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In this work, we address the optimal water management strategies and fair cost distribution among various shale gas companies placed in the same play. A mixed integer non-linear programming (MINLP) formulation with the objective of maximizing the Nash product is presented including the analysis of different policies to determine the most appropriate transportation cost distribution. As a result of Nash product maximization and transfer cost designation formulation, the problem includes non-linearities in the objective function which hinders its resolution. Therefore, to solve the model effectively, we apply logarithmic operation and separable programming approach to reformulate the Nash product and Glover's linearization to reformulate the bilinear terms appearing in the transfer cost designation. Finally, the applicability of the proposed approach is illustrated in a case study comprising 4 companies. Then, an example comprising 10 shale gas companies is performed to analyse the behaviour of the proposed formulation considering a larger problem.

In this article, an optimization-based framework is proposed for integrated production and distribution planning of industrial gas supply chains. The main goal is to minimize the overall cost, whic...

In this paper, an optimisation-based approach to obtain safe multi-floor process plant layout designs using the domino hazard index (a sub-index of the integrated inherent safety index) is presented. A mixed integer linear programming (MILP) model is proposed to obtain the economically optimal multi-floor layout design considering connection by pipes, horizontal and vertical pumping of process fluids, purchase of land, fixed and area-dependent construction of floors, the financial risk associated with hazardous events and their escalation potential, and the installation of passive protection devices. Hazardous events such as pool fires, jet fires, flash fires, fireballs and blast waves resulting from explosions are considered using a novel and more realistic estimation of safety distances between equipment items. A bi-objective optimisation problem is also considered, minimising the layout costs and the total domino hazard index values for the plant, adopting the ϵ -constraint method. The proposed model is then applied to an 11-unit case study susceptible to each of these hazardous events, obtaining results with the optimal layout and protection device configurations in a relatively short amount of time.

Efficient water treatment design has progressively been growing in importance as the usage of water resources increases with population rise and industrial development. Their availability has been reduced with the more evident effects of climate change. Addressing this challenge necessitates more and efficient purification plants which can be realised by optimal design at conceptual stage. In this work, a mixed integer nonlinear programming (MINLP) model for the synthesis and optimisation of water treatment processes is proposed. Due to its numerous non-linearities and consequently, its non-stability, various linearisation, approximation and reformulation techniques have been implemented. Consequently, two improved formulations are derived, i.e. a partially linearised MINLP (plMINLP) and a mixed integer linear fractional programming (MILFP) models. The applicability of the mathematical formulations are investigated in case studies of seawater desalination and surface water treatment for the production of potable water. Finally, the models performance is analysed and compared against each other. Refereed/Peer-reviewed

This work addresses the optimal management of a system through a two-stage stochastic Non-Linear Programming (NLP) formulation. This approach uses a scenario-based mathematical formulation to tackle uncertain information. Accurate representation of uncertainty usually involves increased number of scenarios, which may result in large-scale optimisation models. Thus, the proposed formulation aims to reduce the number of scenarios through a sensitivity analysis approach. The proposed model investigates the use of scenario reduction techniques to reduce computational requirements while maintaining good quality of the final optimal solution.

The development of shale gas resources is subject to technical challenges and markedly affected by volatile markets that can undermine the development of new projects. Consequently, stakeholders can greatly benefit from decision‐making support tools that integrate the complexity of the system along with the uncertainties inherent to the problem. Accordingly, a general methodology is proposed in this work for the evaluation of integrated shale gas and water supply chains under uncertainty. First, key parametric uncertainties are identified from a candidate pool via a global sensitivity analysis based on a deterministic optimization model. Then, a two‐stage stochastic model is developed considering only the key uncertain parameters in the problem. Moreover, the merits of modeling uncertainty and implementing the stochastic solution approach are evaluated using the expected value of perfect information and the value of the stochastic solution metrics. Furthermore, the conditional value‐at‐risk approach was implemented to evaluate different risk‐aversion levels and the corresponding impacts on the shale gas development plan. The proposed methodology is illustrated through two real‐world case studies involving six and eight potential well‐pad locations and two options of well‐pad layouts.

This paper addresses the multi-floor process plant layout problem by developing four mixed integer linear programming (MILP) models. The problem involves decisions concerning the optimal spatial arrangement of process plant equipment and/or auxiliary units considering equipment connectivity, pumping and construction costs, and other factors. These considerations are extended to account for tall equipment items that span across floors and the availability of predefined production sections. The proposed models determine simultaneously the number of floors per section, floor areas per section, plot layout and site layout, and are applied to two case studies with up to 22 units and 6 production sections to demonstrate their applicability.

A medium-term optimization-based approach is proposed for the integration of production planning, scheduling and maintenance. The problem presented in this work considers a multiproduct single-stage batch process plant with parallel units and limited resources. An MILP continuous-time formulation is developed based on the main ideas of travelling salesman problem and precedence-based constraints to deal with, sequence-dependent unit performance decay, flexible recovery operations, resource availability and product lifetime. Small scheduling examples have been solved and compared with adapted formulations from the literature, based on discrete-time and global-time events, demonstrating the effectiveness of the proposed solution approach. Additional planning and scheduling problems have been proposed by considering several time periods. Multi-period examples have been efficiently solved by the model showing the applicability of the solution approach for medium-size problems.

This paper presents an optimization-based approach for the multifloor process plant layout problem. The multifloor process plant layout problem involves determining the most efficient—based on predefined criteria—spatial arrangement of a set of process plant equipment with associated connectivity. A number of cost and management/engineering drivers (e.g., connectivity, operations, land area, safety, construction, retrofit, maintenance, production organization) have been considered over the last two decades in order to achieve potential savings in the overall plant design process. This work constitutes an extension of the work by Patsiatzis and Papageorgiou [ Ind. Eng. Chem. Res. 2003, 42, 811−824;10.1021/ie020586t] to address the multifloor process plant layout problem. New features introduced modeled tall equipment with height greater than the typical floor height in chemical process plants, with connection points at a design-specified height for each piece of equipment. The number of floors, land area, ...

In order to enable a more sustainable transport sector in the future, a mixed-integer linear programming (MILP) model is developed with the aim of designing a pipeline network for hydrogen transmission. The objective of the optimisation is the minimisation of the network cost while taking hydraulics into consideration. Relevant features, i.e., maximum flow rate and facility location problem are included. Furthermore, the objective of pipeline safety is investigated based on an index-based risk assessment by Kim et al. (2011) . To examine the capabilities of the developed model, a case study on Germany is conducted for several scenarios. The optimised networks are discussed and compared. A Pareto frontier is computed in order to study the trade-off between network cost and safety.

Bi-level programming has been used widely to model interactions between hierarchical decision-making problems, and their solution is challenging, especially when the lower-level problem contains discrete decisions. The solution of such mixed-integer linear bi-level problems typically need decomposition, approximation or heuristic-based strategies which either require high computational effort or cannot guarantee a global optimal solution. To overcome these issues, this paper proposes a two-step reformulation strategy in which the first part consists of reformulating the inner mixed-integer problem into a nonlinear one, while in the second step the well-known Karush-Kuhn-Tucker conditions for the nonlinear problem are formulated. This results in a mixed-integer nonlinear problem that can be solved with a global optimiser. The computational and numerical benefits of the proposed reformulation strategy are demonstrated by solving five examples from the literature.

Advanced decision making in the process industries requires efficient use of information available at different decision levels. Traditionally, planning, scheduling, and optimal control problems are solved in a decoupled way, neglecting their strong interdependence. Integrated planning, scheduling and optimal control (iPSC) aims to address this issue. Formulating the iPSC, results in a large scale nonconvex mixed integer nonlinear programming problem. In the present work, we propose a new approach for the iPSC of continuous processes aiming to reduce model and computational complexity. For the planning and scheduling, a Traveling Salesman Problem-based formulation is employed, where the planning periods are modeled in discrete time while the scheduling within each week is in continuous time. Another feature of the proposed iPSC framework is that backlog, idle production time, and multiple customers are introduced. The resulting problem is a mixed integer programming problem and different solution strategi...

Multi-parametric programming has proven to be an invaluable tool for optimisation under uncertainty. Despite the theoretical developments in this area, the ability to handle uncertain parameters on the left-hand side remains limited and as a result, hybrid, or approximate solution strategies have been proposed in the literature. In this work, a new algorithm is introduced for the exact solution of multi-parametric linear programming problems with simultaneous variations in the objective function's coefficients, the right-hand side and the left-hand side of the constraints. The proposed methodology is based on the analytical solution of the system of equations derived from the first order Karush–Kuhn–Tucker conditions for general linear programming problems using symbolic manipulation. Emphasis is given on the ability of the proposed methodology to handle efficiently the LHS uncertainty by computing exactly the corresponding nonconvex critical regions while numerical studies underline further the advantages of the proposed methodology, when compared to existing algorithms.

In the present work, two new, (multi-)parametric programming (mp-P)-inspired algorithms for the solution of mixed-integer nonlinear programming (MINLP) problems are developed, with their main focus being on process synthesis problems. The algorithms are developed for the special case in which the nonlinearities arise because of logarithmic terms, with the first one being developed for the deterministic case, and the second for the parametric case (p-MINLP). The key idea is to formulate and solve the square system of the first-order Karush-Kuhn-Tucker (KKT) conditions in an analytical way, by treating the binary variables and/or uncertain parameters as symbolic parameters. To this effect, symbolic manipulation and solution techniques are employed. In order to demonstrate the applicability and validity of the proposed algorithms, two process synthesis case studies are examined. The corresponding solutions are then validated using state-of-the-art numerical MINLP solvers. For p-MINLP, the solution is given by an optimal solution as an explicit function of the uncertain parameters.

This work addresses the multiscale optimization of the purification processes of antibody fragments. Chromatography decisions in the manufacturing processes are optimized, including the number of chromatography columns and their sizes, the number of cycles per batch, and the operational flow velocities. Data-driven models of chromatography throughput are developed considering loaded mass, flow velocity, and column bed height as the inputs, using manufacturing-scale simulated datasets based on microscale experimental data. The piecewise linear regression modeling method is adapted due to its simplicity and better prediction accuracy in comparison with other methods. Two alternative mixed-integer nonlinear programming (MINLP) models are proposed to minimize the total cost of goods per gram of the antibody purification process, incorporating the data-driven models. These MINLP models are then reformulated as mixed-integer linear programming (MILP) models using linearization techniques and multiparametric disaggregation. Two industrially relevant cases with different chromatography column size alternatives are investigated to demonstrate the applicability of the proposed models. Keywords: Antibody purification, Multiscale optimization, Antigen-binding fragment, Mixed-integer programming, Data-driven model, Piecewise linear regression

This study presents the mathematical formulation and implementation of a comprehensive optimization framework for the assessment of shale gas resources. The framework simultaneously integrates water management and the design and planning of the shale gas supply chain, from the shale formation to final product demand centers and from fresh water supply for hydraulic fracturing to water injection and/or disposal. The framework also addresses some issues regarding wastewater quality, i.e., total dissolved solids (TDS) concentration, as well as spatial and temporal variations in gas composition, features that typically arise in exploiting shale formations. In addition, the proposed framework also considers the integration of different modeling, simulation and optimization tools that are commonly used in the energy sector to evaluate the technical and economic viability of new energy sources. Finally, the capabilities of the proposed framework are illustrated through two case studies (A and B) involving 5 well-pads operating with constant and variable gas composition, respectively. The effects of the modeling of variable TDS concentration in the produced wastewater is also addressed in case study B.

This work addresses the integrated optimization of upstream and downstream processing strategies of a monoclonal antibody (mAb) under uncertainty. In the upstream processing (USP), the bioreactor sizing strategies are optimized, while in the downstream processing (DSP), the chromatography sequencing and column sizing strategies, including the resin at each chromatography step, the number of columns, the column diameter and bed height, and the number of cycles per batch, are determined. Meanwhile, the product’s purity requirement is considered. Under the uncertainties of both upstream titer and chromatography resin yields, a stochastic mixed integer linear programming (MILP) model is developed, using chance constrained programming (CCP) techniques, to minimize the total cost of goods (COG). The model is applied to an industrially relevant example and the impact of different USP:DSP ratios is studied. The computational results of the stochastic optimization model illustrate its advantage over the determinis...

The development of fast, robust and reliable computational tools capable of addressing process management under uncertain conditions is an active topic in the current literature, and more precisely for the process systems engineering one. Particularly, scenario reduction strategies have emerged as an alternative to overcome the traditional issues associated with large-scale scenario-based problems. This work proposes a novel and flexible scenario-reduction alternative that integrates data mining, graph theory and community detection concepts to represent the uncertain information as a network and identify the most efficient communities/clusters. The capabilities of the proposed approach were tested by solving a set of two-stage mixed-integer linear programming problems under uncertainty. For comparison and validation purposes, these problems were also solved using two available methods (SCENRED and OSCAR). This comparison demonstrates that the results obtained by using the proposed approach are at least as good or better, in terms of quality and accuracy, than the results obtained bu using SCENRED and OSCAR. Additionally, the practical advantage of the proposed parameter definition rule is demonstrated as a way to overcome the limitations of the current alternatives (i.e. arbitrary user-defined parameters).

In this work, a new mixed integer linear programming (MILP) model is proposed for the multi-floor process plant layout problem with additional considerations. Multi-floor process plant layout determines the spatial arrangement of process plant units considering their connectivity amongst other factors and affects the cost of constructing the plant, the ease of plant operation and expansion, general safety levels within the plant and its neighbouring environment, as well as operational costs. Over the past years, mathematical programming models have been developed to describe the layout problem considering connectivity costs, pumping costs, installation of safety devices, and piping, in single and multiple floors. Features such the representation of irregularly shaped items, tall equipment spanning multiple floors and others have been successfully modelled. This work builds on such past considerations with additional features that allow multi-floor equipment items extend above the maximum potential number of floors, and the selection of an available number of floors less than the maximum number required by any equipment item. Integer cuts are also developed for the proposed model to enhance its efficiency. The performance and limitations of the proposed model are demonstrated with industry-relevant case studies of up to 25 units, and results show a potential cost savings when compared to existing models with additional computational benefits of the integer cuts in all of the cases explored.

Shale gas production has been the focus of intense debate in recent years. Shale gas supporters claim that it could be the way to transition between fossil fuels and renewable energy sources. For instance, in the United States, power generation from coal is being replaced by power generation from natural gas, which is a cleaner fuel when compared to coal. However, shale gas critics claim that the environmental cost associated with shale gas production is high enough to negate the benefits to society. For example, high water usage as well as the potential for contamination of underground and surface water sources constitute important environmental challenges for the development of shale gas resources. This study presents a methodology for the preliminary assessment of the development of shale gas resources taking into account well-pad design as one of the most important decision variables. To perform the assessment, different performance metrics are proposed to evaluate not only the economics of developing...

This work addresses the optimal downstream chromatography sequencing and column sizing strategies in the manufacturing processes of monoclonal antibodies (mAbs). A mixed integer linear fractional programming (MILFP) model is developed to achieve continuous bed height values. In addition, to ease the computational expense of the literature MILFP model for discrete bed height values, two efficient hierarchical solution approaches are developed involving the two MILFP models, in which, based on its optimal solution of the newly developed MILFP model, the reduced MILFP model is solved with smaller decision region to find the final solution. A Dinkelbach-based algorithm is used as the solution approach of the MILFP models. Finally, a case study with different upstream processing (USP) and downstream processing (DSP) ratios are investigated, and the results show that all proposed approaches have high computational efficiency to satisfy different needs of the decision makers.

This work presents a Mixed Integer Linear Programming (MILP) approach based on a combination of a rolling horizon and stochastic programming formulation. The objective of the proposed formulation is the optimal management of the supply and demand of energy and heat in microgrids under uncertainty, in order to minimise the operational cost. Delays in the starting time of energy demands are allowed within a predefined time windows to tackle flexible demand profiles. This approach uses a scenario-based stochastic programming formulation. These scenarios consider uncertainty in the wind speed forecast, the processing time of the energy tasks and the overall heat demand, to take into account all possible scenarios related to the generation and demand of energy and heat. Nevertheless, embracing all external scenarios associated with wind speed prediction makes their consideration computationally intractable. Thus, updating input information (e.g., wind speed forecast) is required to guarantee good quality and practical solutions. Hence, the two-stage stochastic MILP formulation is introduced into a rolling horizon approach that periodically updates input information.

This paper addresses the planning and scheduling problem of a multiproduct multistage continuous plant by three novel MILP-based (mixed integer linear programming) models. These models combine a TSP (traveling salesman problem) formulation with the main ideas of general precedence and unit-specific general precedence concepts to provide hybrid discrete/continuous time representations of the system. Also, an efficient solution approach involving rolling horizon and iterative-improvement algorithm is derived for solving medium-size instances of the problem. Results analyses for different model’s parameters demonstrate the benefits of the new formulations and the effectiveness of the solution approach presented in this work.

This paper reports the results of a techno-economic performance assessment on three scenarios that reflect waste management strategies and plastics treatment in the Greater London area. The polymeric fraction treated by the three integrated scenarios was part of the municipal solid waste (MSW) produced by the residents of the boroughs of Greenwich, Lewisham, Westminster, Bromley and the City of Exeter, Devon. At present, these boroughs send their MSW to an incineration unit (IU) with combined heat and power (CHP) and a dry materials recovery facility (MRF). This conventional processing of waste treatment was considered as the baseline scenario (scenario 1), and was compared with two others set within the same system boundaries. Scenarios 2 and 3 implement a pyrolysis and a hydrocracking reactor to an extracted stream of the MRF plastics products, respectively. The MRF station incorporated is of an 87.5 ktpa capacity and the IU considered operates on a capacity of 420 ktpa. The effect of increasing the thermo-chemical treatment (TCT) units’ capacity was investigated to match the order of magnitude of both the MRF and IU capacities, ranging from 1 ktpa to 150 ktpa. Fourteen different input parameters have been chosen to perform a sensitivity analysis and the effects of ±10% changes in these variables on the net present value (NPV) and internal rate of return (IRR) have been examined. It was concluded that the hydrocracking scenario is the most favourable option for waste treatment (including the polymeric fraction) at the scale of 150 ktpa.

Considering the performance decay of the chromatography resins in the downstream purification of biopharmaceutical manufacturing, the maintenance decisions should be made at appropriate times to achieve a good performance of the whole manufacturing process. In this paper, on the basis of the literature work on production planning, a mixed integer linear programming optimization model is developed to address the production and maintenance planning of biopharmaceutical manufacturing under performance decay, in which the total operating profit is maximized. The batch production profiles are tracked by binary variables introduced in the proposed model. The proposed model is then applied to two literature-based illustrative examples. Two scenarios are investigated and compared with the optimal solutions. A discussion about the effects of the maintenance duration and cost and the resin’s lifetime is also presented.

Inspired from a real case study of a Saudi oil company, this work addresses the optimal operation of a regional network of gas oil separation plants (GOSPs) in Arabian Gulf Coast Area to ultimately achieve higher savings in operating expenditures (OPEX) than those achieved by adopting single-surface facility optimisation. An originally tailored and integrated mixed integer linear programming (MILP) model is proposed to optimise the crude transfer through swing pipelines and equipment utilisation in each GOSP, to minimise the operating costs of a network of GOSPs. The developed model is applied to an existing network of GOSPs in the Ghawar field, Saudi Arabia, by considering 12 different monthly production scenarios developed from real production rates. Compared to rule-based current practice, an average 12.8% cost saving is realised by the developed model.

This paper presents a mixed integer linear programming (MILP) model for the optimal synthesis of chromatographic protein purification processes including the time line in which our target protein product is collected. The model is linearised using piecewise linear approximation strategies and tested on three example protein mixtures, containing up to 13 contaminants and selecting from a set of up to 21 candidate steps. The results are also compared with previous literature models attempting to solve the same problem and show that the proposed approach offers significant gains in computational efficiency without compromising the quality of the solution.

Assessment of both economical and environmental performance of biofuel supply chains is crucial to have a complete view of the future implications of those systems. This paper presents a multi-objective, static modelling framework for the optimisation of hybrid first/second generation biofuel supply chains. Using the proposed modelling framework, different aspects are analysed including the potential GHG savings, the impact of carbon tax on the economic and environmental performance of a biofuel supply chain, the trade-off between the economic and environmental objectives and the maximum bioethanol throughput that can be achieved at different cap levels on the total supply chain cost. The trade-off between the conflicting objectives is analysed by solving the proposed multi-objective model using the ɛ-constraint method. In addition, the impact of technological learning on the economic and environmental performance of the supply chain throughout time is also analysed using a multi-period model developed based on the proposed static optimisation framework. Bioethanol production in the UK using hybrid first/second generation technologies is considered as the case study to highlight the model applicability.

The shortening of patent life periods, generic competition and public health policies, among other factors, have changed the operating context of the pharmaceutical industry. In this work we address a dynamic allocation/planning problem that optimises the global supply chain planning of a pharmaceutical company, from production stages at primary and secondary sites to product distribution to markets. The model explores different production and distribution costs and tax rates at different locations in order to maximise the company's net profit value (NPV). Large instances of the model are not solvable in realistic time scales, so two decomposition algorithms were developed. In the first method, the supply chain is decomposed into independent primary and secondary subproblems, and each of them is optimised separately. The second algorithm is a temporal decomposition, where the main problem is separated into several independent subproblems, one per each time period. These algorithms enable the solution of large instances of the problem in reasonable time with good quality results.

In areas lacking substantial freshwater resources, the utilisation of alternative water sources, such as desalinated seawater and reclaimed water, is a sustainable alternative option. This paper presents an optimisation approach for the integrated management of water resources, including desalinated seawater, wastewater and reclaimed water, for insular water deficient areas. The proposed mixed integer linear programming (MILP) model takes into account the subdivided regions on the island, the subsequent localised needs for water use (including water quality) and wastewater production, as well as geographical aspects. In addition, the integration of potable and non-potable water systems is considered. The optimal water management decisions, including the location of desalination, wastewater treatment, and reclamation plants, as well as the conveyance infrastructure for desalinated water, wastewater and reclaimed water, are obtained by minimising the annualised total capital and operating costs. Finally, the proposed approach is applied to two Greek islands: Syros and Paros-Antiparos, for case study and scenario analysis.

The E.U. has adopted a target of 10% of energy for transportation coming from renewable sources, including biofuels, by 2020 to tackle the increasing greenhouse gas emissions problem and reduce dependency on fossil fuels. In this paper, mixed integer linear programming (MILP) models are presented for the optimal design of a bioethanol supply chain with the objective of minimizing the total supply chain cost. The models aim to optimize the locations and scales of the bioethanol production plants, biomass and bioethanol flows between regions, and the number of transport units required for the transfer of these products between regions as well as for local delivery. The optimal bioethanol production and biomass cultivation rates are also determined by the model. The applicability of the proposed models is demonstrated with a case study for Northern Italy.

This article considers the short-term scheduling of a single-stage batch edible-oil deodorizer that can process multiple products in several product groups. Sequence-dependent changeovers occur when switching from one product group to another. Based on the incorporation of products into product groups, mixed integer linear programming (MILP) models are proposed for two scenarios, with and without backlogs. Then, the models are successfully applied to a real-world case with 70 product orders over a 128-h planning horizon. Compared with a literature model developed for a similar problem, the proposed models exhibit significantly better performance.

Supply chain management and optimisation is a critical aspect of modern enterprises and a flourishing research area. This paper presents a critical review of methodologies for enhancing the decision-making for process industry supply chains towards the development of optimal infrastructures (assets and network) and planning. The presence of uncertainty within supply chains is discussed as an important issue for efficient capacity utilisation and robust infrastructure decisions. The incorporation of business/financial and sustainability aspects is also considered and future challenges are identified.

Novel and efficient linear formulations are developed for the problem of simultaneously performing an optimal synthesis of chromatographic protein purification processes, and the concomitant selection of peptide purification tags, that result in a maximal process improvement. To this end, two formulations are developed for the solution of this problem: (1) a model that minimizes both the number of chromatographic steps in the final purification process flow sheet and the composition of the tag, by use of weighted objectives, while satisfying minimal purity requirements for the final product; and (2) a model that attempts to find the maximal attainable purity under constraints on the maximum number of separation techniques and tag size. Both models are linearized using a previously developed strategy for obtaining optimal piecewise linear approximations of nonlinear functions. Proposed are models to two case studies based on protein mixtures with different numbers of proteins. Results show that the models are capable of solving to optimality all the implemented cases with computational time requirements of under I s, on average. The results obtained are further compared with previous nonlinear and linear models attempting to solve the same problem, and, thus, show that the approach represents significant gains in robustness and efficiency. (C) 2009 American Institute of Chemical Engineers AIChE J, 55: 2303-2317, 2009

This paper presents an efficient solution approach for large-scale, single-floor process plant layout problems based on mixed integer optimisation. The final plant layouts (i.e. coordinates and dimensions for each equipment item) are determined from an initial feasible solution followed by an iterative improvement procedure. The applicability of the solution algorithm is demonstrated through a number of illustrative examples. The computational results indicate that the proposed approach successfully achieves good quality solutions for examples with up to 36 facilities with modest computational requirements.

In this paper we address a case study, inspired by a real agrochemicals supply chain, with two main objectives, structured in two stages. In the first stage we redesign the global supply chain network and optimise the production and distribution plan considering a time horizon of 1 year, providing a decision support tool for long term investments and strategies. The output decisions from the first stage, mainly the supply chain configuration and allocation decisions, are the input parameters for the second stage where a short term operational model is used to test the accuracy of the derived design and plan. The outputs of this stage are detailed production and distribution plans and an assessment of the customer service level. At the operational level, failure to meet on time the demand fulfilment targets established at the planning stage is usually caused by allocation of too many products/customers to the same resource in the first stage, especially to those surrounding the system bottlenecks. This introduces idle periods in the planning of the bottleneck resources, preventing the whole system from operating at its maximum capacity. An analytical methodology was developed to use the information gathered in the second step to improve the supply chain design and plan by enforcing a more distributed allocation of products/customers to the available resources in each time period.

This paper presents a mathematical programming approach for medium term planning of biopharmaceutical manufacture under uncertainty. The proposed mathematical formulation constitutes a modification of an earlier deterministic model [Lakhdar, K., Zhou, Y.H., Savery, J., Titchener-Hooker, N.J., Papageorgiou L.G., 2005, Medium term planning of biopharmaceutical manufacture using mathematical programming. Biotechnol Prog, 21: 1478–1489] determining the optimal production plans for a biopharmaceutical manufacturing facility, whereby this work allows for uncertain fermentation titres. The overall problem is formulated as a two-stage, multiscenario, mixed integer linear programming (MILP) model. An iterative algorithm is then proposed to allow for the solution of larger instances of the resulting large-scale MILP problem. The applicability of the proposed solution approach is demonstrated via a number of illustrative examples and is found to compare favourably with the deterministic model and the full-space model.

The objective of this work is to develop an optimization model for the medium-term planning of single-stage continuous multiproduct plants with a single processing unit. Several types of stock keeping units (SKUs) are produced. Customers place orders that represent multiples of SKUs that must be delivered at the end of each week. When different SKU types are processed, sequence-dependent changeover times and costs are incurred. The problem is formulated as a mixed-integer linear programming (MILP) model with a hybrid time representation. The objective is to maximize profit that involves sales revenues, production costs, product changeover costs, inventory costs, and late delivery penalties. The proposed optimization-based model is validated in a real-world polymer processing plant. To improve its computational efficiency, integer cuts are developed and added in the model. The model is then applied to two literature examples, and the results are compared with other models of similar nature.

This paper presents a Mixed Integer Linear Programming (MILP) model for the solution of N-dimensional allocation problems. The applicability of the model is presented and demonstrated through some illustrative examples with different numbers of dimensions. Several problems, previously presented in the literature, are solved using the proposed model, such as, one-dimensional scheduling problems, two-dimensional cutting problems, as well as plant layout problems and three-dimensional packing problems. Additionally, some problems in four dimensions are presented and solved using the considered model. The presented model is applicable to a wide variety of allocation problems as it offers a general framework for modelling allocation problems with any given number of continuous or discrete dimensions. The presented problems are formulated as MILP problems where the first four dimensions usually are continuous spatial and time dimensions. Additional dimensions are often of a discrete nature.

This paper presents a novel solution approach for addressing large-scale single-floor process plant layout problems. Based on the mixed-integer linear programming (MILP) representation proposed by Papageorgiou and Rotstein in 1998, the optimal layout (i.e., coordinates and dimensions) is determined through construction-based schemes using mixed-integer optimization. The applicability of the proposed approach is finally demonstrated through four illustrative examples by investigating flowsheets with up to 36 equipment items.

The aim of this work is to propose a mathematical programming model for the economic lot scheduling problem (ELSP) in units that present performance decay. Typical examples in the chemical processing industry include catalyst deactivation and cokeification, as well as fouling in heat exchangers. The main decision related to this problem concerns processing interruption for maintenance so to restore unit performance. The dynamic behaviour of the system along time is represented by an exponential decay function. The problem is formulated as a mixed integer nonlinear programme (MINLP). Moreover, a mixed integer linear programme (MILP) that results from the discretization of cycle time is developed. The models are tested in a wide set of problems with several parameter values and the results for the models with continuous and discrete cycle times are compared. Results show that the MINLP model achieves the optimal solutions in shorter CPU times. Nevertheless, the usefulness of the MILP is shown as it provides tight bounds that provide convergence of the MINLP. Moreover, the formulations are compared to hierarchical approaches.

This paper presents a systematic optimization-based approach for customer demand forecasting through support vector regression (SVR) analysis. The proposed methodology is based on the recently developed statistical learning theory (Vapnik, 1998) and its applications on SVR. The proposed three-step algorithm comprises both nonlinear programming (NLP) and linear programming (LP) mathematical model formulations to determine the regression function while the final step employs a recursive methodology to perform customer demand forecasting. Based on historical sales data, the algorithm features an adaptive and flexible regression function able to identify the underlying customer demand patterns from the available training points so as to capture customer behaviour and derive an accurate forecast. The applicability of our proposed methodology is demonstrated by a number of illustrative examples.

Pipeless plants comprise a number of processing stations and a number of mobile vessels transferring materials to be processed at the stations. Layout considerations has been found to be of particular significance in those plants because they determine the transfer times for the vessels, which can influence scheduling issues. This paper presents a general mathematical programming formulation simultaneously integrating layout, design, and production planning for pipeless plants. The overall problem is formulated as a mixed-integer linear programming model based on a continuous-time-domain representation. The applicability of the model is demonstrated by one illustrative example.

This paper presents a novel hybrid constraint logic programming (CLP) and MILP algorithm for scheduling complex multipurpose batch processes. The scheduling problem is decomposed into two sub-problems: first an aggregate planning problem is solved using an MILP model, and then a sequencing problem is solved using CLP techniques. The CLP model avoids the complexity of explicitly stating complete material balance constraints by instead using precedence constraints between batches to ensure the schedule is feasible. The efficiency of the algorithm is demonstrated with four examples and areas for future improvement are identified.

This paper considers the optimal design and operation of electrodialysis (ED) desalination plants. In general an ED plant aims to produce potable water from a high salinity source, like brackish water or high salinity water. The system is modelled mathematically as mixed-integer non-linear programming (MINLP) optimization problem, determining the number of desalination stages, the membrane area, the total required energy so as to minimise the total annualised cost of the investment accounting for both infrastructure and operating costs. Two examples from the literature illustrate the applicability of the proposed approach and evaluate the quality of the results obtained.

The aim of this work is to propose a mathematical programming model for the economic lot scheduling problem (ELSP) with performance decay. First, the problem is formulated as a mixed integer nonlinear program (MINLP), which is found to be nonconvex. The model is then transformed into a mixed integer linear programming (MILP) model through the discretization of the cycle time. This model is tested in a wide set of randomly generated problems with various degrees of difficulty. The results show that the MILP model can achieve the optimum within satisfactory CPU times. An illustrative example demonstrates the applicability of the MILP model and its potential benefits in comparison with a hierarchical approach.

This paper presents a systematic mathematical programming approach for long-term, multi-site capacity planning under uncertainty in the pharmaceutical industry. The proposed mathematical model constitutes an extension of the work of Papageorgiou et al. (2001) determining both the product portfolio and the multi-site capacity planning in the face of uncertain clinical trials outcomes while taking into account the trading structure of the company. The overall problem is formulated as a two-stage, multi-scenario, mixed-integer linear programming (MILP) model. A hierarchical algorithm is then proposed in order to reduce the computational effort needed for the solution of the resulting large-scale MILP problem. The applicability of the proposed solution approach is demonstrated by a number of illustrative examples. (C) 2004 Elsevier Ltd. All rights reserved.