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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 efficient solution approaches for a new complex NP-hard combinatorial optimization problem, the Pollution Location Inventory Routing problem (PLIRP), which considers both economic and environmental issues. A mixed-integer linear programming model is proposed and first, small problem instances are solved using the CPLEX solver. Due to its computational complexity, General Variable Neighborhood Search-based metaheuristic algorithms are developed for the solution of medium and large instances. The proposed approaches are tested on 30 new randomly generated PLIRP instances. Parameter estimation has been performed for determining the most suitable perturbation strength. An extended numerical analysis illustrates the effectiveness and efficiency of the underlying methods, leading to high-quality solutions with limited computational effort. Furthermore, the impact of holding cost variations to the total cost is studied.

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 work, based on Stackelberg hypothesis, considers a conventional power producer exercising their dominant position in an electricity pool with high penetration of wind power production. A bi-level optimization model is used to provide optimal offer strategies for the aforementioned producer in a jointly cleared energy and reserve pool settled through an hourly auction process. The upper-level problem illustrates the expected profit optimization of the strategic producer while the lower-level problem represents the energy-only market clearing process through a two-stage stochastic program. The first stage clears the day ahead market, and the second stage presents the system operation in balancing time though a set of plausible wind power production realizations. The bi-level problem is recast into a mathematical program with equilibrium constraints which is then reformulated into a mixed integer linear program. These transformations occur using the Karush-Kuhn-Tucker optimality conditions and the strong duality theory. The suggested model provides optimal strategic offers and local marginal prices under different levels of wind penetration and network line transmission capacities.

This work presents a novel framework to simultaneously address the optimal planning of COVID-19 vaccine supply chains and the optimal planning of daily vaccinations in the available vaccination centres. A new mixed integer linear programming (MILP) model is developed to generate optimal decisions regarding the transferred quantities between locations, the inventory profiles of central hubs and vaccination centres and the daily vaccination plans in the vaccination centres of the supply chain network. Specific COVID-19 characteristics, such as special cold storage technologies, limited shelf-life of mRNA vaccines in refrigerated conditions and demanding vaccination targets under extreme time pressure, are aptly modelled. The goal of the model is the minimization of total costs, including storage and transportation costs, costs related to fleet and staff requirements, as well as, indirect costs imposed by wasted doses. A two-step decomposition strategy based on a divide-and-conquer and an aggregation approach is proposed for the solution of large-scale problems. The applicability and efficiency of the proposed optimization-based framework is illustrated on a study case that simulates the Greek nationwide vaccination program. Finally, a rolling horizon technique is employed to reactively deal with possible disturbances in the vaccination plans. The proposed mathematical framework facilitates the decision-making process in COVID-19 vaccine supply chains into minimizing the underlying costs and the number of doses lost. As a result, the efficiency of the distribution network is improved, thus assisting the mass vaccination campaigns against COVID-19.

This work considers the scheduling problem of continuous make-and-pack industries, including flexible intermediate storage vessels, aiming to provide better synchronisation of the production stages. A novel continuous-time, precedence-based, MILP model is developed for the problem under consideration. Mass balance constraints are cleverly satisfied using a continuous-time representation. Extending previously proposed precedence-based frameworks, flexible vessels are used for storing multiple intermediates of the same recipe. Furthermore, new efficient resource-constraints, related to generation and recycling of byproduct waste are introduced to consider additional benefits by their utilisation in the plant. A two-stage MILP-based solution strategy is proposed for the solution of real-life, large-scale industrial problem instances. Several case studies, inspired by consumer goods industries, are used to illustrate the applicability of the proposed framework. Results illustrate that the utilisation of intermediate buffers leads to a better synchronisation of the production stages and increased productivity, as unnecessary idle times, total waste and total plant costs are reduced.

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 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.

This work investigates the interaction between power producers with conventional and wind generation portfolios participating in a network-constrained pool-based market. A stochastic bi-level problem is introduced to model the strategic behavior of each single producer. The upper-level problem maximizes the producers’ expected profits and the lower-level problem optimizes the jointly cleared energy and balancing market under economic dispatch. Market participants’ offers are modeled using linear stepwise curves, and the stochastic wind power generation is realized through a set of plausible wind scenarios. The bi-level problem is recast into a single-level mathematical problem with equilibrium constraints with primal-dual formulation using the Karush-Kuhn-Tacker first order optimality conditions and the strong duality theorem. The joint solution of all strategic producers’ problems constitutes an equilibrium problem with equilibrium constraints. The latter is reduced into an equivalent mixed integer linear program by using disjunctive constraints. Different objective functions are applied to the final program to define the range of market equilibria, and a single-iterate diagonalization process is used to justify those equilibria that are meaningful. The model addresses several cases considering different types of market competition, transmission line congestions, and different levels of wind power penetration and volatility.

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.

This work proposes Adaptive General Variable Neighborhood Search metaheuristic algorithms for the efficient solution of Pollution Location Inventory Routing Problems (PLIRPs). A comparative computational study, between the proposed methods and their corresponding classic General Variable Neighborhood Search versions, illustrates the effectiveness of the intelligent mechanism used for automating the re-ordering of the local search operators in the improvement step of each optimization method. Results on 20 PLIRP benchmark instances show the efficiency of the proposed metaheuristics.

This work considers a power producer with dominant position in electricity market. A bi-level model is constructed to derive optimal offering strategies for this producer. The bi-level model is reformed into a mathematical programming with equilibrium constraints (MPEC) model which is then recast into a mixed integer linear program using strong duality theorem and Karush-Kuhn-Tacker first order optimality conditions. The proposed algorithm results in optimal scheduled thermal and wind energy production as well as reserve deployments for the strategic producer. It also provides endogenous formation of local marginal prices and optimal offers under network constraints and wind generation uncertainty.

This work introduces the Fleet-size and Mix Pollution Location-Inventory-Routing Problem with Just-in-Time replenishment policy and Capacity Planning. This problem extends the strategic-level decisions of classic LIRP by considering capacity selection decisions and heterogeneous fleet composition. An MIP formulation of this new complex combinatorial optimization problem is proposed and small-sized problem instances are solved using the CPLEX solver. For the solution of more realistic-sized problem instances, a General Variable Neighborhood Search (GVNS)-based framework is adopted. Novel adaptive shaking methods are proposed as intelligent components of the developed GVNS algorithms to further improve their performance. To evaluate the proposed GVNS schemes, several problem instances are randomly generated by following specific instructions from the literature and adopting real vehicles’ parameters. Comparisons between these solutions and the corresponding ones achieved by CPLEX are made. The computational results indicate the efficiency of the proposed GVNS-based algorithms, with the best GVNS scheme to produce 7% better solutions than CPLEX for small problems. Finally, the economic and environmental impacts of using either homogeneous or heterogeneous fleet of vehicles are examined.

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.

This work presents a new variant of the Location Inventory Routing Problem (LIRP), called Pollution LIRP (PLIRP). The PLIRP considers both economic and environmental impacts. A Mixed Integer Programming (MIP) formulation is employed and experimental results on ten randomly generated small-sized instances using CPLEX are reported. Furthermore, it is shown that, CPLEX could not compute any feasible solution on another set of ten randomly generated medium-sized instances, with a time limit of five hours. Therefore, for solving more computationally challenging instances, two Basic Variable Neighborhood Search (BVNS) metaheuristic approaches are proposed. A comparative analysis between CPLEX and BVNS on these 20 problem instances is reported.

This work, based on Stackelberg hypothesis, considers a conventional power producer exercising their dominant position in an electricity pool with high penetration of wind power production. A bi-level optimization model is used to provide optimal offer strategies for the aforementioned producer in a jointly cleared energy and reserve pool settled through an hourly auction process. The upper-level problem illustrates the expected profit optimization of the strategic producer while the lower-level problem represents the energy-only market clearing process through a two-stage stochastic program. The first stage clears the day ahead market, and the second stage presents the system operation in balancing time though a set of plausible wind power production realizations. The bi-level problem is recast into mathematical programming with equilibrium constraints (MPEC) which is then reformulated into an MILP. These transformations occur using the Karush-Kuhn-Tucker optimality conditions and the strong duality theory. The suggested model provides optimal strategic offers and local marginal prices under different levels of wind penetration and network line transmission capacities.

This work presents the development and application of an efficient solution strategy for the optimal production scheduling of a real-life food industry. In particular, the case of a canned fish production facility for a large-scale Spanish industry is considered. Main goal is to develop an optimized weekly schedule, in order to minimize the total production makespan. The proposed solution strategy constitutes the basis to develop an efficient and robust approach for this complex scheduling problem. A general precedence Mixed-Integer Linear Programming (MILP) model is utilized for all scheduling-related decisions (unit allocation, timing and sequencing). To solve the scheduling problem in a computational time accepted by the industry, a two-step decomposition algorithm is employed. Salient characteristics of the canned fish industry are aptly modelled, while valid industry-specific heuristics are incorporated. The suggested solution strategy is successfully applied to a real study case, corresponding to the most demanding week of the plant under study.

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.

The production scheduling of a real-life multi-product, mixed batch and continuous food industrial facility is considered in this work. More specifically, the scheduling of canned fish production in a large-scale Spanish industry is studied in detail. The deployment of an efficient solution strategy is proposed to handle the computationally challenging scheduling problem. In particular, a Mixed-Integer Linear Programming (MILP) model is used, in parallel with a decomposition technique. The problem under consideration focuses on two important stages of the plant, the sterilization and the packaging. The proposed strategy takes into account the specific characteristics of the canned fish production facility resulting in interesting results. It should be noted that the same methodology can be used with appropriate modifications in other food process industries with similar production characteristics.

This work presents a generic Mixed-Integer Linear Programming model that integrates a Mid-term Energy Planning model for the optimal integration of power plants into interconnected power generation systems. The time horizon consists of a representative day for each month of the year. The Unit commitment problem is modelled in details to optimally determine the optimal operational strategy in order to meet the electricity demand at a minimum total cost by utilizing the optimal combination of a set of available power generation plants. Furthermore, 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. The possibility of expanding the existing interconnection capacity between systems is also considered. Environmental-related constraints for the production of CO2, NOX, SOX and PMX emissions are also taken into account. The main objective is the minimization of the total annualized cost. The applicability of the proposed model is illustrated in a case study including two interconnected power systems. Finally, a sensitivity analysis is performed in order to investigate the effect of key process parameters on the final power generation policies.

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).

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...

A distributed energy system is a multi-input and multi-output energy system with substantial energy, economic and environmental benefits. The optimal design of such a complex system under energy demand and supply uncertainty poses significant challenges in terms of both modelling and corresponding solution strategies. This paper proposes a two-stage stochastic programming model for the optimal design of distributed energy systems. A two-stage decomposition based solution strategy is used to solve the optimization problem with genetic algorithm performing the search on the first stage variables and a Monte Carlo method dealing with uncertainty in the second stage. The model is applied to the planning of a distributed energy system in a hotel. Detailed computational results are presented and compared with those generated by a deterministic model. The impacts of demand and supply uncertainty on the optimal design of distributed energy systems are systematically investigated using proposed modelling framework and solution approach.

This work presents a generic Mixed Integer Linear Programming model that integrates a Mid-term Energy Planning model, which implements generation and transmission system planning at a yearly level, with a Unit Commitment model, which performs the simulation of the day-ahead electricity market. The applicability of the proposed model is illustrated in a case study of the Greek power system. The proposed modelling framework identifies (or not) the interconnection of an autonomous island to the mainland electric system, as well as the optimum interconnection capacity. It also quantifies the effects of the interconnection options in the day-ahead electricity market and on the energy mix. The proposed model can provide useful insights into the strategic and challenging decisions to be determined by investors and/or policy makers at a national and/or regional level, by providing the optimal energy roadmap and management, as well as clear price signal on critical energy projects under real operating and design constraints.

Fuel cell systems are a promising alternative to traditional power sources for a wide range of portable, automotive and stationary applications and have an increasing potential for wider use as the demand for clean energy is increasing and the focus is shifting towards renewable energy generation. This chapter has a multidisciplinary scope, the design of a computer-aided framework for monitoring and operation of integrated fuel cell systems and the development of advanced model-based control schemes. The behavior of the framework is experimentally verified through the online deployment to an automated small-scale fuel cell unit, demonstrating excellent response in terms of computational effort and accuracy with respect to the control objectives.

This chapter presents a generic mixed integer linear programming (MILP) model that integrates the unit commitment problem (UCP), i.e., daily energy planning with the long-term generation expansion planning (GEP) framework. Typical daily constraints at an hourly level such as start-up and shut-down related decisions (start-up type, minimum up and down time, synchronization, soak and desynchronization time constraints), ramping limits, system reserve requirements are combined with representative yearly constraints such as power capacity additions, power generation bounds of each unit, peak reserve requirements, and energy policy issues (renewables penetration limits, CO2 emissions cap and pricing). For modelling purposes, a representative day (24 h) of each month over a number of years has been employed in order to determine the optimal capacity additions, electricity market clearing prices, and daily operational planning of the studied power system. The model has been tested on an illustrative case study of the Greek power system. Our approach aims to provide useful insight into strategic and challenging decisions to be determined by investors and/or policy makers at a national and/or regional level by providing the optimal energy roadmap under real operating and design constraints.

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.

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.

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

A new model for scheduling fast consumer goods manufacturing processes is developed using mixed-integer linear programming (MILP) techniques combined with a continuous representation of time. Key features of the model include sequence-dependent changeovers and flexible intermediate storage requirements typically arising in industrial manufacturing problems. Due to the utilization of a continuous time representation, the formulation is shown to result in reduced model sizes in terms of both variables and constraints. Near-optimal solutions are reported for the case study under investigation.

This paper presents a new mathematical programming formulation for the problem of determining the optimal manner in which several product rolls of given sizes are to be cut out of raw rolls of one or more standard types. The objective is to perform this task so as to maximize the profit taking account of the revenue from the sales, the costs of the original rolls, the costs of changing the cutting pattern and the costs of disposal of the trim. A mixed integer linear programming (MILP) model is proposed which is solved to global optimality using standard techniques. A number of example problems, including an industrial case study, are presented to illustrate the efficiency and applicability of the proposed model.

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 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.

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.

Plant layout is concerned with the spatial arrangement of processing equipment, storage vessels, and their interconnecting pipework. Deciding a good layout is an important activity in the design of chemical and process plants. A good layout will facilitate a correct operation of the plant. It will also provide an economic acceptable balance between the often conflicting constraints deriving from safety, environment, construction, maintenance, operation, space for future expansion, and process relationships such as those determined by gravity flow. This paper presents a mathematical formulation for addressing the problem of allocating items of equipment in a given two- or three-dimensional space. The objective function to be minimized is the total pumping, connection, and floor construction cost. Detailed cost factors are used to account for the flow direction between two connected units. The problem is formulated as a mixed integer linear programming model. Specific attention is paid to constructing a for...

The article contains sections titled: 1. Introduction 2. Systematic Modeling Methods and Tools 2.1. Introduction 2.2. Model Development 2.3. Model Types and Forms 2.4. Modeling Practice 2.4.1. Problem and Model Definition 2.4.2. Model Conceptualization 2.4.3. Model Data Requirements 2.4.4. Model Construction 2.4.5. Model Solution 2.4.6. Model Verification 2.4.7. Model Validation 2.4.8. Model Deployment and Maintenance 2.5. Computer-Aided Modeling 2.6. Illustrative Example 2.6.1. Model Analysis 2.6.2. Model Structure 2.6.3. Solution Strategy 2.6.4. Incremental Modeling 2.7. Challenges and Opportunities 3. Numerical Methods for Steady-State Simulation 3.1. Introduction 3.2. Numerical Methods and Process Simulation 3.2.1. Newton's Method and Its Variants 3.2.1.1. Newton's Method 3.2.1.2. Finite Difference Method 3.2.1.3. Broyden's Method 3.2.1.4. Hybrid Newton-Quasi-Newton Methods 3.2.1.5. Thermodynamically Consistent Hybrid Methods 3.2.1.6. Other Variants of Newton's Method 3.2.2. Direct and Accelerated Direct Substitution 3.2.2.1. Direct Substitution 3.2.2.2. Newton Acceleration 3.2.2.3. Wegstein Accelerated Direct Substitution 3.2.2.4. Broyden Accelerated Direct Substitution 3.2.2.5. General Dominant Eigenvalue Acceleration 3.2.3. Stabilization Method 3.2.3.1. Line Searching Procedures 3.2.3.2. Trust Region Methods 3.2.3.3. Homotopy-Continuation Methods 3.2.4. Complex Domain Methods 3.2.5. Optimization-Based Methods 3.2.6. Interval Methods 3.3. Numerical Analysis 3.3.1. General Convergence Considerations 3.3.1.1. Newton's Method and Its Variant 3.3.1.2. Direct Substitution and Its Variant 3.3.1.3. Stabilization Methods 3.3.2. Rates of Convergence 3.3.2.1. Newton's Method and Its Variants 3.3.2.2. Direct Substitution and Its Variants 3.3.2.3. Rates of Convergence in Practice 3.3.3. Nonconvergent Behavior 3.3.3.1. Periodic and Chaotic Behavior 3.3.3.2. Julia Sets 3.3.3.3. The Mandelbrot Set 3.3.4. Simple Examples 3.3.5. Two-Dimensional Nonadiabatic Continuous Stirred Tank Reactor 4. Numerical Methods for Dynamic Simulation 4.1. Introduction 4.2. Ordinary Differential Equation Models (ODEs) 4.2.1. Basic Ideas for Solving ODE Systems 4.2.2. Differential Algebraic Equation Models (DAEs) 4.2.3. Implicit Simultaneous Solution of DAEs 4.2.4. Implicit or Explicit Structured Solutions of DAEs 4.2.5. High-Index DAE Problems 4.2.6. Challenges and Opportunities in Dynamic Modeling and Solution 5. Numerical Methods for Distributed Model Simulation 5.1. Introduction 5.2. General Approaches to Solving Distributed System Models 5.3. Population Balance Models (PBMs) 6. Parameter uncertainty estimation in numerical modeling 6.1. Introduction 6.2. Theory of Parameter Uncertainty Estimation 6.2.1. Frequentist Approach 6.2.2. Bayesian Approach 6.2.3. Example: Estimation of Parameters of Michaelis–Menten Kinetics 6.3. Frequentist Compared to Bayesian Approach 7. Simulation Tools 7.1. Introduction 7.2. Well-Known General-Purpose Process Simulation Software Platforms and Applications 7.3. Main Features of General-Purpose Process Simulation Software 7.3.1. Aspen Plus 7.3.2. Aspen Plus Dynamics 7.3.3. Aspen HYSYS 7.3.4. gPROMS 7.3.5. PRO/II 7.3.6. DynSim 7.3.7. ROMeo 7.3.8. ChemCad 7.4. Trends in Process Simulation Engineering 7.4.1. Trends in Process Simulation 7.4.2. Trends in Model Deployment 7.4.3. Trends in Information Technology (IT) Infrastructure 7.4.4. Value Creation Opportunities 8. Acknowledgments

This works presents a novel mixed-integer programming framework and a solution strategy for the optimal production scheduling of multiproduct and multistage food process industries, such as ice-cream production facilities, studied in detail. The overall mathematical framework relies on an efficient modeling approach of the sequencing decisions, the integrated modeling of all production stages, and the inclusion of strong valid integer cuts in the formulation. The simultaneous optimization of all processing stages increases the plant production capacity, reduces the production cost for final products, and facilitates interaction among the different departments of the production facility. Several instances of a real-life industrial case study concerning ice-cream production have been solved to optimality to illustrate the applicability and efficiency of the overall modeling and solution approach.