A new mathematical model for single machine batch scheduling problem for minimizing maximum lateness with deteriorating jobs

This paper presents a mathematical model for the problem of minimizing the maximum lateness on a single machine when the deteriorated jobs are delivered to each customer in various size batches. In reality, this issue may happen within a supply chain in which delivering goods to customers entails cost. Under such situation, keeping completed jobs to deliver in batches may result in reducing delivery costs. In literature review of batch scheduling, minimizing the maximum lateness is known as NP-Hard problem; therefore the present issue aiming at minimizing the costs of delivering, in addition to the aforementioned objective function, remains an NP-Hard problem. In order to solve the proposed model, a Simulation annealing meta-heuristic is used, where the parameters are calibrated by Taguchi approach and the results are compared to the global optimal values generated by Lingo 10 software. Furthermore, in order to check the efficiency of proposed method to solve larger scales of problem, a lower bound is generated. The results are also analyzed based on the effective factors of the problem. Computational study validates the efficiency and the accuracy of the presented model

Serial-batch scheduling – the special case of laser-cutting machines

The dissertation deals with a problem in the field of short-term production planning, namely the scheduling of laser-cutting machines. The object of decision is the grouping of production orders (batching) and the sequencing of these order groups on one or more machines (scheduling). This problem is also known in the literature as "batch scheduling problem" and belongs to the class of combinatorial optimization problems due to the interdependencies between the batching and the scheduling decisions. The concepts and methods used are mainly from production planning, operations research and machine learning

On-line scheduling with delivery time on a single batch machine

AbstractWe consider a single batch machine on-line scheduling problem with jobs arriving over time. A batch processing machine can handle up to B jobs simultaneously as a batch, and the processing time for a batch is equal to the longest processing time among the jobs in it. Each job becomes available at its arrival time, which is not known in advance, and its characteristics, such as processing time and delivery time, become known at its arrival. Once the processing of a job is completed we deliver it to the destination. The objective is to minimize the time by which all jobs have been delivered. In this paper, we deal with two variants: the unbound model where B is sufficiently large and the bounded model where B is finite. We provide on-line algorithms with competitive ratio 2 for the unbounded model and with competitive ratio 3 for the bounded model. For when each job has the same processing time, we provide on-line algorithms with competitive ratios (5+1)/2, and these results are the best possible

Mathematical Models for a Batch Scheduling Problem to Minimize Earliness and Tardiness

Purpose: Today’s manufacturing facilities are challenged by highly customized products and just in time manufacturing and delivery of these products. In this study, a batch scheduling problem has been addressed to enable on-time completion of customer orders in a lean manufacturing environment. The problem is optimizing the partitioning of product components into batches and scheduling of the resulting batches where each customer order is received as a set of products made of various components. Design/methodology/approach: Three different mathematical models for minimization of total earliness and tardiness of customer orders are developed to provide on-time completion of customer orders and also, to avoid excess final product inventory. The first model is a non-linear integer programming model whereas the second is a linearized version of the first. Finally, to solve larger sized instances of the problem, an alternative linear integer model is presented. Findings: Computational study using a suit set of test instances showed that the alternative linear integer model is able to solve all test instances in varying sizes within quite shorter computer times compared to the other two models. It has also been showed that the alternative model is able to solve moderate sized real-world problems. Originality/value: The problem under study differentiates from existing batch scheduling problems in the literature owing to the inclusion of new circumstances that are present in real-world applications. Those are: customer orders consisting of multi-products made of multi-parts, processing of all parts of the same product from different orders in the same batch, and delivering the orders only when all related products are completed. This research also contributes to the literature of batch scheduling problem by presenting new optimization models.Peer Reviewe

PiCo: A Domain-Specific Language for Data Analytics Pipelines

In the world of Big Data analytics, there is a series of tools aiming at simplifying programming applications to be executed on clusters. Although each tool claims to provide better programming, data and execution models—for which only informal (and often confusing) semantics is generally provided—all share a common under- lying model, namely, the Dataflow model. Using this model as a starting point, it is possible to categorize and analyze almost all aspects about Big Data analytics tools from a high level perspective. This analysis can be considered as a first step toward a formal model to be exploited in the design of a (new) framework for Big Data analytics. By putting clear separations between all levels of abstraction (i.e., from the runtime to the user API), it is easier for a programmer or software designer to avoid mixing low level with high level aspects, as we are often used to see in state-of-the-art Big Data analytics frameworks. From the user-level perspective, we think that a clearer and simple semantics is preferable, together with a strong separation of concerns. For this reason, we use the Dataflow model as a starting point to build a programming environment with a simplified programming model implemented as a Domain-Specific Language, that is on top of a stack of layers that build a prototypical framework for Big Data analytics. The contribution of this thesis is twofold: first, we show that the proposed model is (at least) as general as existing batch and streaming frameworks (e.g., Spark, Flink, Storm, Google Dataflow), thus making it easier to understand high-level data-processing applications written in such frameworks. As result of this analysis, we provide a layered model that can represent tools and applications following the Dataflow paradigm and we show how the analyzed tools fit in each level. Second, we propose a programming environment based on such layered model in the form of a Domain-Specific Language (DSL) for processing data collections, called PiCo (Pipeline Composition). The main entity of this programming model is the Pipeline, basically a DAG-composition of processing elements. This model is intended to give the user an unique interface for both stream and batch processing, hiding completely data management and focusing only on operations, which are represented by Pipeline stages. Our DSL will be built on top of the FastFlow library, exploiting both shared and distributed parallelism, and implemented in C++11/14 with the aim of porting C++ into the Big Data world

A common framework and taxonomy for multicriteria scheduling problems with Interfering and competing Jobs: Multi-agent scheduling problems

Most classical scheduling research assumes that the objectives sought are common to all jobs to be scheduled. However, many real-life applications can be modeled by considering different sets of jobs, each one with its own objective(s), and an increasing number of papers addressing these problems has appeared over the last few years. Since so far the area lacks a uni ed view, the studied problems have received different names (such as interfering jobs, multi-agent scheduling, mixed-criteria, etc), some authors do not seem to be aware of important contributions in related problems, and solution procedures are often developed without taking into account existing ones. Therefore, the topic is in need of a common framework that allows for a systematic recollection of existing contributions, as well as a clear de nition of the main research avenues. In this paper we review multicriteria scheduling problems involving two or more sets of jobs and propose an uni ed framework providing a common de nition, name and notation for these problems. Moreover, we systematically review and classify the existing contributions in terms of the complexity of the problems and the proposed solution procedures, discuss the main advances, and point out future research lines in the topic

Performance Optimizations and Operator Semantics for Streaming Data Flow Programs

Unternehmen sammeln mehr Daten als je zuvor und müssen auf diese Informationen zeitnah reagieren. Relationale Datenbanken eignen sich nicht für die latenzfreie Verarbeitung dieser oft unstrukturierten Daten. Um diesen Anforderungen zu begegnen, haben sich in der Datenbankforschung seit dem Anfang der 2000er Jahre zwei neue Forschungsrichtungen etabliert: skalierbare Verarbeitung unstrukturierter Daten und latenzfreie Datenstromverarbeitung. Skalierbare Verarbeitung unstrukturierter Daten, auch bekannt unter dem Begriff "Big Data"-Verarbeitung, hat in der Industrie schnell Einzug erhalten. Gleichzeitig wurden in der Forschung Systeme zur latenzfreien Datenstromverarbeitung entwickelt, die auf eine verteilte Architektur, Skalierbarkeit und datenparallele Verarbeitung setzen. Obwohl diese Systeme in der Industrie vermehrt zum Einsatz kommen, gibt es immer noch große Herausforderungen im praktischen Einsatz. Diese Dissertation verfolgt zwei Hauptziele: Zuerst wird das Laufzeitverhalten von hochskalierbaren datenparallelen Datenstromverarbeitungssystemen untersucht. Im zweiten Hauptteil wird das "Dual Streaming Model" eingeführt, das eine Semantik zur gleichzeitigen Verarbeitung von Datenströmen und Tabellen beschreibt. Das Ziel unserer Untersuchung ist ein besseres Verständnis über das Laufzeitverhalten dieser Systeme zu erhalten und dieses Wissen zu nutzen um Anfragen automatisch ausreichende Rechenkapazität zuzuweisen. Dazu werden ein Kostenmodell und darauf aufbauende Optimierungsalgorithmen für Datenstromanfragen eingeführt, die Datengruppierung und Datenparallelität einbeziehen. Das vorgestellte Datenstromverarbeitungsmodell beschreibt das Ergebnis eines Operators als kontinuierlichen Strom von Veränderugen auf einer Ergebnistabelle. Dabei behandelt unser Modell die Diskrepanz der physikalischen und logischen Ordnung von Datenelementen inhärent und erreicht damit eine deterministische Semantik und eine minimale Verarbeitungslatenz.Modern companies are able to collect more data and require insights from it faster than ever before. Relational databases do not meet the requirements for processing the often unstructured data sets with reasonable performance. The database research community started to address these trends in the early 2000s. Two new research directions have attracted major interest since: large-scale non-relational data processing as well as low-latency data stream processing. Large-scale non-relational data processing, commonly known as "Big Data" processing, was quickly adopted in the industry. In parallel, low latency data stream processing was mainly driven by the research community developing new systems that embrace a distributed architecture, scalability, and exploits data parallelism. While these systems have gained more and more attention in the industry, there are still major challenges to operate them at large scale. The goal of this dissertation is two-fold: First, to investigate runtime characteristics of large scale data-parallel distributed streaming systems. And second, to propose the "Dual Streaming Model" to express semantics of continuous queries over data streams and tables. Our goal is to improve the understanding of system and query runtime behavior with the aim to provision queries automatically. We introduce a cost model for streaming data flow programs taking into account the two techniques of record batching and data parallelization. Additionally, we introduce optimization algorithms that leverage our model for cost-based query provisioning. The proposed Dual Streaming Model expresses the result of a streaming operator as a stream of successive updates to a result table, inducing a duality between streams and tables. Our model handles the inconsistency of the logical and the physical order of records within a data stream natively, which allows for deterministic semantics as well as low latency query execution

Advances and Novel Approaches in Discrete Optimization

Discrete optimization is an important area of Applied Mathematics with a broad spectrum of applications in many fields. This book results from a Special Issue in the journal Mathematics entitled ‘Advances and Novel Approaches in Discrete Optimization’. It contains 17 articles covering a broad spectrum of subjects which have been selected from 43 submitted papers after a thorough refereeing process. Among other topics, it includes seven articles dealing with scheduling problems, e.g., online scheduling, batching, dual and inverse scheduling problems, or uncertain scheduling problems. Other subjects are graphs and applications, evacuation planning, the max-cut problem, capacitated lot-sizing, and packing algorithms