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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 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.

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 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 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.

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).

This paper presents a mixed-integer linear programming (MILP) model for the optimal long-term energy planning of a (national) power generation system. In order to capture more accurately the spatial and technical characteristics of the problem, the underlying geographical area (country) is divided into a number of individual networks that interact with each other. The proposed model determines the optimal planning of the power generation system, the selection of the power generation technologies, the type of fuels and the plant locations so as to meet the expected electricity demand, while satisfying environmental constraints in terms of CO2 emissions. Furthermore, the suggested model determines the electricity imports from neighbouring countries, the electricity transmission as well as the transportation of primary energy resources between domestic networks. A real case study concerning the Greek energy planning problem demonstrates the applicability of the proposed approach, which can provide policy makers with a systematic computer-aided tool to analyse various scenarios and technology options. Finally, a sensitivity analysis was conducted in order to capture the influence of some key parameters such as electricity demand, natural gas and CO2 emission price as well as wind power investment cost.

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.

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.

A promising and shortly emerging energy supply chain network based on residential-scale microgeneration through micro combined heat and power systems is proposed, modeled and optimized in this work. Interchange of electrical energy can take place among the members of this domestic microgrid, which is connected to the main electrical grid for potential power interchange with it. A mathematical programming framework is developed for the operational planning of such energy supply chain networks. The minimization of total costs (including microgeneration system’s startup and operating costs as well as electricity production revenue, sales, and purchases), under full heat demand satisfaction, constitutes the objective function in this study. Additionally, an alternative microgrid structure that allows the heat interchange within subgroups of the overall microgrid is proposed, and the initial mathematical programming formulation is extended to deal with this new aspect. An illustrative example is presented in order to highlight the particular significance of selecting a proper optimization goal that thoroughly takes into account the major operational, technical and economic driven factors of the problem in question. Also, a number of real-world size case studies are used to illustrate the efficiency, applicability and the potential benefits of the microgeneration energy supply chain networks suggested in this study. Finally, some concluding remarks are drawn and potential future research directions are identified.

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.

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.

In the current paper the dynamic behaviour of an industrial heterogeneous catalytic packed-bed reactor for the steam reforming of methane is examined. The model consists of a set of partial differential equations describing the physico-chemical processes that take place both in solid and gas phases accounting for diffusional limitations within the catalyst particles. The model was validated against literature data, while the heat provided to the reactor wall was optimised in terms of the optimal H2 yield using a quadratic wall temperature profile. The values of the physico-chemical properties were adjusted to the severe operating conditions (high pressures and temperatures) of the reactor accounting for multicomponent gas mixture properties. It is shown that the 2-phase reactor concept along with the optimised wall temperature profile capture very well the dynamic conversion, the temperature and the partial pressure profiles both at bed and at particle level.

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...

The presented procedure aims to establish an in-depth understanding of a derived mathematical model for drug distribution, pharmacokinetics, and drug effect, pharmacodynamics, during volatile anesthesia. A physiologically based, patient-specific model is derived, where the pharmacokinetic (PK) part consists of multiple blood and tissue compartmental models, each adjusted to the weight, height, gender, and age of the patient. The pharmacodynamic (PD) part is described by an effect site compartment and the Hill equation both linking the hypnotic effect measured by the Bispectral Index (BIS) to the arterial anesthetic concentration. Via a global sensitivity analysis the patient-specific PK and PD variables and parameters are analyzed regarding their influence on the measurable outputs, which are the end-tidal concentration of the volatile anesthetic and the BIS. Via this analysis, the uncertainty introduced by PD variability is identified to be more significant than the uncertainty introduced by PK variability. A case study of isoflurane-based anesthesia shows that the simulation results of the individualized PK variables are in good accordance with the measured end-tidal concentration. However, the PD parameters need to be estimated online to predict the hypnotic depth, measured by the BIS, correctly. As a result of this study, the aim should be to focus on the individual identification of the PD parameters before and during anesthesia with future application in safe and robust model predictive control.

This paper presents a physiologically based, patient-specific, compartmental model for volatile anesthesia, consisting of a multiple blood and tissue compartmental model, adjusted to the weight, height, sex and age of the patient. The predicted hypnotic effect measured by the Bispectral Index is linked to the arterial anesthetic concentration by an effect site compartment and the Hill-Equation. To gain an in-depth understanding about the influence of individual patient variables and characteristics, the pharmacokinetic and pharmacodynamic variables are analyzed for application of the model in future model predictive control. In this study the pharmacodynamic variables are identified to have a higher influence on the modeling output and are therefore more important to be identified accurately. The initial sensitivity of the patient is calculated based on default physiological variables and updated during the course of anesthesia as a function of the obtained measurement of the Bispectral Index.

The aim of this work is to present an integrated framework for the on-line control of a Polymer Electrolyte Membrane (PEM) fuel cell system using an optimization-based control methodology. The framework consists of a nonlinear model predictive control (NMPC) scheme and an on-line supervisory control and data acquisition system (SCADA). The solution of the NMPC problem is achieved by a direct optimization method which involves the use of orthogonal collocation on finite elements and represents the optimal control problem as a nonlinear programming problem (NLP). The on-line application of the multivariable controller shows that the proposed framework can accomplish the desired objectives for power fulfilment in the context of a safe operating region. Furthermore the controller exhibits excellent performance in terms of computational requirements and can follow load changes with a negligible error in its response.

In this work we present a general framework for the design and validation of explicit/multi-parametric MPC controllers for Solid Oxide Fuel Cells (SOFC). The framework features four key steps comprising the development of a dynamic mathematical model of the process at hand, the development of a reduced order model of the process and the design of an explicit/multi-parametric MPC for online control. The framework is illustrated on a SOFC system.

A compartmental mathematical model describing the insulin-glucose system of patients with type 1Diabetes is presented in this paper. The model consists of several subsystems including insulin infusion and absorption, exogenous and endogenous glucose introduction/production, glucose distribution in the periphery and provides a realistic prediction of the blood glucose concentration of an individual, under suggested insulin treatment. The simulation results describe daily profiles of glucose concentration in the blood and the influence of insulin on the underlying processes during an open loop insulin therapy. The validation of this model is the first step of designing a closed loop system which will automatically deliver the appropriate amount of insulin for the specific patient and will guarantee the prevention of hyperglycaemia and mainly hypoglycaemia, a condition of high severity.

The simultaneous lot-sizing and production scheduling problem of a real-life large-scale industrial facility of packaged consumer goods is considered in this work. The problem under consideration is mainly focused on the packing stage which constitutes the major production bottleneck. Several packing lines, illustrating different design and operational characteristics, operate continuously in parallel. An efficient solution strategy is implemented to reduce the high computational cost. A Mixed-Integer Linear Programming model (MILP) is used in parallel with a decomposition-based algorithm. Appropriate constraints, referring to the production/formulation stage of the plant, are also imposed in order to ensure the generation of feasible production schedules. The model relies on tight timing and sequencing and products allocation constraints. The main objective is the minimization of the makespan. A number of different case studies have been considered and detailed optimal production schedules have been generated for over 130 products scheduled weekly. The obtained results lead to nearly-optimal scheduling solutions in reasonable computation times. The proposed model can assist decision makers towards rigorous scheduling plans in a dynamic production environment under realistic uncertainty.

Scheduling is a major component for the efficient operation of the process industries. Especially in the current competitive globalized market, scheduling is of vital importance to most industries, since profit margins are miniscule. Prof. Sargent was one of the first to acknowledge this. His breakthrough contributions paved the way to other researchers to develop optimization-based methods that can address a plethora of process scheduling problems. Despite the plethora of works published by the scientific community, the practical implementation of optimization-based scheduling in industrial real-life applications is limited. In most industries, the optimization of production scheduling is seen as an extremely complex task and most schedulers prefer the use of a simulation-based software or manual decision, which result to suboptimal solutions. This work presents a comprehensive review of the theoretical concepts that emerged in the last 30 years. Moreover, an overview of the contributions that address real-life industrial case studies of process scheduling is illustrated. Finally, the major reasons that impede the application of optimization-based scheduling are critically analyzed and possible remedies are discussed.