An Improved Robust Optimization Approach for Scheduling Under Uncertainty

In practice, the uncertainty in processing time data frequently affects the feasibility of optimal solution of the nominal production scheduling problem. Using the unit-specific event-based continuous time model for scheduling, we develop a novel multi-stage robust approach with corrective action to ensure robust feasibility of the worst case solution while reducing the conservatism arising from traditional robust optimization approaches. We quantify the probability of constraint satisfaction by using a priori and a posteriori probabilistic bounds for known and unknown uncertainty distributions, consequently, improving the objective value for a given risk scenario. Computational experiments on several examples were carried out to measure the effectiveness of the proposed method. For a given constraint satisfaction probability, the proposed method improves the objective value compared to the traditional robust optimization approaches

Solution Strategies in Short-term Scheduling for Multitasking Multipurpose Plants

This thesis addresses challenges in short-term scheduling of multipurpose facilities using mathematical optimization. Such approach involves the formulation of a predictive model and an objective function, and the development of a solution strategy around such scheduling model formulation in order to obtain an operating schedule that achieves certain objectives, such as maximization of throughput or minimization of makespan. There are many choices that must be made in these aspects of short-term scheduling, and these choices often lead to a trade-off between the solution quality and computational time. This thesis presents two studies analyzing the quality-CPU time trade-off in two major aspects: time representations in model formulation, and the strategy for handling multiple conflicting objectives. The ultimate goal is to develop bi-objective short-term scheduling approaches to tackle industrial-sized problems for multitasking multipurpose plants that are computationally inexpensive, but provide practical schedules with a good balance between throughput and makespan. The first study addresses the first aspect of interest and compares two different time representation approaches: discrete-time and continuous-time approaches. This comparison is made considering maximization of throughput as the sole objective. We show that, for the modeling framework implemented in this work, the selected discrete-time formulation typically obtained higher quality solutions, and required less time to solve compared to the selected continuous-time formulation, as the continuous-time formulation exhibited detrimental trade-off between computational time and solution quality. We also show that within the scope of this study, non-uniform discretization schemes typically yielded solutions of similar quality compared to a fine uniform discretization scheme, but required only a fraction of the computational time. The second study builds on the first study and develops a strategy around an efficient non-uniform discretization approach to handle the conflicting objectives of throughput maximization and makespan minimization, focusing on a priori multi-objective methods. Two main contributions are presented in this regard. The first contribution is to propose a priori bi-objective methods based on the hybridization of compromise programming and the U+03B5-constraint method. The second is to present short-term operational objective functions, that can be used within short-term scheduling to optimize desired long term objectives of maximizing throughput and minimizing makespan. Two numerical case studies, one in a semiconductor processing plant and an analytical services facility, are presented using a rolling horizon framework, which demonstrate the potential for the proposed methods to improve solution quality over a traditional a priori approac

An Improved Robust Optimization Approach for Scheduling Under Uncertainty

In practice, the uncertainty in processing time data frequently affects the feasibility of optimal solution of the nominal production scheduling problem. Using the unit-specific event-based continuous time model for scheduling, we develop a novel multi-stage robust approach with corrective action to ensure robust feasibility of the worst case solution while reducing the conservatism arising from traditional robust optimization approaches. We quantify the probability of constraint satisfaction by using a priori and a posteriori probabilistic bounds for known and unknown uncertainty distributions, consequently, improving the objective value for a given risk scenario. Computational experiments on several examples were carried out to measure the effectiveness of the proposed method. For a given constraint satisfaction probability, the proposed method improves the objective value compared to the traditional robust optimization approaches

Global optimization with piecewise linear approximation

textGlobal optimization deals with the development of solution methodologies for nonlinear nonconvex optimization problems. These problems, which could arise in diverse situations ranging from optimizing hydro-power generation schedules to estimating coefficients of non-linear regression models, are difficult for traditional nonlinear solvers that iteratively search the neighborhood around a starting point. The Piecewise Linear Approximation (PLA) method that we study in this dissertation seeks to generate ‘good’ starting points, hopefully ones that lie in the basin of attraction of the globally optimal solution. In this approach, we approximate the non-linear functions in the optimization problem by piecewise linear functions defined over the vertices of a grid that partitions the domain of each nonlinear function into cells. Based on this approximation, we convert the original nonlinear program into a mixed integer program (MIP) and use the solution to this MIP as a starting point for a local nonlinear solver. In this dissertation, we validate the effectiveness of the PLA approach as a global optimization approach by applying it to a diverse set of continuous and discrete nonlinear optimization problems. Further, we develop various modeling and algorithmic strategies for enhancing the basic approach. Our computational results demonstrate that the PLA approach works well on non-convex problems and can, in some cases, provide better solutions than those provided by existing nonlinear solvers.Information, Risk, and Operations Management (IROM

A computational study of practical issues arising in short-term scheduling of a multipurpose facility

This thesis focuses on two important considerations when solving short term scheduling problems for multipurpose facilities: deciding when rescheduling should be performed and choosing efficient time representations for the scheduling problems. This class of scheduling problems is of practical importance as it may be used for scheduling chemical production facilities, flexible manufacturing systems, and analytical services facilities, among others. In these cases, improving the efficiency of scheduling operations may lead to increased yield, or reduced makespan, resulting in greater profits or customer satisfaction. Therefore, efficiently solving these problems is of great practical interest. One aspect of real world implementations of these problems is the presence of uncertainty, such as in the form of new jobs arriving, or a machine breaking down. In these cases, one may want or need to reschedule operations subject to the new disturbance. An investigation into how often to perform these reschedulings is addressed in the first part of the thesis. When formulating these problems, one must also choose a time representation for executing scheduling operations over. A dynamic approach is proposed in the second part of the thesis which we show can potentially yield substantial computational savings when scheduling over large instances. The first part of this thesis addresses the question of when to reschedule operations for a facility that receives new jobs on a daily basis. Through computational experiments that vary plant parameters, such as the load and the capacity of a facility, we investigate the effects these parameters have on plant performance under periodic rescheduling. These experiments are carried out using real data from an industrial-scale facility. The results show that choosing a suitable rescheduling policy depends on some key plant parameters. In particular, by modifying various parameters of the facility, the performance ranking of the various rescheduling policies may be reversed compared to the results obtained with nominal parameter values. This highlights the need to consider both facility characteristics and what the crucial objective of the facility is when selecting a rescheduling policy. The second part of this thesis deals with the issue of deciding which timepoints to include in our model formulations. In general, adding more timepoints to the model will offer more flexibility to the solver and hence result in more accurate schedules. However, these extra timepoints will also increase the size of the model and accordingly the computational cost of solving the model. We propose an iterative framework to refine an initial coarse uniform discretization, by adding key timepoints that may be most beneficial, and removing timepoints which are unnecessary from the model. This framework is compared against existing static discretizations using computational experiments on an analytical services facility. The results of these experiments demonstrate that when problems are sufficiently large, our proposed dynamic method is able to achieve a better tradeoff between objective value and CPU time than the currently used discretizations in the literature

Otimização do scheduling de nafta petroquímica utilizando algoritmos genéticos

Atualmente, as indústrias petroquímicas enfrentam um aumento nos preços da nafta, matéria-prima para a primeira geração, o que torna necessária a busca por novos fornecedores e, muitas vezes, a compra de lotes que apresentam preços mais baixos em função da presença de contaminantes. O gerenciamento otimizado dos lotes recebidos através de operações de blending viabiliza o recebimento dos lotes que apresentam contaminantes e o enquadramento destes nos limites de processamento das unidades. Desta forma, técnicas de otimização aplicadas ao blending e ao scheduling dos recebimentos podem fornecer ferramentas que ajudem a flexibilizar a compra de matérias-primas, diminuindo os gastos com este insumo e aumentando o lucro da empresa. O objetivo principal deste estudo é a solução do problema de recebimento de matéria-prima de uma indústria petroquímica de primeira geração via otimização matemática, visando auxiliar no processo de tomada de decisões. Como resultado, tem-se a definição das quantidades das matérias-primas disponíveis que irão compor a mistura final que será entregue para processamento nas unidades. O modelo leva em consideração os estoques de nafta disponíveis e a suas respectivas composições no instante inicial da otimização, a disponibilidade de navios para descarregamento, as demandas de consumo das unidades, as restrições operacionais de bombeamento e armazenagem e as restrições de qualidade. Estas últimas englobam os limites de processamento de contaminantes e o percentual mínimo de parafinicidade, principal parâmetro de rendimento da nafta, que serve como parâmetro para definir a mistura ideal dos componentes de modo a maximizar o seu rendimento em produtos finais desejados para cada cenário de produção. O modelo de otimização foi desenvolvido baseado em programação mista inteira não-linear (MINLP), com representação discreta do tempo. As variáveis de decisão envolvem a alocação de descarga de navios em tanques de armazenagem, bem como operações de transferência entre tanques de diferentes parques de tancagem através de oleodutos. Sendo assim, para fins de modelagem, as variáveis de decisão do problema foram descritas como o status de abertura e fechamento das válvulas de entrada e saída de cada tanque do sistema, as quais totalizam 34 válvulas, para cada um dos instantes da simulação, os quais totalizam 56, obtendo-se assim um total de 1.904 variáveis de decisão. Foram consideradas restrições operacionais relacionadas a volumes de produto nos tanques, status de abertura e fechamento das válvulas dos tanques e trocas excessivas de tanques de recebimento/expedição, assim como restrições de qualidade relacionadas aos limites de processamento de contaminantes das unidades. Para a resolução do problema de otimização, foi empregado um algoritmo genético e adotado um horizonte de predição de tamanho igual a 56. O modelo proposto foi aplicado ao sistema de recebimento de matéria-prima de uma indústria petroquímica real e os resultados mostram o desempenho do modelo quando aplicado a cenários distintos, envolvendo diferentes graus de dificuldade. A partir dos resultados obtidos e do seu comparativo com uma programação realizada por um especialista ad hoc através da Tabela 2, evidenciou-se que o algoritmo foi capaz de resolver cada um dos cenários avaliados, sempre mostrando aderência à estratégia de blending adotada pela indústria

A Study of Time Representation in a Class of Short Term Scheduling Problems

The problem of scheduling operations has received significant attention from academia and industrial practitioners in the past few decades. A key decision in various scheduling operations problems is when to perform an operation and thus the quality of the final schedule can be seriously affected by the choice of how to model the times at which such a decision may take place. The two most commonly used approaches for modeling these times are: Discrete time approaches, which pre-specify a finite set of time points when any decision may be taken, and continuous time approaches, in which the optimization model determines, through the use of continuous decision variables, at which point in time the operation will be performed. The focus of this thesis will be to study the benefits and limitations of each of these approaches within the context of an analytical services facility. Such a facility receives a large number of samples that need to be analyzed/processed through a specific sequence of limited resources/machines before its analysis is completed. The results of these analyses form a basis for many of the decisions made in their client industries (e.g. oil and mining), which in turn indicates the economic importance of the analytical services sector. The operations of such facilities have several particular conditions that need to be modeled and a particularly important one is called multitasking. If analyzing each type of samples is regarded as a task, then the machines in such facilities have the ability to perform multiple tasks at the same time as they are able to analyze different types of samples together at the same (as long as their capacity is not overloaded). The above mentioned study will be performed through an empirical comparison of the discrete and continuous approaches that take into account all the conditions in such facilities, including multitasking. While discrete and continuous approaches have often been independently employed, few studies have considered a comparison between them [37, 28, 39]. In addition, none of these studies consider the operational conditions that are present in short-term scheduling of operations in an analytical services facility. Since the continuous time formulations in the literature are not capable of accounting for multitasking, this thesis presents a novel continuous time mixed-integer linear programming (MILP) formulation that is capable of accommodating such feature and several other operational constraints present at analytical services facilities. The performance of the presented formulation is studied in comparison with a singletasking formulation. The results show that, while the multitasking formulation is not more costly in terms of solution time, it is capable of producing significantly better solutions. Furthermore, this thesis extends the idea of flexible time discretization for discrete time formulations, previously proposed by Velez and Maravelias [40], to be able to account for the operational constraints of an analytical services facility