Modeling Multi-period Operations using the P–graph Methodology

Heckl, István; Halász, László; Szlama, Adrián; Cabezas, Heriberto; Friedler, Ferenc

doi:10.1016/b978-0-444-63456-6.50164-2

Cited by 6 publications

(5 citation statements)

References 14 publications

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“…Many other contributions have employed the methodology in dealing with a variety of instances related to PNS in chemical and environmental engineering. These instances include the optimal use of renewable resources in process synthesis ; the optimal design of a process for benzaldehyde production ; the reduction of CO 2 emissions in energy‐generation systems ; the assessment of sustainability criteria in selecting industrial reaction pathways ; the identification of waste‐generation sources in batch processes ; the planning of systems for carbon capture ; and the synthesis and modeling of multiperiod systems where the material loads to the operating units involved in these systems may vary in different periods of time . Recently, the P‐graph methodology has also been applied for the solution of instances pertaining to supply chains.…”

Section: Introductionmentioning

confidence: 99%

Design and engineering of sustainable process systems and supply chains by the P‐graph framework

Cabezas

Argoti

Friedler

et al. 2018

Env Prog and Sustain Energy

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The design of sustainable manufacturing processes and supply chains is rapidly becoming a critical issue. The reason is the necessity of providing for the needs of a growing human population which is increasingly prosperous across the globe. To this purpose, this review article explores the most important elements of sustainability science and couples them with the P‐graph framework, thereby rendering it possible to design feasible process and supply structures with great ease. Structure is an often‐overlooked aspect of process and supply chain design, in part because even relative simple processes or supply chains can have an enormous number of feasible structures. We further illustrate the application of these ideas with examples of energy generation processes and supply chains. © 2017 American Institute of Chemical Engineers Environ Prog, 37: 624–636, 2018

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Section: Introductionmentioning

confidence: 99%

Design and engineering of sustainable process systems and supply chains by the P‐graph framework

Cabezas

Argoti

Friedler

et al. 2018

Env Prog and Sustain Energy

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show abstract

“…Time-constrained PNS problems allow timing constraints [36], making it possible to address scheduling problems [37]. The multi-period modeling scheme allows the time span of a process network to be segmented to account for significant fluctuations of supplies, demands, and storage requirements [38].…”

Section: P-graph Frameworkmentioning

confidence: 99%

“…The issue with Equation ( 37) is that the investment cost should not scale down if a fermenter is used below full capacity and consumes less. For this reason, the slack biogas amount g slack k,i,l is also calculated for each fermenter, by a new Constraint (38). This slack is the amount that is actually not produced but would be if the fermenter was working at full capacity.…”

Section: Modified Milp Model With Flexible Inputsmentioning

confidence: 99%

Modeling of a Biomass-Based Energy Production Case Study Using Flexible Inputs with the P-Graph Framework

Éles,

Heckl,

Cabezas

2024

Energies

Self Cite

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In this work, a modeling technique utilizing the P-Graph framework was used for a case study involving biomass-based local energy production. In recent years, distributed energy systems gained attention. These systems aim to satisfy energy supply demands, support the local economy, decrease transportation needs and dependence on imports, and, in general, obtain a more sustainable energy production process. Designing such systems is a challenge, for which novel optimization approaches were developed to help decision making. Previous work used the P-Graph framework to optimize energy production in a small rural area, involving manure, intercrops, grass, and corn silage as inputs and fermenters. Biogas is produced in fermenters, and Combined Heat and Power (CHP) plants provide heat and electricity. A more recent result introduced the concept of operations with flexible inputs in the P-Graph framework. In this work, the concept of flexible inputs was applied to model fermenters in the original case study. A new implementation of the original decision problem was made both as a Mixed-Integer Linear Programming (MILP) model and as a purely P-Graph model by using the flexible input technique. Both approaches provided the same optimal solution, with a 31% larger profit than the fixed input model.

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“…Time-Constrained PNS problems allow timing constraints [33], making it possible to address scheduling problems [34]. The multi-period modeling scheme allows the time span of a process network to be segmented to account for significant fluctuations of supplies, demands, and storage requirements [35].…”

Section: Of 21mentioning

confidence: 99%

Modeling of a Biomass-based Energy Production Case Study Using Flexible Inputs with the P-Graph Framework

Éles,

Heckl,

Cabezas

2023

Preprint

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In this work, a modeling technique utilizing the P-Graph framework was used for a case 1 study involving biomass-based local energy production. In recent years, distributed energy systems 2 gained attention. These systems aim at satisfying energy supply demands, supporting the local 3 economy, decreasing transportation needs and dependence on imports, and in general obtaining a 4 more sustainable energy production process. Designing such systems is a challenge, for which novel 5 optimization approaches were developed to help decision-making. Previous work used the P-Graph 6 framework to optimize energy production in a small rural area, involving manure, intercrops, grass, 7 and corn silage as inputs, and fermenters. Biogas is produced in fermenters, and Combined Heat 8 and Power (CHP) plants provide heat and electricity. A more recent result introduced the concept of 9 operations with flexible inputs in the P-Graph framework. In this work, the concept of flexible inputs 10 was applied to model fermenters in the original case study. A new implementation of the original 11 decision problem was made both as a Mixed-Integer Linear Programming (MILP) model and as a 12 purely P-Graph model by using the flexible input technique. Both approaches provided the same 13 optimal solution, with a 31% larger profit than originally reported.

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Modeling Multi-period Operations using the P–graph Methodology

Cited by 6 publications

References 14 publications

Design and engineering of sustainable process systems and supply chains by the P‐graph framework

Design and engineering of sustainable process systems and supply chains by the P‐graph framework

Modeling of a Biomass-Based Energy Production Case Study Using Flexible Inputs with the P-Graph Framework

Modeling of a Biomass-based Energy Production Case Study Using Flexible Inputs with the P-Graph Framework

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