Supporting Information document to submission for European Symposium of Computer Aided Process Engineering 2026

Aluminium cold rolling is an energy-intensive process that has a substantial impact on CO₂ emis-sions and production cost, yet plant-level optimization remains challenging due to strong process nonlinearities and various operational constraints. This study develops a physics-consistent hy-brid model that combines a Stone–Hitchcock–Ludwik analytical rolling-energy formulation with a residual deep neural network to predict the daily electricity consumption of three single-stand cold rolling mills. Using plant raw data, the hybrid model achieves lower prediction errors than conventional data driven model and yields line-specific physical parameters that agree well with the observed behaviour of each mill. On this basis, an NSGA-II-based tri-objective optimization is carried out to minimise daily energy use, CO₂ emissions, and specific production cost (SPC) by adjusting pass-wise reduction and tension schedules and line-wise production allocation. Case studies on a representative operating... [more]

This supplementary material contains tables and figures with the data necessary to replicate the results described in the manuscript.

The source code contains a run_experiments.sh script, which can be used to replicate the results described in the manuscript.

Emerging sectors within the biopharmaceutical industry are undergoing rapid scale-up due to the market boom of gene therapies and vaccine platform technologies. Manufacturers are pressured to orchestrate resources and plan investments under future demand uncertainty and, critically, an early-stage process uncertainty for platforms still under development. In this work, a multi-product multi-stage stochastic optimization problem integrating demand uncertainty is presented and augmented with a worst-case optimization approach with respect to process uncertainty. Results focus on a comparison between fixed equipment facilities and modular technologies, highlighting an inherent flexibility of the latter option due to shorter recourse actions for capacity scale-out. The impact of process uncertainty integration is quantified. With more conservative decisions taken in first-stages of the time horizon, expected costs result lower for modular single-use equipment. This suggests that capacity a... [more]

Optimizing greenhouse operations in arid regions is essential for sustainable agriculture due to limited water resources and high energy demands for climate control. This paper proposes a multi-objective optimization framework aimed at minimizing both the operational costs and environmental emissions of a climate-controlled greenhouse. The framework determines optimal allocation of growing area among three crops (tomato, cucumber, and bell pepper) throughout the year. These crops were selected for their varying growth conditions, which induce variability in energy and water inputs, providing a comprehensive assessment of the optimization model. The model integrates factors such as temperature, humidity, light intensity, and irrigation requirements specific to each crop. It is solved using a genetic algorithm combined with Pareto front analysis to address the multi-objective nature effectively. This approach facilitates the identification of optimal trade-offs between cost, emissions, a... [more]

In recent years, several strategies have been developed to reduce the carbon dioxide (CO2) released into the atmosphere. Carbon Capture, Storage and Utilisation (CCUS) is one of the proposed solutions. However, CCUS systems are expensive to install and operate. Furthermore, most studies in the literature have focused on CO2 utilisation and storage separately, without accounting for the effects of other CO2 emission management strategies. To address this gap, a Mixed Integer Linear Programming (MILP) framework for a supply chain network is developed in this work, incorporating CO2 storage, utilisation, permit trading, and carbon emission taxation. Multi-criteria decision analysis (MCDA) techniques are implemented to select CO2-based products for CO2 utilisation. The MILP framework is set to achieve the maximum environmental and economic performance using a Multi-Objective Optimisation (MOO) approach. This involves using the e-constraint method as a solution procedure to minimise the tot... [more]

This study designs a green hydrogen supply chain for Portugal, focusing on minimizing both economic costs and water stress. The research uses a multi-objective simulated annealing algorithm to address the trade-offs between the two objectives. The process of producing hydrogen via electrolysis is highly water-intensive, posing a challenge in water-scarce regions like southern Portugal. The study considers Portugal's uneven water distribution, renewable energy availability and, different hydrological conditions across districts. An aggregate indicator, Water Stress Index (TWSI), quantify the pressure on water resources covering all the Portugal´s districts in a single score. This study explores four scenarios, a baseline scenario, a green hydrogen scenario using only renewable energy, drought conditions, and increased demand in major cities with drought conditions. The quasi pareto front illustrates the trade-offs between supply chain cost and TWSI, enabling decision-makers to select s... [more]

Decarbonizing industries could significantly increase electricity demand, necessitating strategic grid expansion. This study evaluates the impact of decarbonizing the Pulp and Paper Sector under four 2050 scenarios: carbon capture, biomass-based, direct electrification, and indirect electrification. A bottom-up approach is employed to estimate 2020 final energy demand by heat grade and subsector. Both final and primary energy demand systems are modeled, accounting for the efficiencies of end-use technologies and primary energy transformation processes. The analysis compares primary renewable energy demand (electricity and biomass) normalized per ton of equivalent CO2 avoided against a business-as-usual scenario. It also considers the requirements for wood residues, organic waste, and CO2 storage. The carbon capture scenario, while low in electricity demand, requires significant organic waste for renewable natural gas production and 2.6 Mt of CO2 storage to offset direct and indirect em... [more]

This study optimizes the Sustainable Aviation Fuel Supply Chain Network (SAFSCN) in the Czech Republic, using wheat straw as feedstock. It integrates geospatial data, transportation logistics, and economic feasibility, applying mixed-integer linear programming (MILP) to optimize pyrolysis plant locations and minimize costs. Sensitivity analysis varied wheat production growth by ±0.1% and ±0.2%. Results confirm Sustainable Aviation Fuel (SAF) production is technically and economically viable, with costs projected to decline up to 30.64% and revenues rising 49.07% from 2030 to 2050 due to technological advancements, improved logistics, and economies of scale. The findings underscore the critical role of SAF in achieving EU aviation decarbonization targets and highlight the importance of efficient supply chain planning for scaling SAF production.

The analysis of large chemical reaction space sheds light on reaction patterns between molecules and can inform subsequent reaction pathway planning. With the aim to discover more sustainable production systems, it became worthwhile to explicitly model the reaction space reachable from biobased feedstocks. In particular, the space that reactions in integrated biorefineries span for optimised biorefinery planning is of interest. In this work we show a network-theoretical analysis of biorefinery reaction data. We utilise the directed all-to-all mapping between reactants and products to compare the reaction space obtained from biorefineries with the entire network of organic chemistry (NOC). In our results, we find that despite having 1000 times fewer molecules, the constructed network resembles the NOC in terms of its scale-free nature and shares similarities regarding its small-world property. Additionally, we analyse the coverage rate of the biorefinery reaction data and find that many... [more]

Currently, state-of-the-art approaches to solving complex optimization problems have focused solely on methods requiring high computational time and unable to find the global optimal solution. In this work, a methodology based on quantum computing is presented to overcome these drawbacks. The novelty of this framework stems from the quantum computer’s architecture and taking into consideration the quantum phenomena that take place to solve optimization problems with specific structure. The proposed methodology includes steps for the transformation of the initial optimization problem into an unconstrainted optimization problem with binary variables and its embedding onto a quantum device. Moreover, different resolution levels for the transformation step and different architectures for the embedding process are utilized. To illustrate the procedure, a case study based on Haverly’s pooling and blending problem is examined while demonstrating the potential of the proposed approach. The res... [more]

Processes increasingly need to consider electricity markets, which shifts the traditional demand side management scope towards a more dynamic nature. Instead of only focusing on day-ahead energy trading, demand-side management scope should be broadened towards being able to support the power grid stability during frequency events. This paper studies an artificial example process, similar to the melt-shop process from the steel industry, highlighting the challenges and opportunities of an energy intensive process. We show the potential benefits of having a battery energy storage system on-site, as well as opportunities in lowering the electricity cost by participating in the bidding process of various ancillary products.

Bilevel optimization is an active area of research within the operations research community due to its ability to capture the interdependencies between two levels of decisions. This study introduces a metamodeling approach for addressing mixed-integer bilevel optimization problems, exploiting the approximation capabilities of neural networks. The proposed methodology employs neural network embeddings to approximate the optimal follower's response, bypassing the inner optimization problem by parametrizing it with continuous leader’s decisions. The use of Rectified Linear Unit (ReLU) activations allows the forward pass of the neural network to be represented as a set of mixed-integer linear constraints. Thereby, the bilevel structure is simplified into a single-level optimization model. A case study based on a two-echelon supply chain demonstrates the effectiveness of the approach, with solutions comparable to traditional bilevel optimization methods. The results suggest that neural netw... [more]

Uncertainty plays a crucial role in strategic supply chain design. In this study, we explore robust approaches to model uncertainty when the non-deterministic parameters are placed in the independent term, on the right-hand side (RHS) of the constraints. We consider the "disjunctive adjustable column-wise robust optimization" (DACWRO), a disjunctive formulation introduced previously in our group, and compare it with the adjustable column-wise robust optimization (ACWRO) formulation, a specific technique for solving robust optimization problems when the original robust optimization approach may assume too-conservative results. Given that the proposed method is based on the generalized disjunctive programming (GDP) technique, it is a higher lever modelling approach that represents the discrete nature of the decision process. In addition, it provides alternative MILP representations that can be further tested and compared. The analysis assesses the computational performance and reformulat... [more]

Real-world flowshop problems which are very common in the chemical industry are often difficult to solve in a reasonable time with allocation, sequencing, and lot-sizing decisions. Although great progress has been made in the last 20 years regarding MILP model formulations and solution algorithms, realistically-sized flowshop problems with resource and buffer constraints are still difficult to solve. On the other hand, discrete-event simulation (DES) allows for very detailed modelling of process plants, but lacking of optimization capabilities. Simulation Optimization (SO) combines the high-detail DES with mathematical optimization. We show that is possible to integrate MILP and DES using Benders decomposition. We explain the Benders-DES (BDES) approach with a small motivation example with makespan minimization objective and apply it to a real-world case study of a formulation plant with seven formulation and filling lines with sequencing, allocation, and lot-sizing decisions. We show... [more]

Despite the potential benefits of decision-level integration for process and energy supply chains (SCs), these systems are traditionally assessed and optimised by incorporating simplified unit operation models within a spatially distributed network. The desired organisational-level integration cannot be achieved without leveraging complex computational tools and concepts. This work proposes a multi-scale agent-based model to facilitate the transition from traditional practices to coordinated SCs. The proposed multi-agent system framework incorporates different enterprise dimensions of the process and energy SCs, including raw material suppliers, rigorous processing plants, and consumers. The behaviour of each agent type and its interactions are implemented, and their impact on the overall system is investigated. This approach allows for the simultaneous assessment and optimisation of process and SC decisions. By integrating each decision level into the operation, the devised framework... [more]

To address the dynamic operational demands of the gas processing sector, which is continuously evolving due to gas market opening, increase in natural gas production, and the growing challenge of upstream-midstream integration in a competitive environment, this work presents the Integrated-Gas-Scheduling-System, IntegraGAS. The proposed methodology innovates by using first principles rigorous process simulation coupled with a scheduling tool for short/medium/long-term, enabling gas plants to swiftly adapt to varying operational conditions and meet the requirements of this new market. IntegraGAS was implemented in Petrobras and has significantly enhanced scheduling efficiency, reducing execution time by up to 99.2% and avoiding approx. US$ 2.3 million in annual labor costs, optimizing resource utilization. By integrating Excel for the frontend, Aspen HYSYS for process simulation, VBA for automation, and Microsoft PowerBI for real-time data visualization, IntegraGAS improves decision-mak... [more]

Production scheduling in the process industry is an area of significant activity in research and of great practical importance for the performance of industrial companies. In the vast majority of research papers, the scheduling problem is formulated as an off-line problem where a number of jobs is scheduled on a number of resources and the efficiency of the formulation and the solution algorithms is discussed. In reality, however, scheduling is a continuous activity that has to react to the arrival of new orders, to variations in processing times, breakdowns, lack of resources etc. This is termed real-time (or online) scheduling. Available commercial solutions usually provide solutions with relatively long update intervals due to the necessary computation times and a delayed flow of information from the manufacturing execution systems where the data on the current state of the production is collected. Thus the computed schedules are outdated quickly, if not already at the point in time... [more]

Perishable consumer products like food, cosmetics, and household chemicals face challenges in supply chain management due to limited shelf life and uncertainties in demand and transportation. To address some of these issues, this work proposes a robust optimization framework for jointly optimizing facility allocation and inventory management. The framework determines optimal locations for distribution centers and their assigned customers, as well as inventory policies that minimize the total costs related to transportation, distribution, and storage under uncertain demand in a robust setting. Specifically, we develop a two-stage mixed-integer linear programming (MILP) model is that incorporates First-In-First-Out (FIFO) inventory policy to reduce spoilage. The bilinear FIFO constraints are linearized to improve computational efficiency. Social equity is integrated by defining a fairness index and incorporating it in facility allocation. Demand uncertainty is tackled using a robust opti... [more]

This study aims to develop an optimization-based approach to design the carbon capture, utilization, and storage (CCUS) supply chain and analyze the optimal configuration and investment strategies. To achieve this goal, we develop an optimization model that determines the logistic decision-making to maximize the net present value (NPV) and minimize the net CO2 emissions (NCE) of the strategies of the CCUS supply chain under logical and practical constraints. We estimate the technical (production scale and energy consumption), economic (capital and operating expenditure), and carbon-related (CO2 emissions) parameters based on the literature. By adjusting major cost drivers and economic bottlenecks, we determined major decision-making problems in the CCUS framework, such as sequestration vs. utilization. As a real case study, the future CCUS system of South Korea was evaluated, which includes three major CO2 emitting industries in South Korea (power plants, steel, and chemicals), as well... [more]

The unit commitment problem determines the optimal strategy to meet the electricity demand at minimum cost by committing power generation units at each point of time. Solving the unit commitment problem gives rise to a challenging optimization problem due to its combinatorial complexity and potentially long solution time requirements. Our proposed solution approach utilizes a decomposition method in conjunction with alternative models from the EGRET library. Results of this decomposition approach tested against four benchmarking systems show that significant computational speed ups are achieved.

Commodity chemicals and energy supply chains are an essential part of the hydrocarbon industry in several countries. As these supply chains are susceptible to disruptions caused by various risks, the economies of countries that depend on the hydrocarbon sector as a major source of income might be negatively affected. One major risk is the price fluctuations of the resources used in the multiple stages of the supply chains. Investment decisions in this sector aim to secure the investment portfolio's financial returns against the risk of price fluctuations. This work introduces an adaptation of a portfolio optimization technique, the modern portfolio theory (MPT) to the case of commodity chemicals and energy supply chain investments by considering all supply chain stages in formulating the MPT framework. A case study considering four chemical commodities and three potential importing countries is presented with a sensitivity analysis that studies the impact of changing the costs associat... [more]

With increasing emphasis on energy efficiency, more researchers are focusing on energy-efficient flexible job shop scheduling problems. Mathematical programming is a commonly used optimization method for such scheduling challenges, offering the advantages of achieving global optima and serving as a foundation for other approaches. However, current mathematical programming formulations face several challenges, including insufficient consideration of various forms of energy consumption and low efficiency, particularly in handling large-scale instances, which struggle to converge. In this study, we propose a novel global sequence-based approach with high computational efficiency. In this model, immediate precedence relationships are identified using constraints, enabling the precise determination of idle durations within any idle slots. The proposed formulation achieves a significant reduction in energy consumption by up to 20% relative to other formulations. Furthermore, it successfully... [more]

The growing size and complexity of energy system optimization models, driven by high-resolution spatial data, pose significant computational challenges. This study introduces methods to reduce model’s size and improve computational efficiency while preserving solution accuracy. First, a composite-curve-based approach is proposed to aggregate granular data into larger resolutions without averaging out specific properties. Second, a general clustering method groups geographically proximate fields, replacing multiple transportation arcs with a single arc to reduce transportation-related variables. Lastly, a two-step algorithm that decomposes the supply chain design problems into two smaller, more manageable subproblems is introduced. These methods are applied to a case study of switchgrass-to-biofuels network design in eight U.S. Midwest states, demonstrating their effectiveness with realistic and detailed spatial data.