Model approximation for batch flow shop scheduling with fixed batch sizes

Batch flow shops model systems that process a variety of job types using a fixed infrastructure. This model has applications in several areas including chemical manufacturing, building construction, and assembly lines. Since the throughput of such systems depends, often strongly, on the sequence in which they produce various products, scheduling these systems becomes a problem with very practical consequences. Nevertheless, optimally scheduling these systems is NP-complete. This paper demonstrates that batch flow shops can be represented as a particular kind of heap model in the max-plus algebra. These models are shown to belong to a special class of linear systems that are globally stable over finite input sequences, indicating that information about past states is forgotten in finite time. This fact motivates a new solution method to the scheduling problem by optimally solving scheduling problems on finite-memory approximations of the original system. Error in solutions for these “t-step” approximations is bounded and monotonically improving with increasing model complexity, eventually becoming zero when the complexity of the approximation reaches the complexity of the original system.United States. Department of Homeland Security. Science and Technology Directorate (Contract HSHQDC-13-C-B0052)United States. Air Force Research Laboratory (Contract FA8750-09-2-0219)ATK Thiokol Inc

电力系统能量与备用联合优化与精确调度

随着能源与环境危机日益严重,如何建立精确调度模型成为电力市场逐步完善过程中的一个迫切需要研究的课题.目前广泛采用的建模方式是将时间离散化,建立离散时间调度模型,本文首先举例说明离散时间调度模型中所定义的备用容量上、下限存在不可达的情况,即离散时间调度模型中的备用容量上、下限约束条件不严格,从而造成实际调度时存在旋转备用容量无法满足实际需求的情况.通过对机组出力方式与爬坡率关系的详细分析,证明了任意调度时段内机组精确可达的备用容量上、下限与该时段首末时刻机组输出功率相关,并给出了精确可达备用上、下限的计算方法.基于上面的分析结果,建立了能量与备用联合优化与精确调度模型,该模型将能量与备用联合精确调度这样一个连续时间最优控制问题建模成一个非线性规划问题,从而极大地降低了问题的复杂性,避免连续时间最优控制问题所存在的求解困难.应用序列二次规划法对模型进行了数值求解,并对结果进行了讨论,进而验证了模型的有效性.国家自然科学基金(批准号:60921003;60736027;61174161;60974101);高等学校博士学科点专项科研基金(批准号:20090121110022);中央高校基本科研业务费专项资金(批准号:2011121047;201112G018;CXB2011035);福建省重点科技计划项目(批准号:2009H0044);厦门大学国家“211工程”三期项目(批准号:0630-E72000)资

불확실성하에서 항공기 도착 시퀀싱과 스케줄링을 위한 결정론적 및 확률론적 최적화

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 기계항공공학부, 2018. 2. 김유단.As the demand for air transportation increases, air traffic congestion is becoming a critical issue in the current air traffic control system. In particular, many researchers have recognized the need for decision support tools for human air traffic controllers in the terminal area, where incoming arrivals and outgoing departures are concentrated in a limited airspace surrounding airports. Although uncertainty comes from various sources in the terminal area, only a few existing works consider uncertainty with respect to the aircraft sequencing and scheduling problem. In this dissertation, two different robust optimization approaches for aircraft arrival sequencing and scheduling are presented that consider the uncertainty of fight time. First, robust optimization based on deterministic programming is proposed, which has a two-level hierarchical architecture. At the higher level, an extra buffer is introduced in the aircraft safe separation constraint by adopting the typical deterministic programming. The extra buffer size is analytically derived based on a deterministic robust counterpart problem. However, robust solutions obtained at the higher level can only be implemented in restricted situations where the magnitude of uncertainty is less than a predetermined constant value. Therefore, at the lower level, to compensate for the effects of unexpected situations under a dynamic environment, robust solutions obtained at the higher level are adjusted by using a heuristic adjustment with a sliding time window. Second, two-stage stochastic programming based on Particle Swarm Optimization (PSO) is proposed to determine less conservative robust solutions than the robust optimization based on deterministic programming. First and second stage decision problems are defined as aircraft sequencing and scheduling, respectively. PSO is utilized for a randomized search to make the first stage decision under incomplete information about uncertain parameters. A random key representation is adopted to apply PSO to a discrete aircraft sequencing problem because PSO has a continuous nature. Next, the second stage decision is made by solving a mixed integer linear programming problem after the realization of uncertain parameters. The performances of the two proposed robust optimization methodologies are verified through numerical simulations with historical flight data. Monte Carlo simulations are also performed for randomly generated air traffic situations.Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Literature Review 7 1.2.1 Aircraft Sequencing and Scheduling 7 1.2.2 Deterministic Programming under Uncertainty 10 1.2.3 Stochastic Programming under Uncertainty 12 1.3 Contributions 15 1.3.1 Systematic Problem Formulation 15 1.3.2 Robust Optimization: Deterministic Programming 16 1.3.3 Robust Optimization: Stochastic Programming 17 1.4 Dissertation Organization 18 Chapter 2 Mixed Integer Linear Programming for Aircraft Arrival Sequencing and Scheduling 19 2.1 Point Merge System (PMS) 20 2.1.1 Configuration of PMS 20 2.1.2 Arrival Procedure through PMS 20 2.1.3 Characteristic of PMS 21 2.2 Concept of Operation 22 2.3 Problem Formulation 24 2.3.1 Decision Variables 24 2.3.2 Objective Function 24 2.3.3 Constraints 25 2.3.4 Mathematical Formulation 27 Chapter 3 Deterministic Programming for Aircraft Arrival Sequencing and Scheduling under Uncertainty 28 3.1 Hierarchical Architecture 29 3.2 Deterministic Programming 30 3.2.1 Impact of Uncertainty 30 3.2.2 Determination of Extra Buffer Size [15] 30 3.2.3 Mathematical Formulation 33 3.3 Algorithm Enhancements for Dynamic Environments 35 3.3.1 Heuristic Adjustment 35 3.3.2 Sliding Time Window 39 3.4 Algorithm Summary 41 3.5 Historical Data Analysis 44 3.6 Toy Problem 50 3.7 Numerical Simulation 60 Chapter 4 Stochastic Programming for Aircraft Arrival Sequencing and Scheduling under Uncertainty 68 4.1 Two-Stage Stochastic Programming 69 4.1.1 Deterministic Equivalent Programming (DEP) 70 4.1.2 Two-Stage Stochastic Programming based on GA 71 4.2 Two-Stage Stochastic Programming based on PSO 72 4.2.1 Master and Sub-Problems 72 4.2.2 Random Key Representation 74 4.2.3 Algorithm Summary 76 4.3 Toy Problem 79 4.4 Numerical Simulation 83 4.4.1 Numerical Analysis on the Number of Scenarios 84 4.4.2 Comparison with Deterministic Programming 89 4.4.3 Comparison with Other Stochastic Programming 95 Chapter 5 Conclusions 100 5.1 Summary 100 5.2 Future Research Directions 104 5.2.1 Applications of Multi-Objective Optimization 104 5.2.2 Extensions of Airport Surface Traffic Optimization 105 5.2.3 Consideration of Various Uncertainties 105 Bibliography 107 Abstract (in Korean) 121Docto

Methods and algorithms for integrated multi-scale optimisation of production planning and scheduling

Imperial Users onl

Proactive management of uncertainty to improve scheduling robustness in proces industries

Dinamisme, capacitat de resposta i flexibilitat són característiques essencials en el desenvolupament de la societat actual. Les noves tendències de globalització i els avenços en tecnologies de la informació i comunicació fan que s'evolucioni en un entorn altament dinàmic i incert. La incertesa present en tot procés esdevé un factor crític a l'hora de prendre decisions, així com un repte altament reconegut en l'àrea d'Enginyeria de Sistemes de Procés (PSE). En el context de programació de les operacions, els models de suport a la decisió proposats fins ara, així com també software comercial de planificació i programació d'operacions avançada, es basen generalment en dades estimades, assumint implícitament que el programa d'operacions s'executarà sense desviacions. La reacció davant els efectes de la incertesa en temps d'execució és una pràctica habitual, però no sempre resulta efectiva o factible. L'alternativa és considerar la incertesa de forma proactiva, és a dir, en el moment de prendre decisions, explotant el coneixement disponible en el propi sistema de modelització.Davant aquesta situació es plantegen les següents preguntes: què s'entén per incertesa? Com es pot considerar la incertesa en el problema de programació d'operacions? Què s'entén per robustesa i flexibilitat d'un programa d'operacions? Com es pot millorar aquesta robustesa? Quins beneficis comporta? Aquesta tesi respon a aquestes preguntes en el marc d'anàlisis operacionals en l'àrea de PSE. La incertesa es considera no de la forma reactiva tradicional, sinó amb el desenvolupament de sistemes proactius de suport a la decisió amb l'objectiu d'identificar programes d'operació robustos que serveixin com a referència pel nivell inferior de control de planta, així com també per altres centres en un entorn de cadenes de subministrament. Aquest treball de recerca estableix les bases per formalitzar el concepte de robustesa d'un programa d'operacions de forma sistemàtica. Segons aquest formalisme, els temps d'operació i les ruptures d'equip són considerats inicialment com a principals fonts d'incertesa presents a nivell de programació de la producció. El problema es modelitza mitjançant programació estocàstica, desenvolupant-se finalment un entorn d'optimització basat en simulació que captura les múltiples fonts d'incertesa, així com també estratègies de programació d'operacions reactiva, de forma proactiva. La metodologia desenvolupada en el context de programació de la producció s'estén posteriorment per incloure les operacions de transport en sistemes de múltiples entitats i incertesa en els temps de distribució. Amb aquesta perspectiva més àmplia del nivell d'operació s'estudia la coordinació de les activitats de producció i transport, fins ara centrada en nivells estratègic o tàctic. L'estudi final considera l'efecte de la incertesa en la demanda en les decisions de programació de la producció a curt termini. El problema s'analitza des del punt de vista de gestió del risc, i s'avaluen diferents mesures per controlar l'eficiència del sistema en un entorn incert.En general, la tesi posa de manifest els avantatges en reconèixer i modelitzar la incertesa, amb la identificació de programes d'operació robustos capaços d'adaptar-se a un ampli rang de situacions possibles, enlloc de programes d'operació òptims per un escenari hipotètic. La metodologia proposada a nivell d'operació es pot considerar com un pas inicial per estendre's a nivells de decisió estratègics i tàctics. Alhora, la visió proactiva del problema permet reduir el buit existent entre la teoria i la pràctica industrial, i resulta en un major coneixement del procés, visibilitat per planificar activitats futures, així com també millora l'efectivitat de les tècniques reactives i de tot el sistema en general, característiques altament desitjables per mantenir-se actiu davant la globalitat, competitivitat i dinàmica que envolten un procés.Dynamism, responsiveness, and flexibility are essential features in the development of the current society. Globalization trends and fast advances in communication and information technologies make all evolve in a highly dynamic and uncertain environment. The uncertainty involved in a process system becomes a critical problem in decision making, as well as a recognized challenge in the area of Process Systems Engineering (PSE). In the context of scheduling, decision-support models developed up to this point, as well as commercial advanced planning and scheduling systems, rely generally on estimated input information, implicitly assuming that a schedule will be executed without deviations. The reaction to the effects of the uncertainty at execution time becomes a common practice, but it is not always effective or even possible. The alternative is to address the uncertainty proactively, i.e., at the time of reasoning, exploiting the available knowledge in the modeling procedure itself. In view of this situation, the following questions arise: what do we understand for uncertainty? How can uncertainty be considered within scheduling modeling systems? What is understood for schedule robustness and flexibility? How can schedule robustness be improved? What are the benefits? This thesis answers these questions in the context of operational analysis in PSE. Uncertainty is managed not from the traditional reactive viewpoint, but with the development of proactive decision-support systems aimed at identifying robust schedules that serve as a useful guidance for the lower control level, as well as for dependent entities in a supply chain environment. A basis to formalize the concept of schedule robustness is established. Based on this formalism, variable operation times and equipment breakdowns are first considered as the main uncertainties in short-term production scheduling. The problem is initially modeled using stochastic programming, and a simulation-based stochastic optimization framework is finally developed, which captures the multiple sources of uncertainty, as well as rescheduling strategies, proactively. The procedure-oriented system developed in the context of production scheduling is next extended to involve transport scheduling in multi-site systems with uncertain travel times. With this broader operational perspective, the coordination of production and transport activities, considered so far mainly in strategic and tactical analysis, is assessed. The final research point focuses on the effect of demands uncertainty in short-term scheduling decisions. The problem is analyzed from a risk management viewpoint, and alternative measures are assessed and compared to control the performance of the system in the uncertain environment.Overall, this research work reveals the advantages of recognizing and modeling uncertainty, with the identification of more robust schedules able to adapt to a wide range of possible situations, rather than optimal schedules for a hypothetical scenario. The management of uncertainty proposed from an operational perspective can be considered as a first step towards its extension to tactical and strategic levels of decision. The proactive perspective of the problem results in a more realistic view of the process system, and it is a promising way to reduce the gap between theory and industrial practices. Besides, it provides valuable insight on the process, visibility for future activities, as well as it improves the efficiency of reactive techniques and of the overall system, all highly desirable features to remain alive in the global, competitive, and dynamic process environment

Is operational research in UK universities fit-for-purpose for the growing field of analytics?

Over the last decade considerable interest has been generated into the use of analytical methods in organisations. Along with this, many have reported a significant gap between organisational demand for analytical-trained staff, and the number of potential recruits qualified for such roles. This interest is of high relevance to the operational research discipline, both in terms of raising the profile of the field, as well as in the teaching and training of graduates to fill these roles. However, what is less clear, is the extent to which operational research teaching in universities, or indeed teaching on the various courses labelled as analytics , are offering a curriculum that can prepare graduates for these roles. It is within this space that this research is positioned, specifically seeking to analyse the suitability of current provisions, limited to master s education in UK universities, and to make recommendations on how curricula may be developed. To do so, a mixed methods research design, in the pragmatic tradition, is presented. This includes a variety of research instruments. Firstly, a computational literature review is presented on analytics, assessing (amongst other things) the amount of research into analytics from a range of disciplines. Secondly, a historical analysis is performed of the literature regarding elements that can be seen as the pre-cursor of analytics, such as management information systems, decision support systems and business intelligence. Thirdly, an analysis of job adverts is included, utilising an online topic model and correlations analyses. Fourthly, online materials from UK universities concerning relevant degrees are analysed using a bagged support vector classifier and a bespoke module analysis algorithm. Finally, interviews with both potential employers of graduates, and also academics involved in analytics courses, are presented. The results of these separate analyses are synthesised and contrasted. The outcome of this is an assessment of the current state of the market, some reflections on the role operational research make have, and a framework for the development of analytics curricula. The principal contribution of this work is practical; providing tangible recommendations on curricula design and development, as well as to the operational research community in general in respect to how it may react to the growth of analytics. Additional contributions are made in respect to methodology, with a novel, mixed-method approach employed, and to theory, with insights as to the nature of how trends develop in both the jobs market and in academia. It is hoped that the insights here, may be of value to course designers seeking to react to similar trends in a wide range of disciplines and fields

Planning and scheduling in pharmaceutical supply chains

Ph.DDOCTOR OF PHILOSOPH