Botond Bertok

16318349400

Publications - 8

Overview of Hungarian operations research based on the VOCAL 2022 conference

Botond Bertok Marianna E.-Nagy Péter Biró

Publication Name: Central European Journal of Operations Research

Publication Date: 2024-12-01

Volume: 32

Issue: 4

Page Range: 897-902

Description:

The latest results of the Hungarian operations research community is reviewed based on the presentations given at the VOCAL 2022 conference. International collaborations and the continuation of research published at previous conferences of the series are also summarized.

Open Access: Yes

DOI: 10.1007/s10100-024-00930-3

Scheduling Manufacturing with Flexible Recipes to Maximize the Utilization of Renewable Energy

Botond Bertok Károly Kalauz Márton Frits

Publication Name: Chemical Engineering Transactions

Publication Date: 2024-01-01

Volume: 114

Issue: Unknown

Page Range: 955-960

Description:

The production schedule has a direct impact on the periodic utilization and energy consumption of equipment units. Meanwhile, for companies operating small power plants, the available renewable solar or wind energy changes continuously during the day, as does the hourly market price of the energy that can be purchased. Fortunately, the flexibility of production, possible schedules, or alternative recipes allow not only the minimization of costs but also the maximum use of renewable resources. The novelty of the P-graph-based method proposed here is the integration of three component problems into a single optimization model, namely the production scheduling by discrete event formulation, the management of flexible recipes by process synthesis, and the maximal renewable energy utilization according to discrete-time energy production and market price forecasts by representing them with temporarily available resources. The challenge of formalizing the optimization problem lies in synchronizing the time model of production scheduling with the resolution of market price and renewable energy production forecasts. The results show that the flexibility to alter both the sequence and schedule of operations by the integrated optimization model plays a critical role in optimizing energy usage.

Open Access: Yes

DOI: 10.3303/CET24114160

Synthesis and Techno-Economic Analysis of Pyrolysis-Oil-Based Biorefineries Using P-Graph

Botond Bertok Abid H. Tanzil Anamaria Paiva Pinheiro Pires Lina Martinez-Valencia István Heckl Juan C. García-Ojeda Ferenc Friedler Manuel Garcia-Perez Andres Argoti

Publication Name: Energy and Fuels

Publication Date: 2021-08-19

Volume: 35

Issue: 16

Page Range: 13159-13169

Description:

The production of renewable fuels and chemicals is a critical component of global strategies to reduce greenhouse gas emissions. In this regard, pyrolysis oil obtained from biomass comprises hundreds of chemical compounds, thus rendering it a good precursor for manufacturing a variety of fuel products of commercial interest. Despite the large number of contributions describing the products' extraction, upgrading, and potential refining schemes, no bio-oil refinery is currently in operation. The main challenge in building a bio-oil refinery lies in the lack of an economically viable process configuration. Systematic studies comparing alternative refinery concepts, or configurations, are needed to identify the most promising configuration. To the best of our knowledge, this study is the first to use process graph (P-graph) methodology for the synthesis of pyrolysis oil refineries. In particular, this work shows the effectiveness of P-graph methodology in simultaneously calculating the profitability of various biorefinery designs by using data reported in the literature and providing information on how the introduction of new technologies to the database will impact the formation of profitable biorefinery concepts. Our work demonstrates a methodology for the addition of new unit operations to the database generated from the literature. The addition of a centrifuge for water extraction and a wet oxidation system for acetic acid production resulted in the generation of 330 biorefinery configurations, seven of which have a profitability ranging from $1,650 to $23,666/h (USD) with acetic acid and levoglucosan as the main products, respectively. This demonstrates that P-graph methodology is useful for discovering optimum techno-economic scenarios that may otherwise be overlooked.

Open Access: Yes

DOI: 10.1021/acs.energyfuels.1c01299

Algorithmic model generation for multi-site multi-period planning of clean processes by P-graphs

Botond Bertok Károly Kalauz Márton Frits

Publication Name: Journal of Cleaner Production

Publication Date: 2024-01-01

Volume: 434

Issue: Unknown

Page Range: Unknown

Description:

Optimal clean process design requires strict constraints to enforce waste and byproduct management, all of which can be formulated in the language of mathematical programming. However, waste management and the utilization of by-products are often carried out in locations or periods other than the production process. The paper describes all modeling steps by P-graphs sufficient to represent raw material availability and production capacities in multiple time periods at multiple sites, as well as transportation and storage capacities of process materials and wastes. These steps are integrated into a single comprehensive model generation algorithm. For easier understanding, each model generation step is illustrated by a case study of planning a multi-site multi-period furniture production process alongside the recent challenges of energy supply and waste management. Finally, the case study of furniture production is analyzed under various circumstances to highlight the power of the proposed tools in daily production and transportation planning. Accordingly, the proposed method provides such alternative 5 best manufacturing and logistics plans that, in the event of a complete failure or overloading of one of the production capacities at either locations, there is still an alternative plan within a 3% profit decrease.

Open Access: Yes

DOI: 10.1016/j.jclepro.2023.140192

Comparative Analysis of Discrete-Time and Precedence-Based MILP Formulations for Sustainable Scheduling in Furniture Manufacturing

Botond Bertok Károly Kalauz Márton Frits

Publication Name: Chemical Engineering Transactions

Publication Date: 2025-01-01

Volume: 121

Issue: Unknown

Page Range: 151-156

Description:

Efficient production scheduling plays a pivotal role in enhancing productivity and reducing energy consumption in mass manufacturing environments. This study presents a comparative evaluation of two mixed-integer linear programming (MILP) formulations - Discrete-Time Process Network Synthesis (PNS) and Precedence-Based Time-Constrained Process Network Synthesis (TCPNS) - for optimizing production scheduling in furniture manufacturing. Both approaches are grounded in the P-graph framework, which excels at representing complex, flexible process recipes commonly found in large-scale production systems. The TCPNS model, with its precedence-based structure, offers high-resolution scheduling capabilities and accurately manages complex changeover constraints. It enables the computation of exact start times and resource allocations, leading to highly optimized schedules. However, this precision comes with increased computational demand, which can become impractical for large-scale instances. Conversely, the PNS approach discretizes the planning horizon into time slots, significantly reducing model size and complexity. While this may result in less granular schedules, the formulation allows for faster solution times and easier integration of combinatorial simplifications, making it a practical alternative for real-time applications. The research also explores automated model generation techniques for both formulations, highlighting multi-resolution capabilities in the discrete-time approach that allow flexible trade-offs between accuracy and computational effort. A real-life case study from the furniture manufacturing sector is used to benchmark the two optimization strategies. The results demonstrate the practical implications of each method in terms of schedule precision, computational performance, and energy-aware utilization, i.e., if minute-to-minute scheduling is sufficient instead of milliseconds, then traditional PNS algorithms can offer the same sustainable solution with 10,000 times faster computation.

Open Access: Yes

DOI: 10.3303/CET25121026

Exhaustive Generation of the Complete Multidimensional Pareto Front for Multi-Objective Process Network Synthesis

Botond Bertok Károly Kalauz Márton Frits

Publication Name: Chemical Engineering Transactions

Publication Date: 2025-01-01

Volume: 121

Issue: Unknown

Page Range: 157-162

Description:

In sustainable systems design, optimizing complex process networks often involves multiple conflicting objectives, such as minimizing cost, reducing environmental impact, and maximizing performance. Traditional single-objective optimization methods frequently fail to address this complexity, resulting in suboptimal and inflexible solutions. This study focuses on a comprehensive approach to multi-objective optimization for a single fixed process structure, where all integer decisions are predetermined through a prior process synthesis phase, such as the Solution Structure Generator algorithm from the P-graph framework. The remaining task involves optimizing continuous parameters—specifically, the operational volumes within the network—to generate the complete Pareto front, representing all non-dominated solutions. Each objective function is assumed to be a linear function of operational volumes, allowing for a scalable mathematical formulation. An algorithmic framework is developed to address the challenges associated with generating infinite-point Pareto fronts in high-dimensional spaces, incorporating genetic algorithms, machine learning models, and the P-graph methodology. This hybrid approach supports dynamic adaptation to changing data and improves computational efficiency. The methodology is demonstrated through a case study. The example highlights how balancing cost and environmental criteria using Pareto optimal solutions leads to more sustainable system designs. Ultimately, this work underscores the practical importance of generating and evaluating the complete set of Pareto optimal solutions in sustainable system design. Moving beyond a single optimal configuration, the proposed methodology offers robust decision support across diverse industrial applications, bridging the gap between theoretical optimality and real-world implementation.

Open Access: Yes

DOI: 10.3303/CET25121027

Optimal Planning of Routes, Schedules, and Charging Times of Automated Guided Electric Vehicles

Botond Bertok Károly Kalauz Márton Frits Petar Sabev Varbanov

Publication Name: Energies

Publication Date: 2026-02-01

Volume: 19

Issue: 3

Page Range: Unknown

Description:

In traditional industry setups, Automated Guided Vehicles (AGVs) follow trajectories planned together with the layout of the storage or production facility and supported by fixed markers on the floor or on the walls. Traffic rules manage the avoidance of multiple vehicles, while fleet management gets movement and transportation commands completed as soon as possible. In contrast, recent developments in navigation and advanced computing, sensor, and communication capabilities make their free movement safe and manageable. Detailed route planning and scheduling can guarantee that the vehicles keep a safe distance in time and space. A recent challenge of electric AGVs is that their charging may take several hours, which must be factored into their schedule. This has made minimal energy demand a key objective alongside earliest delivery and strictly meeting the deadlines. This paper presents a method for detailed routing and scheduling of AGV fleets to minimize energy consumption while considering battery levels and charging times. The optimization method is illustrated by a case study where multiple delivery tasks are performed by synchronized movement of vehicles on a complex warehouse layout. In the optimal solution, the scheduled waiting times for collision avoidance are utilized by the vehicles to pre-charge their batteries.

Open Access: Yes

DOI: 10.3390/en19030813

Modelling optimal investment planning for household photovoltaic and battery systems under dynamic electricity market conditions

Botond Bertok Márton Frits D. J.S. Chong

Publication Name: Discover Sustainability

Publication Date: 2026-12-01

Volume: 7

Issue: 1

Page Range: Unknown

Description:

Capacity sizing and calculating cost savings for residential households in a rapidly evolving energy market, influenced by fluctuating electricity prices and changing government incentives, is a highly complex problem. The key challenges stem from multiple interacting factors, including retail electricity prices, the desired payback period, household size, applicable electricity schemes, and the capacity factor of the photovoltaic (PV) system. The nominal power output of the solar energy system is constrained by both the specifications and the number of installed inverters and PV panels. As solar generation is intermittent and non-dispatchable, it is inherently weather-dependent and often unable to align with the dynamic fluctuations in household electricity consumption. From a financial modelling perspective, the length of the accounting period directly determines the time resolution of the model, influencing both the accuracy of cash flow estimation and investment decision-making. The proposed two-level investment planning model is based on the process network synthesis approach. At the upper level of the process model, solar generation technologies, including inverters and solar panels, are technically and economically assessed. At the lower level, which represents the load consumption side, the periodical energy balances for production, storage, demand, and purchase are considered. In order to accurately evaluate the solar energy system, the model is developed with both a monthly framework and a detailed hourly framework. The time resolution allows the model to account for grid intake, electricity sold, and storage inventory conditions over the defined periods, ultimately providing the optimal sizing for a solar system equipped with battery storage. Case studies are conducted to investigate the effects of household size, extended payback periods, varying retail electricity prices, and grid reliability. These scenarios demonstrate the key parameters that significantly influence the economic feasibility and optimal sizing of the solar energy system, which are discussed in detail in this paper.

Open Access: Yes

DOI: 10.1007/s43621-026-02683-2