Discrete Production Research Articles

Synergistic action of novel maltohexaose-forming amylase and branching enzyme improves the enzymatic conversion of starch to specific maltooligosaccharide

As attractive functional ingredients, maltooligosaccharides (MOS) are typically prepared by controlled enzymatic hydrolysis of starch. However, the random attack mode of amylase often leads to discrete product distribution, thereby reducing yields and purities. In this study, a novel glycoside hydrolase family 13 amylase AmyEs from marine myxobacteria Enhygromyxa salina was identified efficient maltohexaose (G6)-forming ability (40 %, w/w). By deciphering external chain length, we found that the high density of α-1,6-branching points benefits the G6 formation of AmyEs with high purity (71–82 %), indicating the substrate selectivity of AmyEs toward high-branched starch. Based on this, asynchronous conversion strategy was designed to enhance specific MOS yield from corn starch by exploiting branching enzymes and AmyEs, and the purity and yield of G6 respectively increased by 9.5 % and 5 % compared to single AmyEs treatment. Our results demonstrate that combinatorial catalysis of MOS-forming amylases and branching enzymes provides a favorable industrial preparation of specific MOS.

A research agenda to advance the study of implementation mechanisms

BackgroundImplementation science scholars have made significant progress identifying factors that enable or obstruct the implementation of evidence-based interventions, and testing strategies that may modify those factors. However, little research sheds light on how or why strategies work, in what contexts, and for whom. Studying implementation mechanisms—the processes responsible for change—is crucial for advancing the field of implementation science and enhancing its value in facilitating equitable policy and practice change. The Agency for Healthcare Research and Quality funded a conference series to achieve two aims: (1) develop a research agenda on implementation mechanisms, and (2) actively disseminate the research agenda to research, policy, and practice audiences. This article presents the resulting research agenda, including priorities and actions to encourage its execution.MethodBuilding on prior concept mapping work, in a semi-structured, 3-day, in-person working meeting, 23 US-based researchers used a modified nominal group process to generate priorities and actions for addressing challenges to studying implementation mechanisms. During each of the three 120-min sessions, small groups responded to the prompt: “What actions need to be taken to move this research forward?” The groups brainstormed actions, which were then shared with the full group and discussed with the support of facilitators trained in structured group processes. Facilitators grouped critical and novel ideas into themes. Attendees voted on six themes they prioritized to discuss in a fourth, 120-min session, during which small groups operationalized prioritized actions. Subsequently, all ideas were collated, combined, and revised for clarity by a subset of the authorship team.ResultsFrom this multistep process, 150 actions emerged across 10 priority areas, which together constitute the research agenda. Actions included discrete activities, projects, or products, and ways to shift how research is conducted to strengthen the study of implementation mechanisms.ConclusionsThis research agenda elevates actions to guide the selection, design, and evaluation of implementation mechanisms. By delineating recommended actions to address the challenges of studying implementation mechanisms, this research agenda facilitates expanding the field of implementation science, beyond studying what works to how and why strategies work, in what contexts, for whom, and with which interventions.

Abstract Mo118: Myofilament proteolysis may underlie contractile remodeling in atrial fibrillation

Atrial fibrillation (AFib) is the most common cardiac rhythm disturbance. Treatment of AFib involves restoration of the atrial electrical rhythm. Following rhythm restoration, a period of depressed mechanical function, including decreased blood flow velocity and reduced atrial contractility, known as atrial stunning, occurs. This suggests that defects in contractility occur in AFib and are revealed upon restoration of rhythm. To assess contractile function, we used a canine atrial tachypacing model of induced AFib. Mass spectrometry analysis showed dysregulation of contractile proteins in samples from AFib compared to sinus rhythm atria. In atrial cardiomyocytes that were useable for skinned single cardiomyocyte force-calcium studies, we found reduced force of contraction. There were no significant differences in myosin heavy chain isoform expression. Resting tension is decreased in the AFib samples correlating with reduced full-length titin in the sarcomere. We measured degradation of other myofilament proteins including cMyBP-C, actinin, MHC, and cTnI, showing significant degradation in the AFib samples compared to sinus rhythm atria. Many of the protein degradation products appeared as discrete cleavage products that are generated by calpain proteolysis. We assessed calpain activity and found it to be significantly increased. Skinned cardiomyocytes from AFib atria showed increased calcium sensitivity that was consistent with increased cTnI degradation and decreased TnI phosphorylation. These results provide an understanding of the contractile remodeling that occurs in AFib.

Proteolytic degradation of atrial sarcomere proteins underlies contractile defects in atrial fibrillation.

Atrial fibrillation (AFib) is the most common cardiac rhythm disturbance, often treated via electrical cardioversion. Following rhythm restoration, a period of depressed mechanical function known as atrial stunning occurs, suggesting that defects in contractility occur in AFib and are revealed upon restoration of rhythm. This project aims to define the contractile remodeling that occurs in AFib. To assess contractile function, we used a canine atrial tachypacing model of induced AFib. Mass spectrometry analysis showed dysregulation of contractile proteins in samples from AFib compared with sinus rhythm atria. Atrial cardiomyocytes show reduced force of contraction, decreased resting tension, and increased calcium sensitivity in skinned single cardiomyocyte studies. These alterations correlated with degradation of myofilament proteins including myosin heavy chain altering force of contraction, titin altering resting tension, and troponin I altering calcium sensitivity. We measured degradation of other myofilament proteins, including cardiac myosin binding protein C and actinin, that show degradation products in the AFib samples that are absent in the sinus rhythm atria. Many of the degradation products appeared as discrete cleavage products that are generated by calpain proteolysis. We assessed calpain activity and found it to be significantly increased. These results provide an understanding of the contractile remodeling that occurs in AFib and provide insight into the molecular explanation for atrial stunning and the increased risk of atrial thrombus and stroke in AFib.NEW & NOTEWORTHY Atrial fibrillation is the most common cardiac rhythm disorder, and remodeling during atrial fibrillation is highly variable between patients. This study has defined the biophysical changes in contractility that occur in atrial fibrillation along with identifying potential molecular mechanisms that may drive this remodeling. This includes proteolysis of several myofilament proteins including titin, troponin I, myosin heavy chain, myosin binding protein C, and actinin, which is consistent with the observed contractile deficits.

The impact of high arousal and displeasure on online review helpfulness: Exploring the moderating role of product involvement

Online reviews help consumers make purchasing decisions on e-commerce platforms by addressing uncertainties in online shopping. In the context of information overload, the value of review helpfulness has become increasingly evident. This study aims to explore the effects of discrete emotions on helpfulness by categorizing Ekman’s six basic emotions based on arousal and valence, and extracting their probabilities from Amazon reviews using BERT (Bidirectional Encoder Representations from Transformers). The results indicate high arousal or negative emotions adversely influence review usefulness. Furthermore, anger, disgust, and fear, characterized by high arousal and displeasure, significantly affect the perceived helpfulness of the reviews. Additionally, we identify product involvement as a significant moderator, suggesting that consumers’ investment in products influences their interpretation of reviews’ emotional content. This study contributes to understanding the relationship between discrete emotions, product involvement, and review helpfulness in e-commerce, offering insights for online retailers and platform developers to enhance consumer decision-making.

A Combined Discrete Event Simulation and Factorial Design Experiment for the Scheduling Problem in a Hybrid Flow Shop

Production plants have always been confronted with the problem of scheduling, as this has a direct impact on production time and therefore on production costs. This is especially true in today's world, where it is necessary to produce a quality product at a low price and in a short time, while at the same time responding flexibly to customer demands. Due to the complexity and for economic reasons, testing different variants in a real production environment is insufficient and ineffective. For this reason, this paper proposes a new method that combines discrete event simulation and factorial design experiment to find the optimal schedule in hybrid flow shop. It was tested with the goal of achieving the minimum makespan. The results show that this method makes it possible to find improved solution very quickly. Compared to the original production schedule, the makespan could be reduced by 3 hours and 31 minutes which is reduction of 16.3%. The proposed methodology can be used in many discrete and process production plants.

Active runout compensation using the guide elements on metal band saws for a longer tool life and reduced material loss

AbstractAt a time of rising energy and material costs, manufacturing process efficiency is becoming increasingly important. This is one reason why cutting and especially sawing processes, usually the first step in most manufacturing chains in discrete part production, have to be investigated more intensively. Due to problems with runout and poor surface finishes, raw material is conventionally cut to oversize by either circular sawing or band sawing. This oversize has to be removed by following processes, costing extra energy and wasting material. Since the problem of runout increases with increasing tool wear due to higher deflections of the thin and compliant tools, an even larger oversize is required. This paper describes an approach to reduce the need of oversize even with increasing tool wear in band sawing by tilting the saw band in order to compensate for tool deflections during cutting. To achieve this, it is necessary to measure and understand the saw band runout. The next step is to present a system design and controller for tilting the saw band. Finally, tests are carried out to analyse the effectiveness of the system. In addition, the approach allows the use of increased process parameters to the end of the tool life without losing more material. The tool can therefore be used productively for a longer time period.

Properties of Convex Lattice Sets under the Discrete Legendre Transform

The discrete Legendre transform is a powerful tool for analyzing the properties of convex lattice sets. In this paper, for t>0, we study a class of convex lattice sets and establish a relationship between vertices of the polar of convex lattice sets and vertices of the polar of its t−dilation. Subsequently, we show that there exists a class of convex lattice sets such that its polar is itself. In addition, we calculate upper and lower bounds for the discrete Mahler product of a class of convex lattice sets.

Integrated Subsystems of Materials and Information Flow for Continuous Manufacturing of Coal and Steel

Abstract With the concept of Industry 4.0 production processes are moving towards autonomy and intelligence. Technologies equipped with artificial intelligence (AI) are involved into processes that are more and more digitized. Collaborative technologies are a feature of discrete processes. The automotive industry has achieved many successes in the process innovation towards smart factories. Other plants, such as smelters or coal mining are also striving to develop smart manufacturing with integrated computer systems to support processes. A continuous production is different from a discrete or batch production. Industry 4.0 concept is focused on discrete production (with high level of automation and robotization of manufacturing) meanwhile there is a gap in implementation of these approach in the continuous production. The objective of the publication is to prepare and design the integrated computer management system based on processes realized in coal and steel manufacturing. Coal and steel production are key elements in a chain of any industrial manufacturing e.g. automotive or machinery engineering. These processes are crucial in building of smart value chain. In our paper we present the structure of processes for the continuous production. Based the processes model we proposed the next steps to build the smart manufacturing for continuous production.

Real-world waste dispersion modelling for benthic integrated multi-trophic aquaculture.

In real-world situations, marine fish farms accommodate multiple fish species and cohorts within the farm, leading to diverse farm layouts influenced by cage dimensions, configurations, and intricate arrangements. These cage management practices are essential to meet production demands, however, farm-level complexities can impact model predictions of waste deposition and benthic impact near fish cages. This is of particular importance when the cages are used for integrated multi-trophic aquaculture (IMTA) with benthic feeders, where this waste not only affects environmental conditions but also provides a potential food source. The Cage Aquaculture Particulate Output and Transport (CAPOT) model incorporated multiple species, cohorts, and cage arrangements to estimate waste distribution from a commercial fish farm in the Mediterranean between October 2018 and July 2019. This spreadsheet model estimated dispersion for individual fish cages using a grid resolution of 5 m x 5 m. The study categorized discrete production periods for each fish cage every month, aligning with intermittent changes in biomass and food inputs due to different cage management practices throughout production. This approach facilitated the use of detailed input data and enhanced model representativeness by considering variations in cage biomass, food types, settling velocities, and configurations. Model outputs, represented in contour plots, indicated higher deposition directly below fish cages that varied monthly throughout fish production cycles. Deposition footprints reflected changes in cage biomass, food inputs, and farm-level practices reflecting this real-world scenario where aquaculture does not follow a production continuum. Moreover, cohort dynamics and cage movements associated with the cage management practices of the fish farm influenced the quantity and fate of wastes distributed around fish cages, revealing variability in deposition footprints. Clearly, these findings have important implications for the design of benthic IMTA systems, with species such as sea cucumber and polychaetes. Variability in waste deposition creates challenges in identifying where the benthic organisms should be placed to allow optimal uptake of waste to meet their food requirements and increase survivability. Evidently, models have an important role to play and this study emphasizes the need for representative input data to describe actual food inputs, cage biomass changes, and management practices for more representative farm-scale modelling and essentially to improve particulate waste management. To effectively mitigate benthic impacts through IMTA, models must quantify and resolve particulate waste distribution and impact around fish farms to maintain a balanced system with net removal of wastes. Resolving farm-level complexities provides vital information about the variability of food availability and quality for extractive organisms that helps improve recycling of organic wastes in integrated systems, demanding a more representative modelling approach.

Minimum cost with consensus constraint to support multi-attribute product design

Classical discrete multi-attribute product design (DMAPD) problem aims to design the product with the maximum number of approval individuals. However, the consensus constraint, which measures the uniformity of the opinions among different individuals, is rarely considered in the existing DMAPD studies. To fill this gap, we propose a novel minimum cost discrete multi-attribute product design (MCDMAPD) model with consensus constraint. Firstly, we provide a method to determine the multi-attribute satisfaction degrees and the satisfaction threshold. Then, under the constraint of the limited design budget, the DMAPD model maximizing the number of approval individuals is developed. Next, we define a consensus measure on the designed product, and provide the method for determining the unit adjustment cost of individuals. Furthermore, by considering the strategic proof and the envy-free constraints, the MCDMAPD model with consensus constraint is developed to reach the acceptable consensus. Finally, we conduct the simulation analysis and comparison analysis to justify the MCDMAPD model.

A knowledge-guided Estimation of Distribution Algorithm for energy-efficient Joint Robotic Assembly Line Balancing and Feeding Problem

The assembly line serves as a fundamental system in discrete production. To address the challenges in balancing robotic assembly lines, timely part feeding, and the need for sustainable manufacturing, this paper studies an energy-efficient Joint Robotic Assembly Line Balancing and Feeding Problem (JRALB-FP) with the criteria of minimizing both cycle time and total fuel consumption cost. Considering the complexity of the multi-problem and multi-objective optimization, a knowledge-guided Estimation of Distribution Algorithm (KEDA) is proposed to solve energy-efficient JRALB-FP. First, a probability model of EDA for task-workstation allocation paired with a heuristic method-based sampling mechanism is created. Using this probability model, a specific encoding mechanism is designed for part-trailer allocation, and good initial solutions are produced. Second, several properties of the bi-objective problem are analyzed to guide the design of local search operators for both objectives optimization. Third, the updating mechanism of the probability model is designed to learn from the elite solutions. Fourth, two knowledge-guided local search operators are designed and implemented to exploit better non-dominated solutions sufficiently. A design of experiment is carried out to determine the parameters. Extensive computational tests and comparisons with the state-of-the-art multi-objective algorithms are carried out, which verify the effectiveness of the knowledge-guided local search operators, the problem-oriented heuristic-based sampling mechanism, and the special designs of the KEDA in solving the energy-efficient JRALB-FP.

Developing an IoT and Machine Learning-Based Monitoring System for Discrete Production Processes

Developing an IoT and Machine Learning-Based Monitoring System for Discrete Production Processes

Critical Reflections on Universities, Publishing, and the Early Career Experience

This paper is a critical reflection on the changing relationship between university institutions, academic publishing, and young researchers. It emerges from a current project in assessing the role and development of Warwick University’s research journals (and their editors), but also takes into account two recent Warwick Institute of Advanced Study seminars discussing the practical and strategic challenge of publishing for early career scholars and PhD students. While these seminars concerned publishing in general, and the question of career trajectories, this reflection paper takes into account the current shifts in publishing and our understanding of research as knowledge production more broadly. This reflection maintains that, in part provoked by digital media, the status of research knowledge vis-à-vis its traditional presentation in the discrete products of the ‘article’, and the book, has become unstable, and this instability has opened up a range of economic and systemic conditions of knowledge production that have long since been concealed. Current shifts thus offer younger scholars and early career researchers significant opportunities: this short paper sets out the initial framework for a current research project focussing on university publishing, then it refers to the two above seminars in order to conclude with some critical issues for academic practice, research and for early career scholars.

Optimization of a parametric product design using techno-economic assessment and environmental characteristics with application to an electric traction motor

Accelerating the development of clean energy technologies is required to move towards a sustainable future. New design approaches are being proposed to help accelerate these developments. This study proposes and improves a novel design framework that incorporates life cycle assessment (LCA) and techno-economic assessment (TEA) with an optimization-based design model of a discrete product at early stage. Objective functions for mass, energy consumption, and two metrics relating to manufacturer and consumer economic interests are considered; these objectives are minimized using a Pareto-like approach. An electric traction motor for an electric vehicle is used as a discrete product case study. The approach demonstrates the utility of considering four-objectives in the design problem, uncertainty analysis via Monte Carlo simulation, and the power of employing LCA and TEA methods. Future work may explore a broader range of objective functions to cover different challenges that inhibit the development of clean energy technologies.

Digital Twin-Driven Multi-Factor Production Capacity Prediction for Discrete Manufacturing Workshop

Traditional capacity forecasting algorithms lack effective data interaction, leading to a disconnection between the actual plan and production. This paper discusses the multi-factor model based on a discrete manufacturing workshop and proposes a digital twin-driven discrete manufacturing workshop capacity prediction method. Firstly, this paper gives a system framework for production capacity prediction in discrete manufacturing workshops based on digital twins. Then, a mathematical model is described for discrete manufacturing workshop production capacity under multiple disturbance factors. Furthermore, an innovative production capacity prediction method, using the “digital twin + Long-Short-Term Memory Network (LSTM) algorithm”, is presented. Finally, a discrete manufacturing workshop twin platform is deployed using a commemorative disk custom production line as the prototype platform. The verification shows that the proposed method can achieve a prediction accuracy rate of 91.8% for production line capacity. By integrating the optimization feedback function of the digital twin system into the production process control, this paper enables an accurate perception of the current state and future changes in the production system, effectively evaluating the production capacity and delivery date of discrete manufacturing workshops.

Resilient anatomy and local plasticity of naive and stress haematopoiesis

The bone marrow adjusts blood cell production to meet physiological demands in response to insults. The spatial organization of normal and stress responses are unknown owing to the lack of methods to visualize most steps of blood production. Here we develop strategies to image multipotent haematopoiesis, erythropoiesis and lymphopoiesis in mice. We combine these with imaging of myelopoiesis1 to define the anatomy of normal and stress haematopoiesis. In the steady state, across the skeleton, single stem cells and multipotent progenitors distribute through the marrow enriched near megakaryocytes. Lineage-committed progenitors are recruited to blood vessels, where they contribute to lineage-specific microanatomical structures composed of progenitors and immature cells, which function as the production sites for each major blood lineage. This overall anatomy is resilient to insults, as it was maintained after haemorrhage, systemic bacterial infection and granulocyte colony-stimulating factor (G-CSF) treatment, and during ageing. Production sites enable haematopoietic plasticity as they differentially and selectively modulate their numbers and output in response to insults. We found that stress responses are variable across the skeleton: the tibia and the sternum respond in opposite ways to G-CSF, and the skull does not increase erythropoiesis after haemorrhage. Our studies enable in situ analyses of haematopoiesis, define the anatomy of normal and stress responses, identify discrete microanatomical production sites that confer plasticity to haematopoiesis, and uncover unprecedented heterogeneity of stress responses across the skeleton.

Intelligent Analysis of Import and Export in Green Trade Barrier Based on Big Data Analysis

Abstract With the rapid development of economic globalisation, global economic and trade activities are escalating. However, environmental problems and the emergence of green economy, a response to these problems, has led to the widespread introduction of green trade barriers. These barriers implicitly limit the development of trade activities. This paper focuses on the export difficulties caused by green trade barriers and proposes a method to quantify discrete product characteristics, explore the internal characteristics of commodities and decide optimally on intended export regions. Firstly, the discrete feature of products is quantified by quantitative transformation method. Secondly, the quantitative data are used to derive the best decision for export regions through support vector regression (SVR) method. Particle swarm optimisation is used in optimising SVR parameters to achieve high-precision decision making. Comparison with historical data from the industry park shows the identification accuracy of the optimised SVR model to be better than that of the traditional regression model. This finding presents a novel perspective for developing import and export under the background of green trade barriers.

Multijoints and Factorisation

We solve the dual multijoint problem and prove the existence of so-called factorisations for arbitrary fields and multijoints of kj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_j$$\\end{document}-planes. More generally, we deduce a discrete analogue of a theorem due in essence to Bourgain and Guth. Our result is a universal statement which describes a property of the discrete wedge product without any explicit reference to multijoints and is stated as follows: Suppose that k1+…+kd=n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_1 + \\ldots + k_d = n$$\\end{document}. There is a constant C=C(n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C=C(n)$$\\end{document} so that for any field F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {F}$$\\end{document} and for any finitely supported function S:Fn→R≥0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S : \\mathbb {F}^n \\rightarrow \\mathbb {R}_{\\ge 0}$$\\end{document}, there are factorising functions skj:Fn×Gr(kj,Fn)→R≥0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s_{k_j} : \\mathbb {F}^n\ imes {{\\,\\mathrm{{Gr}}\\,}}(k_j, \\mathbb {F}^n)\\rightarrow \\mathbb {R}_{\\ge 0}$$\\end{document} such that V1∧⋯∧VdSpd≤∏j=1dskjp,Vj,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\left( V_1 \\wedge \\cdots \\wedge V_d\\right) S\\left( p\\right) ^d \\le \\prod _{j=1}^d s_{k_j}\\left( p, V_j\\right) , \\end{aligned}$$\\end{document}for every p∈Fn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p\\in \\mathbb {F}^n$$\\end{document} and every tuple of planes Vj∈Gr(kj,Fn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_j\\in {{\\,\\mathrm{{Gr}}\\,}}(k_j, \\mathbb {F}^n)$$\\end{document}, and ∑p∈πjs(p,e(πj))=CSd,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\sum _{p\\in \\pi _j} s(p, e(\\pi _j)) =C \\left| \\left| S\\right| \\right| _d, \\end{aligned}$$\\end{document}for every kj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_j$$\\end{document}-plane πj⊂Fn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi _j\\subset \\mathbb {F}^n$$\\end{document}, where e(πj)∈Gr(kj,Fn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e(\\pi _j)\\in {{\\,\\mathrm{{Gr}}\\,}}(k_j,\\mathbb {F}^n)$$\\end{document}, is the translate of πj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi _j$$\\end{document} that contains the origin and ∧\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\wedge $$\\end{document} denotes the discrete wedge product.

A Suboptimal Economic Model Predictive Control Algorithm for Large and Infrequent Disturbances

We present a suboptimal economic model predictive control (MPC) algorithm that combines the strengths of two common suboptimal MPC approaches, one based on a warm start and one based on an optimality gap. This algorithm is specifically designed to address a class of large and infrequent disturbances that are relevant when considering discrete actuators and production scheduling in control problems. We establish that this algorithm provides the same nominal performance guarantee as optimal economic MPC and is inherently robust, in an economic context, to large and infrequent disturbances. This inherent robustness guarantee is not attained by either individual algorithm. We conclude with a small production scheduling example to demonstrate the benefits of the proposed algorithm for a practical application.