A note on optimization in deteriorating systems using scheduling problems with the aging effect and resource allocation models

AbstractThis paper concerns scheduling problems with the aging effect and additional resource allocation. A measurable result of the aging phenomenon is that the time required to perform a job increases whereas the additional resource allocation allows one to decrease it. As an example of a deteriorating system that can be described and optimized by the application of the models and algorithms considered, we choose the pickling process, where cleaning of metal items decreases the efficiency of the pickling (cleaning) bath (i.e., one containing an active substance), whereas heating it up can improve the efficiency. In particular, we focus on the optimization problems for such systems and model them as single-machine scheduling problems with job processing times dependent on the fatigue of a machine and on the allocation of additional resources. The objectives considered are the minimization of time criteria (the maximum completion time and the maximum lateness) under a given resource consumption as well as the minimization of the resource consumption under given time criteria. The computational complexity of the problems is determined and solution properties are proved. On the basis of these, we construct optimal polynomial time algorithms for some cases of the problems considered

Optimal Composition Ordering Problems for Piecewise Linear Functions

In this paper, we introduce maximum composition ordering problems. The input is $n$ real functions $f_1,\dots,f_n:\mathbb{R}\to\mathbb{R}$ and a constant $c\in\mathbb{R}$. We consider two settings: total and partial compositions. The maximum total composition ordering problem is to compute a permutation $\sigma:[n]\to[n]$ which maximizes $f_{\sigma(n)}\circ f_{\sigma(n-1)}\circ\dots\circ f_{\sigma(1)}(c)$, where $[n]=\{1,\dots,n\}$. The maximum partial composition ordering problem is to compute a permutation $\sigma:[n]\to[n]$ and a nonnegative integer $k~(0\le k\le n)$ which maximize $f_{\sigma(k)}\circ f_{\sigma(k-1)}\circ\dots\circ f_{\sigma(1)}(c)$. We propose $O(n\log n)$ time algorithms for the maximum total and partial composition ordering problems for monotone linear functions $f_i$, which generalize linear deterioration and shortening models for the time-dependent scheduling problem. We also show that the maximum partial composition ordering problem can be solved in polynomial time if $f_i$ is of form $\max\{a_ix+b_i,c_i\}$ for some constants $a_i\,(\ge 0)$, $b_i$ and $c_i$. We finally prove that there exists no constant-factor approximation algorithm for the problems, even if $f_i$'s are monotone, piecewise linear functions with at most two pieces, unless P=NP.Comment: 19 pages, 4 figure

A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts. --project scheduling,modeling,resource constraints,temporal constraints,networks

Use Of Genetic Algorithms in Supply Chain Management. Literature Review and Current Trends

For the past few decades SCM has been one of the main objectives in research and practice. Since that time researchers have developed a lot of methods and procedures which optimized this process. To create an efficient supply chain network the resources and factories must be tightly integrated. The most supply chain network designs have multiple layers, members, periods, products, and comparative resources constraints exist between different layers. Supply chain networks design is related to the problems which are very popular in literature. The subject of this paper is to present the variants, configurations and parameters of genetic algorithm (GA) for solving supply chain network design problems. We focus on references from 2000 to 2011. Furthermore, current trends are introduced and discussed

Scheduling Problems with Learning and Ageing Effects: A Survey

In recent years, many papers concerning scheduling problems with simultaneous learning and ageing effects were published. In this paper, the state of the art of research concerning these problems is presented. In order to facilitate understanding this subject, the scheduling problems where these effects occur separately, are firstly explained. Then, the papers devoted to scheduling problems combining the effects of learning and ageing are discussed. Particular attention was paid on practical applications of the considered scheduling problems. After thorough analysis it turned out that both scheduling problems with learning effect, and with ageing effect, as well as, in particular, the problems with models merging learning and ageing effects do not have any reasonable real-life applications. This is because the learning and ageing effects are in general long time horizon phenomena observed in repetitive systems and scheduling theory concerns either with repetitive short-horizon planning problems or single long-horizon projects. Therefore, there is no sense to continue research considering these scheduling problems from practical (computer engineering, automatic control, technical and economical) point of view, unless such reasonable real-life example appears

Solving Resource Constrained Project Scheduling Problems (RCPSP) with Remanufacturing

Scheduling is one of the crucial issues in the project planning phase. Completing the project in the desired duration with the available resources with minimum cost is a big challenge for project managers. In the recent decades, several approaches have been proposed to deal with the resource constraints in scheduling. It can create a serious bottleneck and drastically change the flow of the activities. Moreover, resource constrains can change the project duration in crashing the project even if the activity (which creates the bottleneck) is not on the critical path. To address this issue, a new approach for Resource Constrained Project Scheduling (RCPS) is proposed when the remanufacturing option for some activities is available in order to crash the project. In this research, first a mathematical model for RCPS is presented. Then, a new algorithm is proposed to shorten the project duration by activating remanufacturing line (if possible) or paying the crash cost. The proposed algorithm is implemented in MATLAB and some computational experiments have been done to demonstrate the effectiveness and sensitivity of the proposed procedures. The algorithm is also validated on a practical case study which is a manufacturing industry in the northern Ontario

Planning and Scheduling Optimization

Although planning and scheduling optimization have been explored in the literature for many years now, it still remains a hot topic in the current scientific research. The changing market trends, globalization, technical and technological progress, and sustainability considerations make it necessary to deal with new optimization challenges in modern manufacturing, engineering, and healthcare systems. This book provides an overview of the recent advances in different areas connected with operations research models and other applications of intelligent computing techniques used for planning and scheduling optimization. The wide range of theoretical and practical research findings reported in this book confirms that the planning and scheduling problem is a complex issue that is present in different industrial sectors and organizations and opens promising and dynamic perspectives of research and development

Parallel optimization algorithms for high performance computing : application to thermal systems

The need of optimization is present in every field of engineering. Moreover, applications requiring a multidisciplinary approach in order to make a step forward are increasing. This leads to the need of solving complex optimization problems that exceed the capacity of human brain or intuition. A standard way of proceeding is to use evolutionary algorithms, among which genetic algorithms hold a prominent place. These are characterized by their robustness and versatility, as well as their high computational cost and low convergence speed. Many optimization packages are available under free software licenses and are representative of the current state of the art in optimization technology. However, the ability of optimization algorithms to adapt to massively parallel computers reaching satisfactory efficiency levels is still an open issue. Even packages suited for multilevel parallelism encounter difficulties when dealing with objective functions involving long and variable simulation times. This variability is common in Computational Fluid Dynamics and Heat Transfer (CFD & HT), nonlinear mechanics, etc. and is nowadays a dominant concern for large scale applications. Current research in improving the performance of evolutionary algorithms is mainly focused on developing new search algorithms. Nevertheless, there is a vast knowledge of sequential well-performing algorithmic suitable for being implemented in parallel computers. The gap to be covered is efficient parallelization. Moreover, advances in the research of both new search algorithms and efficient parallelization are additive, so that the enhancement of current state of the art optimization software can be accelerated if both fronts are tackled simultaneously. The motivation of this Doctoral Thesis is to make a step forward towards the successful integration of Optimization and High Performance Computing capabilities, which has the potential to boost technological development by providing better designs, shortening product development times and minimizing the required resources. After conducting a thorough state of the art study of the mathematical optimization techniques available to date, a generic mathematical optimization tool has been developed putting a special focus on the application of the library to the field of Computational Fluid Dynamics and Heat Transfer (CFD & HT). Then the main shortcomings of the standard parallelization strategies available for genetic algorithms and similar population-based optimization methods have been analyzed. Computational load imbalance has been identified to be the key point causing the degradation of the optimization algorithm¿s scalability (i.e. parallel efficiency) in case the average makespan of the batch of individuals is greater than the average time required by the optimizer for performing inter-processor communications. It occurs because processors are often unable to finish the evaluation of their queue of individuals simultaneously and need to be synchronized before the next batch of individuals is created. Consequently, the computational load imbalance is translated into idle time in some processors. Several load balancing algorithms have been proposed and exhaustively tested, being extendable to any other population-based optimization method that needs to synchronize all processors after the evaluation of each batch of individuals. Finally, a real-world engineering application that consists on optimizing the refrigeration system of a power electronic device has been presented as an illustrative example in which the use of the proposed load balancing algorithms is able to reduce the simulation time required by the optimization tool.El aumento de las aplicaciones que requieren de una aproximación multidisciplinar para poder avanzar se constata en todos los campos de la ingeniería, lo cual conlleva la necesidad de resolver problemas de optimización complejos que exceden la capacidad del cerebro humano o de la intuición. En estos casos es habitual el uso de algoritmos evolutivos, principalmente de los algoritmos genéticos, caracterizados por su robustez y versatilidad, así como por su gran coste computacional y baja velocidad de convergencia. La multitud de paquetes de optimización disponibles con licencias de software libre representan el estado del arte actual en tecnología de optimización. Sin embargo, la capacidad de adaptación de los algoritmos de optimización a ordenadores masivamente paralelos alcanzando niveles de eficiencia satisfactorios es todavía una tarea pendiente. Incluso los paquetes adaptados al paralelismo multinivel tienen dificultades para gestionar funciones objetivo que requieren de tiempos de simulación largos y variables. Esta variabilidad es común en la Dinámica de Fluidos Computacional y la Transferencia de Calor (CFD & HT), mecánica no lineal, etc. y es una de las principales preocupaciones en aplicaciones a gran escala a día de hoy. La investigación actual que tiene por objetivo la mejora del rendimiento de los algoritmos evolutivos está enfocada principalmente al desarrollo de nuevos algoritmos de búsqueda. Sin embargo, ya se conoce una gran variedad de algoritmos secuenciales apropiados para su implementación en ordenadores paralelos. La tarea pendiente es conseguir una paralelización eficiente. Además, los avances en la investigación de nuevos algoritmos de búsqueda y la paralelización son aditivos, por lo que el proceso de mejora del software de optimización actual se verá incrementada si se atacan ambos frentes simultáneamente. La motivación de esta Tesis Doctoral es avanzar hacia una integración completa de las capacidades de Optimización y Computación de Alto Rendimiento para así impulsar el desarrollo tecnológico proporcionando mejores diseños, acortando los tiempos de desarrollo del producto y minimizando los recursos necesarios. Tras un exhaustivo estudio del estado del arte de las técnicas de optimización matemática disponibles a día de hoy, se ha diseñado una librería de optimización orientada al campo de la Dinámica de Fluidos Computacional y la Transferencia de Calor (CFD & HT). A continuación se han analizado las principales limitaciones de las estrategias de paralelización disponibles para algoritmos genéticos y otros métodos de optimización basados en poblaciones. En el caso en que el tiempo de evaluación medio de la tanda de individuos sea mayor que el tiempo medio que necesita el optimizador para llevar a cabo comunicaciones entre procesadores, se ha detectado que la causa principal de la degradación de la escalabilidad o eficiencia paralela del algoritmo de optimización es el desequilibrio de la carga computacional. El motivo es que a menudo los procesadores no terminan de evaluar su cola de individuos simultáneamente y deben sincronizarse antes de que se cree la siguiente tanda de individuos. Por consiguiente, el desequilibrio de la carga computacional se convierte en tiempo de inactividad en algunos procesadores. Se han propuesto y testado exhaustivamente varios algoritmos de equilibrado de carga aplicables a cualquier método de optimización basado en una población que necesite sincronizar los procesadores tras cada tanda de evaluaciones. Finalmente, se ha presentado como ejemplo ilustrativo un caso real de ingeniería que consiste en optimizar el sistema de refrigeración de un dispositivo de electrónica de potencia. En él queda demostrado que el uso de los algoritmos de equilibrado de carga computacional propuestos es capaz de reducir el tiempo de simulación que necesita la herramienta de optimización

Cell Production System Design: A Literature Review

Purpose In a cell production system, a number of machines that differ in function are housed in the same cell. The task of these cells is to complete operations on similar parts that are in the same group. Determining the family of machine parts and cells is one of the major design problems of production cells. Cell production system design methods include clustering, graph theory, artificial intelligence, meta-heuristic, simulation, mathematical programming. This article discusses the operation of methods and research in the field of cell production system design. Methodology: To examine these methods, from 187 articles published in this field by authoritative scientific sources, based on the year of publication and the number of restrictions considered and close to reality, which are searched using the keywords of these restrictions and among them articles Various aspects of production and design problems, such as considering machine costs and cell size and process routing, have been selected simultaneously. Findings: Finally, the distribution diagram of the use of these methods and the limitations considered by their researchers, shows the use and efficiency of each of these methods. By examining them, more efficient and efficient design fields of this type of production system can be identified. Originality/Value: In this article, the literature on cell production system from 1972 to 2021 has been reviewed