Conference Agenda

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Optimal production scheduling is crucial for industries aiming to remain competitive, since profit margins are constantly shrinking. Efficient scheduling guarantees that companies can minimize delays, avoid overproduction, and allocate resources efficiently, which boosts profitability and customer satisfaction. However, achieving optimal scheduling is a complex task due to the dynamic and interconnected nature of modern production systems.

Traditionally, production scheduling is usually modeled and solved using mathematical optimization techniques (Georgiadis et al., 2019), such as MILP. However, applying these optimization methods in industry presents significant challenges (Harjunkoski, 2016). To make the scheduling problem computationally solvable, researchers often use approximate representations that do not fully capture the complexity of the actual production environment.

To overcome these limitations, we propose a novel process representation that offers a more granular but accurate depiction of the timing interrelations between production stages. In traditional representations, each processing stage is treated as a single, rigid block utilizing some resource and precedence constraints are implemented to sequence these stages. In reality, however, steps in chemical processing do not follow each other in a strict sense; most of the times they overlap in time and this overlap is determined by the timing of “finer” operating tasks executed in processing. In addition, these finer subtasks may require the use of auxiliary equipment whose occupancy must also be captured in addition to that of the main equipment.

For those reasons, it is important to break down processing tasks (procedures) into shorter, more primitive steps which will be called operations. Operations can be used to time the start or end of the procedure they belong or of other procedures. Both procedures and operations can make use of resources such as equipment or labor. The execution of operations is “tied” by constraints that mandate their sequencing in a strict way. In some cases, there is flexibility in the execution of an operation (e.g. a tank can have a dirty-hold time before it is cleaned). These flexibilities can be embedded in the representation by being modeled as dummy operations with flexible durations. So, even though the breaking-down of the process into procedures and operations seems to make the representation more complex, the implementation of actual constraints in the recipe execution ties in a deterministic way the start and end of all tasks within a batch (with the exception of flexible starts) making the scheduling problem simpler.

This detailed representation generates data that can be fed into a MIP model, improving the accuracy and reliability of scheduling decisions. Equipment-dependent durations, task-equipment matching constraints, connectivity/compatibility constraints can also be incorporated into the model for a more accurate representation of the industrial setting. The developed model can be adapted to different objectives, such as makespan minimization, as will be shown with the help of case studies presented in the paper.

Harjunkoski, I. (2016). Deploying scheduling solutions in an industrial environment. Computers &Chemical Engineering, 91, 127-135

Georgiadis, G., Elekidis, A., Georgiadis, M. (2019). Optimization-based scheduling for the process industries: from theory to real-life industrial applications. Processes, 7, 438.

As global competition rises and customer expectations increase, manufacturing industries must embrace digital transformation to remain competitive and operationally effective. In complex production environments, digital technologies can offer solutions to optimize key areas. Fluctuating demands (Hubbs et. al, 2020), equipment breakdowns and raw material availability are some challenges that necessitate for schedules to be flexible, to adapt quickly to changing conditions without causing order delays or increased costs. This is particularly difficult in the presence of frequent and expensive product changeovers, since production schedules are typically handled manually and combinatorial complexity of real-life industrial instances does not allow exact methods to deliver optimal solutions quickly.

This study focuses on optimizing production scheduling in multi-product plants with shared resources and costly changeover operations. Specifically, two main challenges are addressed, the unknown changeover behavior of new products and the need for rapid schedule generation when unforeseen events happen. An innovative framework integrating Machine Learning (ML) techniques with Mixed-Integer Linear Programming (MILP) is proposed. Initially, a regression model predicts unknown changeover times based on key product attributes. Then, a representation space (Passalis & Tefas, 2016) where distances correlate with changeover times is compiled through multidimensional scaling, allowing constrained clustering to group production orders according to available packing lines. Ultimately, the MILP model generates the production schedule within a constrained solution space, utilizing optimal product-to-line allocation from cluster segmentation.

A case study inspired by a Greek construction materials plant is used to validate the proposed approach. The results showed that this framework improves scheduling efficiency by providing rapid solutions, reducing downtime and facilitating the introduction of new products. Overall, a novel scheduling solution is proposed for manufacturing industries that face unknown production data and need quick schedule alternations without extra changeover costs.

References

Hubbs, C. D., Li, C., Sahinidis, N. V., Grossmann, I. E., & Wassick, J. M. (2020). A deep reinforcement learning approach for chemical production scheduling. Computers & Chemical Engineering, 141, 106982.

Passalis, N., & Tefas, A. (2016). Information clustering using manifold-based optimization of the bag-of-features representation. IEEE transactions on cybernetics, 48(1), 52-63.

The development of industrial and transportation activities has increased CO₂ emissions, raising atmospheric CO₂ from 300 ppm in the late 19^th century to 425 ppm in 2024 [1], causing a 1ºC temperature rise. Synthetic methane emerges as an interesting alternative, aligning with circular economy principles to reduce reliance on imported fossil fuels. There are two alternatives to capture CO₂ and produce synthetic natural gas (SNG), biomass growth, and its capture from the air and other sources using human-made technologies.

This work develops a systematic comprehensive comparison to model the production of renewable methane from lignocellulosic dry residues via gasification and anaerobic digestion of wet waste, and synthetic methane production from captured CO₂ and renewable electrolytic hydrogen using a multiscale approach. First, a techno-economic evaluation determines key performance indicators (KPI) of facilities and renewable energy sources. Then, a Facility Location Problem (FLP) identifies production capacities and the optimal facility locations. The decentralized use of lignocellulosic and wet waste, along with CO₂ captured from point and dilute sources is analyzed due to the availability of the raw material and the high transportation costs. The problem is formulated as a Mixed-integer linear programming (MILP) model, optimizing waste and CO₂ utilization, plant locations, PV panel surface areas, and wind turbines across Spain, at the level of agricultural shires, 356. It considers budget variations and carbon taxes for the years 2022, 2030, and 2050. A maximum of 2% of shires' surfaces, 10,120 km², is employed, installing between 20 and 50 wind turbines per shire.

Lignocellulosic dry waste and point sources for CO₂ capture using MEA are preferred as predicted by the MILP model. PV panels are mainly selected due to their competitive cost, increasing their surface from 147 km² to 1,511 km² for the time horizon from 2022 to 2050, and using wind turbines to generate additional power, from 7.3 GW to 52.8 GW in the same period. The maximum synthetic biomethane production from lignocellulosic dry waste reaches 14,086 kt/year of synthetic methane. The CO₂ captured from point sources is prioritized. Southeastern and coastal shires are selected, utilizing 1.46% of the available surface producing 11,104 kt/year of methane. The investment of 14,440 M€ for waste treatments, CO₂ capture from point sources, and methane synthesis in the year 2022. A sensitivity analysis reveals methane prices range from 3.818 €/MMBTU to 13.837 €/MMBTU in the period from 2022 to 2050, requiring from 66% to 410% of the budget to achieve 100% methane self-sufficiency. Considering carbon taxes, the price of 3.146 €/MMBTU is projected for 2050, which is competitive with current natural gas prices.

[1] NASA, 2024. Carbon Dioxide. Direct measurements, 1958-Present. https://climate.nasa.gov/vital-signs/carbon-dioxide/?intent=121 (Accessed April 2024).

With increment energy awareness, there has been growing recognition of the importance on incorporating energy considerations into the flexible job shop scheduling problem (FJSSP). To accommodate the energy-efficient FJSSP, three strategies have been explored: (i) speed-scaling framework, (ii) incorporation of time-of-use electricity price, and (iii) switching machines to a power-saving mode while idle. The third strategy is significant, as 65% of the total energy consumption (TEC) occurs while machines are idle [1]. Consequently, effective management of machine modes while idle has garnered increasing attention, although it remains in the early stage of exploration.

Many approaches, such as mathematical programming [1-4] and metaheuristics [2,3], have been attempted to tackle the energy-efficient FJSSP with consideration of machine modes. The mathematical programming approach prioritizes guaranteeing solution optimality and evaluating solution quality. Zhang et al. [2] proposed a mixed integer linear programming (MILP) model to minimize TEC. However, their model fails to generate energy-efficient solutions for industrial-scale problems. Followingly, the same problems are addressed by MILP models from Meng et al. [3] and Rakovitis et al. [1]. Although these models are more effective, they lack the robustness to efficiently address all industrial-scale cases. Moreover, Meng et al. [3] did not incorporate the turn on/off energy strategy, leading to high energy waste during machine idle periods. Li et al. [4] developed a local sequence-based formulation to manage the machine mode selection. However, they introduce excessive binary variables, resulting in computational inefficiency. It appears that no mathematical programming approach has been developed to effectively solve the energy-efficient FJSSP by managing machine modes at an industrial scale.

In this work, we proposed a novel global sequence-based mathematical formulation (MG) to optimize the energy-efficient FJSSP. Machines can select a power-saving mode between standby and turn-on/off while idle. A big-M constraint is introduced to identify the immediate successor operation of a given operation, allowing us to account for the idle duration between them. Computational results demonstrate that the proposed MG is robust to generate feasible solutions in highly complex examples. MG generates better TEC results in 64% of the examples relative to existing models, with a maximum reduction of 27.6%. More importantly, as the complexity of problems increases, the advantage of MG becomes more apparent.

[1] Rakovitis, N., Li, D., Zhang, N., Li, J., Zhang, L., & Xiao, X. (2022). Novel approach to energy-efficient flexible job-shop scheduling problems. Energy, 238, 121773.

[2] Zhang, L., Tang, Q., Wu, Z., & Wang, F. (2017). Mathematical modeling and evolutionary generation of rule sets for energy-efficient flexible job shops. Energy, 138, 210-227.

[3] Meng, L., Zhang, C., Shao, X., & Ren, Y. (2019). MILP models for energy-aware flexible job shop scheduling problem. Journal of cleaner production, 210, 710-723.

[4] Li, D., Zheng, T., Li, J., & Teymourifar, A. (2023). A hybrid framework integrating machine-learning and mathematical programming approaches for sustainable scheduling of flexible job-shop problems. Chemical Engineering Transactions, 103, 385-390.

As electrification becomes a major trend in the area of Process Systems engineering, the Unit Commitment (UC) problem is a critical optimization challenge that arises in the energy systems. The major goal in this problem is to schedule power-generating units while minimizing operational costs and adhering to physical and operational constraints. As energy systems grow more complex and electricity demands continue to rise, solving the UC problem efficiently is paramount to ensuring both cost-effectiveness and grid reliability. Various methodologies have been developed to address this problem, ranging from sophisticated optimization algorithms to heuristic-based methods[1]. Techniques used include genetic algorithms, Lagrangean relaxation, and Mixed-Integer Linear Programming (MILP), with each approach yielding varying degrees of optimality depending on the problem’s complexity[1]. Notably, the transition from Lagrangean relaxation (once employed by PJM Independent System Operators) to MILP has yielded significant cost savings, estimated at $5 billion annually for the energy sector[2].

In this work, we address the UC problem using MILP formulations and leverage the EGRET library to build an efficient, scalable model[3]. EGRET offers two new formulations, tight and compact formulation, which have been shown to be computationally competitive with the formulations from the literature. To further enhance computational efficiency, we integrate a Shrinking Horizon strategy. This strategy consists of an iterative decomposition method, where the binary variables are relaxed beyond a rolling time window, so that smaller integer programming subproblems are successively solved in the rolling window.

A significant advantage of the Shrinking Horizon method lies in its ability to balance computational performance with solution quality. By breaking down the problem into manageable chunks, it reduces computational complexity without compromising much on the optimality of the schedules generated. The decomposition framework enables the model to handle larger and more complex power systems, which is crucial as grids become increasingly integrated with renewable energy sources and distributed generation.

This approach has been tested on several benchmark case studies, including IEEE 118, WP2383, SP3120, and CASE6468RTE, each of which represents a system of varying size and complexity. These tests provide a rigorous evaluation of the method’s scalability, robustness, and practicality. Results demonstrate that the Shrinking Horizon approach achieves large computational speedup, reducing model-solving time significantly, at least up to an average of 22.2%. At the same time, the proposed approach does not compromise high-quality solutions since they are comparable to those obtained through traditional full-horizon methods, making it particularly well-suited for large-scale UC problems in real-world energy systems. These findings suggest that the combination of EGRET’s tight formulations and the Shrinking Horizon method can offer a promising solution for future large-scale UC applications.

References:

[1] N. P. Padhy, "Unit commitment-a bibliographical survey," in IEEE Transactions on Power Systems, vol. 19, no. 2, pp. 1196-1205, May 2004, doi: 10.1109/TPWRS.2003.821611
[2]O’Neill, R. P., Dautel, T., & Krall, E. (2011). Recent ISO software enhancements and future software and modeling plans. Federal Energy Regulatory Commission, Tech. Rep.
[3] Knueven, B., Ostrowski, J., & Watson, J. P. (2020). On mixed-integer programming formulations for the unit commitment problem. INFORMS Journal on Computing, 32(4), 857-876.