized production/warehousing nodes that can receive any material from any potential supplier or any other generalized production/warehousing node and deliver any material to any market or any other generalized production/warehousing node. The model is formulated as a mixed integer linear programming problem that aims to find the optimal structure of the network in order to satisfy market demand with the minimum overall capital and operational cost. The applicability of the proposed generalized supply chain network design model is illustrated by using a real case study from a European consumer goods company whereas its robustness and value are documented through sensitivity analysis and through a comparison with a counterpart model that utilizes the m...

Energy planning aims at improving the overall efficiency, economic viability and reducing the environmental impact of energy management systems. Deregulation of electricity markets along with technology development have increased the level of competition allowing energy consumers to select among a variety of energy technologies, fuels and/or suppliers. This work presents a linear mixed integer programming model for the optimal design and operational planning of energy networks based on combined heat and power generators. The studied area is divided into a number of sections, each of which is characterized by a specific heat and electricity demand. Various energy generation technologies and heat storage tanks are modeled, while interchange of electricity can take place among the sections of the network, which is connected to the main power grid for potential power trade with it. There is also the option of an external heat source (i.e., a refinery) constituting an alternative supplier of heat to the sectors of the network. The objective function represents the minimization of total cost under full heat and electricity demand satisfaction. The applicability of the proposed model is illustrated using two illustrative examples, including a residential and an urban energy network. Finally, Monte Carlo simulations have been utilized to capture the effect of uncertainty characterizing some varying parameters, such as the heat demand (residential energy network) as well as the available heat from the refinery (urban energy network).

A distributed energy system refers to an energy system where energy production is close to end use, typically relying on small-scale energy distributed technologies. It is a multi-input and multi-output energy system with substantial energy, economic and environmental benefits. However, distributed energy systems such as micro-grids in residential applications may not be able to produce the potential benefits due to lack of appropriate system configurations and suitable operation strategies. The optimal design, scheduling and control of such a complex system are of great importance towards their successful practical realization in real application studies. This paper presents a short review and an energy systems engineering approach to the modeling and optimization of micro-grids for residential applications, offering a clear vision of the latest research advances in this field. Challenges and prospects of the modeling and optimization of such distributed energy systems are also highlighted in this work.

AML is a cancer of the blood and bone marrow which results from the combined effects of genetic mutations, aberrant interactions in the microenvironment and altered networks of complex chemical reactions at the molecular and cellular level, some of which can be targeted with anti-neoplastic drugs called chemotherapy. AML can be treated with chemotherapy, the types and doses of which are dependent on characteristics of the patient, the sub-type of the tumor and the use of other, often synergistic, anti-cancer drugs, and the doses for which are limited by toxic adverse effects of treatment. Current treatment protocols are designed based on pre-clinical animal experiments and on empirical clinical trials as well as the acquired experience of subspecialist physicians. Mathematical modeling can assist in improving chemotherapy effectiveness and limiting toxicity through a systematic approach in designing treatment protocols. Specifically, these mathematical models should enable a description of the normal and the leukemic cell populations as dependent on disease characteristics (cell cycle distribution into phases, proliferation rate, initial disease and normal population state) and on physiological characteristics of the patient such as age, sex, body surface area that control and define the drug kinetics (concentration profile in tumor site). Such a model can then lead to an optimal management of the available drug kinetics in order to effectively eradicate the maximum possible tumor volume while limiting toxicity of the normal cell population and that will be maintained within certain defined limits. Herein, a model is presented for the first cycle of chemotherapy induction treatment for AML using daunorubicin (DNR) and cytarabine (Ara-C) anti-leukemic agents, a standard intensive treatment protocol for AML. The proposed model combines critical targets of drug actions on the cell cycle, together with pharmacokinetic (PK) and pharmacodynamic (PD) aspects providing a complete description of drug diffusion and action after administration. Tumor-specific characteristics, such as tumor burden and cell cycle times, as well as patient-specific characteristics, such as gender, age, weight and height, are incorporated into the model in an attempt to gain insights into the personalized cell dynamics during treatment. Moreover, an optimal control problem is formulated and solved so as to obtain the chemotherapeutic schedule which would maximize leukemic cell kill (therapeutic efficacy) while minimizing death of the normal cell population, thereby reducing toxicities. Simulation results for a standard treatment protocol are obtained for a patient case study; an optimized treatment schedule is also obtained and the cell populations are analyzed and compared in detail for both the standard and the optimized treatment protocols.

Fuel cell (FC) systems are part of a prominent key enabling technology for achieving efficient and carbon-free electricity generation and, as such, their optimum operation is of great importance. This work presents the combination of two advanced model predictive control (MPC) methodologies to guarantee the optimal operation of a polymer electrolyte membrane (PEM) fuel cell system. More specifically, at the core of the proposed framework is a nonlinear model predictive control (NMPC) formulation that solves online a nonlinear programming (NLP) problem using a simultaneous direct transcription optimization method. The performance of the NLP solver is enhanced by a warm-start initialization and a search space reduction (SSR) technique. A piecewise affine (PWA) approximation of the variable’s feasible space is used to define the boundaries of the search space computed offline, using a multiparametric quadratic programming (mpQP) method. The proposed unified framework is developed and deployed online to an in...

Optimal design and operation of combined cooling, heating and power (CCHP) systems are complicated due to the fluctuating energy demands. Many mathematical models for the design and/or operation of CCHP systems have been developed. Most of them adopt a constant efficiency assumption, whilst others take equipment off-design characteristics into account. In this paper, we present two mathematical models for the optimal design and operation of CCHP systems with the target of minimising the total annual cost. One model is formulated using the constant efficiency assumption. In the other model, off-design characteristics of all equipments are considered. Comparative studies using different models were performed to examine the impacts of equipment off-design characteristics on the accuracy of the optimal design of CCHP systems. Results show that introduction of thermal storage facilities, connection to power grid and well designed operation strategies can diminish the negative impacts of adopting the constant efficiency assumption.

Inherent uncertainties and risks in the economic environment are diffused to all vital operations of a supply chain network (SCN). However, the great impact of this contagion is on the financial operation due to its interdependence with financial markets and business conditions. Economic uncertainty poses uncertainty in the financial status of SCNs and this in turns leads to sustainability and growth risks. Financial performance and credit solvency are two essential pillars of financial status capable of providing the necessary capitals to a SCN. As each of these pillars focuses on a different aspect of investment attractiveness, underlined trade-offs exist, under various economic conditions, and challenge further investigation. This paper aims to enrich the SCN design literature by introducing a mathematical model that integrates financial performance and credit solvency modelling with SCN design decisions under economic uncertainty. The proposed multi-objective mixed integer non linear programming (moMINLP) model enchases financial performance through economic value added (EVA™) and credit solvency through a valid credit scoring model (Altman's Z-score). The applicability of the model is illustrated by using a real case study. The model could be used as an effective strategic decision tool by managers responsible for strategic SCN design.

This work presents new mixed-integer linear programming models for the deterministic single- and multi-mode resource constrained project scheduling problem with renewable and non-renewable resources. The modeling approach relies on the Resource-Task Network (RTN) representation, a network representation technique used in process scheduling problems, based on continuous time models. First, we propose new RTN-based network representation methods, and then we efficiently transform them into mathematical formulations including a set of constraints describing precedence relations and different types of resources. Finally, the applicability of the proposed formulations is illustrated using several example problems under the most commonly addressed objective, the makespan minimization.

The aim of this work is the development and experimental validation of a detailed dynamic fuel cell model using the gPROMS modeling environment. The model is oriented towards optimization and control and it relies on material and energy balances as well as electrochemical equations including semi-empirical equations. For the experimental validation of the model a fully automated and integrated hydrogen fuel cell testing unit was used. The predictive power of the model has been compared with the data obtained during load change experiments. A sensitivity analysis has been employed to reveal the most critical empirical model parameters that should be estimated using a systematic estimation procedure. Model predictions are in good agreement with experimental data under a wide range of operating conditions.

Huge and ever-increasing energy consumption and consequent greenhouse gas (GHG) emissions pose unprecedented challenges to the sustainable development of the international human society. Our existing energy systems, where primary energy is converted to all sorts of final energy services, remain the major contributor to these global energy and environmental challenges. It is becoming a consensus that the conventional energy conversion and utilization mode should make place for a more sustainable one with higher energy conversion efficiency, lower air pollutions and GHG emissions, less dependence on fossil fuels, and more utilization of renewable energy. However, although there exist many technical options and technology pathways to enable this transition, they are usually treated separately by their very own technical communities and political groups without coordination with others, and the overall effect and potential is therefore greatly constrained as compared to a systematic approach where all alterna...

We present a general framework for the optimal design and control of a metal-hydride bed under hydrogen desorption operation. The framework features: (i) a detailed two-dimension dynamic process model, (ii) a design and operational dynamic optimization step, and (iii) an explicit/multi-parametric model predictive controller design step. For the controller design, a reduced order approximate model is obtained, based on which nominal and robust multi-parametric controllers are designed.

This work presents a systematic approach for the optimal design and optimization of metal-hydride materials and processes for efficiency hydrogen storage. Techniques for the synthesis and characterization of novel metal-hydride materials are presented in a view of designing material to enhance storage efficiency. More specifically the synthesis of a composite intermetallic hydride by using theoretical and experimental procedures is investigated and a pseudobinary Zr–Ti–Cr–Ni–V compound has been developed. The X-ray diffraction pattern analysis revealed two Laves phases and a Rietveld analysis has been performed for the determination of the structural characteristics. A unique composite structure is responsible for the desorbed ∼280 ml of H2 per gram of the material obtained after 15 min at 100 °C. A small-scale metal-hydride tank has been designed in order to investigate its capacity and efficiency from 20 °C to 100 °C. Then, a dynamic model that has developed previously by the authors provides the basis for investigating systematic optimization and online control studies. The objective is to find the optimal process design (e.g. cooling systems design) and online operating strategy (e.g. cooling fluid profile over time) so as to minimize the storing time, while satisfying, a number of operating constraints. Optimization results indicate that significant improvement on the storage time can be achieved, compared the case where the system is not optimized and control. Trade-offs between various objectives, alternative design options and optimal cooling control policies are systematically revealed illustrating the potential offered by modern optimization and control techniques.

This work presents an optimization framework for complex pressure swing adsorption (PSA) processes including multibed configurations and multilayered adsorbents. The number of beds, PSA cycle configuration, and various operating and design parameters have been systematically optimized using recent advances on process optimization. The Unibed principle has been adopted relying on the simulation over times of only one bed while storage buffers have been used to model bed interactions. A novel state transition network (STN) representation is employed for the efficient simulation and optimization of the processes. Two large-scale multicomponent separation processes have been used to illustrate the applicability and potential of the proposed approach in terms of improvement of product purity and recovery. Results indicate that significant improvements can be achieved over base case designs.

This work studies three differential equation models of the leukemia cell cycle: a population balance model (PBM) using intracellular protein expression levels as state variables representing phase progress; a delay differential equation model (DDE) with temporal phase durations as delays; and an ordinary differential equation model (ODE) of phase-to-phase progression. In each type of model, global sensitivity analysis determines the most significant parameters while parameter estimation fits experimental data. To compare models based on the output of their structural properties, an expected behavior was defined, and each model was coupled to a pharmacokinetic/pharmacodynamic model of chemotherapy delivery. Results suggest that the particular cell cycle model chosen highly affects the simulated treatment outcome, given the same steady state kinetic parameters and drug dosage/scheduling. The manuscript shows how cell cycle models should be selected according to the complexity, sensitivity, and parameter av...

The aim of the present study is the development of a multiscale modeling and optimization framework for hydrogen storage in carbon-based nanoporous adsorbents. The outlined methodology is generic and can be easily adapted to the storage of several gases of relevant importance and/or different physisorbing nanoporous materials. The results indicate clearly how operating constraints (such as temperature limitations arising from safety considerations) can affect the material design in terms of its pore size distribution and how material design constraints (such as those arising from manufacturing limitations) can effect the operation and efficiency of the process. The ultimate objective is to systematically reveal the strong and highly related synergistic benefits between process design/operation decisions and material design aspects so as to ensure an economically attractive, technically feasible, and safe process. © 2006 American Institute of Chemical Engineers AIChE J, 2006

This work presents the detailed mathematical modelling and advanced optimization of a number of zeolite membrane process structures for gas separations. First, a general model for the separation of binary gas mixtures is developed based on the generalized Maxwell–Stefan (GMS) approach. Accordingly, the model is used in the simulation of various process structures including co-current and counter-current operation, recycle modules and membrane cascades. The model is validated against available experimental data of methane-ethane and methane–propane mixtures on silicalite membranes. A non-linear programming approach is then employed to determine optimal design options for different process performance objectives. Various trade-offs between different optimization objectives are systematically revealed. The impact of the detailed GMS model on the optimization results is investigated through a comparison with corresponding results obtained using the single-file diffusion model, which ignores diffusional adsorbate–adsorbate interactions.

A new mathematical formulation for scheduling multipurpose continuous processes is presented. The formulation is based on the state-task network representation, coupled with an event-driven representation of time, resulting in a mixed-integer linear programming model. Event points are defined by the end of task execution for all continuous tasks in the process. Timing constraints are applied to continuous tasks involving the same material state to ensure feasibility of rate-based material balances. The formulation allows for unit-dependent variable processing rates, sequence-dependent changeovers, and dedicated and flexible intermediate storage requirements. Several variants of a medium to large scale continuous manufacturing process are examined to illustrate the applicability and efficiency of the method. The formulation is shown to compare favorably with existing continuous-time models; a new optimal solution on the finite intermediate storage case of the process is also established.

A new continuous-time formulation for scheduling short-term multipurpose batch processes is presented. The formulation gives rise to a mixed-integer linear programming (MILP) model. The state−task network (STN) representation forms the basis of the proposed approach. A number of event points is prepostulated, which is the same for all tasks in the process. Event times are defined by the ends of task execution, and they are generally different for different tasks of the process, giving rise to a nonuniform time grid. The necessary time monotonicity for single tasks is guaranteed by means of simple duration constraints. Suitable sequencing constraints, applicable to batch tasks involving the same state, are also introduced, so that state balances are properly posed in the context of the nonuniform time grid. The expression of duration and sequencing constraints is greatly simplified by hiding all unit information within the task data. Three benchmark problems are used to illustrate the efficiency and applic...

A practical instance of a one-dimensional cutting stock problem arising frequently in the paper industry is considered. Given a set of raw paper rolls of known length and width, a set of product paper rolls of known length (equal to the length of raw paper rolls) and width, practical cutting constraints on a single cutting machine, and demand orders for all products, the problem requires the determination of an optimal cutting schedule to maximize the overall cutting process profitability while satisfying all demands and cutting constraints. A purely mixed-integer linear programing (MILP) model is developed that does not require the a priori determination of all feasible cutting combinations. A complex objective function including trim loss, overproduction, knife (pattern) changeover costs, and format (raw material type) changeover costs is optimized. A salient feature of the model is that intermediate demand orders are taken into consideration as an integral part of the formulation. A number of example p...

This work presents a new mathematical programming formulation for the problem of scheduling cutting operations on multiple parallel slitting machines. A Mixed-Integer Linear Programming (MILP) model is proposed, solved to optimality using standard techniques. A continuous time representation is used to avoid unnecessary time intervals and to limit the number of variables in the formulation. One important feature of the model is the explicit treatment of change-over times as an important part of a multiple objective cost function, which may be adapted to minimizing makespan, or total flow time, or any weighted combination of the two. An industrial case study from the paper-converting industry is presented to illustrate the applicability and efficiency of the proposed model.

This work presents the mathematical modelling and simulation of complex plate heat exchanger arrangements under milk fouling, using detailed dynamic models. A complex fouling model based on a reaction/mass transfer scheme is coupled with a general thermal dynamic model of plate heat exchangers. All the important factors affecting milk heat treatment are formally quantified. The final model comprises a set of partial differential, integral and algebraic equations. Parameter estimation analysis is performed based on the solution of a dynamic optimization problem. The simulation results are in a good agreement with available experimental work. Three different configurations with complex flow arrangements are considered to illustrate aspects of fouling behaviour. The simulation results provide significant insight into the key factors affecting milk fouling.

This paper addresses the problem of cyclic cleaning and energy scheduling in special classes of heat exchanger networks (HENs). A salient characteristic of this problem is that the performance of each heat exchanger decreases with time and can then be restored to its initial state by performing cleaning operations. Due to the cyclic nature of the schedule, some operations may span successive cycles (wrap-around) which is taken into account in the mathematical model. A tight mixed integer linear programming (MILP) model is presented which is solved to global optimality. A detailed objective function is used to account for cleaning cost and energy requirements. The formulations can model serial and parallel HENs, as well as network arrangements arising from the combination of these basic cases. The optimization algorithm determines simultaneously: (i) the number of cleaning operations required along with their corresponding timings and (ii) the optimal utility utilization profile over time. A complex heat exchanger network example is presented to illustrate the applicability of the proposed model.

This paper addresses the problem of short-term cleaning scheduling in a special class of heat-exchanger networks (HENs). A salient characteristic of this problem is that the performance of each heat exchanger decreases with time and can then be restored to its initial state by performing cleaning operations. Because of its practical importance, a specific problem has been considered here involving decaying equipment performance due to milk fouling. A mixed-integer nonlinear-programming (MINLP) model is first presented incorporating general fouling profiles. This model is then linearized to a tight mixed-integer linear-programming (MILP) model which can be solved to global optimality. A detailed objective function is used to account for cleaning cost and energy requirements. The formulations can model serial and parallel HENs as well as network arrangements arising from the combination of these basic cases. The optimization algorithm determines simultaneously: (i) the number of cleaning operation tasks required along with their corresponding timings and (ii) the optimal utility utilization profile over time. A number of complex heat-exchanger networks examples are presented to illustrate the applicability of the proposed models together with comparative performance results between the MINLP and MILP models.

The generation of a good layout is an important stage in the design of a new plant or the retrofit of an existing facility. Layout decisions affect piping, electrics, instrumentation and therefore have a great impact on the total plant cost. Moreover, layout has a large impact on the safety, operability and maintainability of any chemical plant. This paper presents a general mathematical programming approach for addressing the problem of allocating items of equipment in a given two or three dimensional space. The problem is formulated as a mixed integer linear programming model where equipment of various sizes and geometries are taken into account. The objective function to be minimized accounts for the total transport, connection, land and floor construction cost. This optimization procedure results in the coordinates of each unit (location), the total piping length, and the land occupied. Three case studies are presented to illustrate the applicability of the proposed approach.

This work addresses the problem of cyclic cleaning scheduling in heat exchanger networks (HENs). A salient characteristic of this problem is that the performance of each heat exchanger decreases with time which can then be restored to its initial state by performing cleaning operations. Due to the cyclic nature of the schedule, some operations may span successive cycles (wrap-around) which should be taken into account in the mathematical models. A tight mixed integer linear programming (MILP) model is proposed minimising cleaning cost and energy requirements. A complex heat exchanger network example is presented to illustrate the applicability of the proposed model.

This paper presents developments toward a unified framework for incorporating both process flexibility and robustness (in terms of product quality) criteria in process optimization under uncertainty. A robust design methodology, known as the Taguchi approach, is discussed in the context of uncertainty, and some limitations are identified. Taguchi's method is then extended to take into account process constraints and probabilistic uncertainty. A framework for establishing the interactions and synergistic benefits between the two operability objectives is proposed, based on an expected measure, where product quality losses are taken into account explicitly. Tradeoffs between stochastic flexibility and a robust criterion are explored in order to depict optimal operating policies in the presence of uncertainty; extensions toward design optimization are also briefly discussed. A number of examples is presented to illustrate the applicability of the proposed framework.

This article presents a procedure for the simultaneous optimization of the design and operation of heat exchangers under milk fouling. This scheme is based on a highly accurate dynamic model described by integral, partial differential, and algebraic equations. Design and operating parameters determined by the dynamic optimization include the length and diameter of the exchanger, the control policy, and the timing of the key operating steps. An economic objective function is used to account for the important factors related to milk heat treatment, and many operating constraints are imposed. Three heat exchanger configurations are considered to study the effect of fouling on the optimal plant design. Optimization indicates that the cost factor due to the interruption of production is dominant, while an increase in energy consumption due to fouling is not very important. The constant wall temperature configuration proved to be the most economical. The economic impact of different control structures was also explored.

A mathematical model for single shell and tube heat exchangers under milk fouling is presented. A fouling model based on a reaction/mass-transfer scheme is detailed in which the main factors during milk heat treatment are quantified in a formal way. This model is coupled with a detailed dynamic model of a shell-and-tube heat exchanger where both radial and axial domains are taken into account. An analytical procedure for the calculation of key parameters provides the means to achieve more accuracy. The simulation results agree well with available experimental work. Four different heat exchanger arrangements are then considered to illustrate their impact on the fouling behavior. The results are encouraging enough to validate current operating industrial techniques for fouling mitigation. For a given thermal duty, short heat exchangers are more prone to fouling due to high-temperature requirements and milk should be heated 11s gradually as possible to minimize fouling. The results show that there are main tradeoffs between design and operation issues.

This paper presents the detailed mathematical modelling and simulation of complex plate heat exchangers under milk fouling, using computational fluid dynamics models. A complex fouling model based on a reaction/mass transfer scheme is described where all the important factors during milk heat treatment are quantified in a formal way. This model is coupled with detailed dynamic models of plate heat exchangers (PHEs). The final model comprises a set of partial differential, integral and algebraic equations. Parameter estimation analysis is performed based on the solution of a dynamic optimization problem. The simulation results have been compared with available experimental work and a satisfactory agreement has been found. Three different industrial configurations with complex flow arrangement are considered to illustrate aspects of fouling behaviour.