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

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

Production Scheduling

Generally speaking, scheduling is the procedure of mapping a set of tasks or jobs (studied objects) to a set of target resources efficiently. More specifically, as a part of a larger planning and scheduling process, production scheduling is essential for the proper functioning of a manufacturing enterprise. This book presents ten chapters divided into five sections. Section 1 discusses rescheduling strategies, policies, and methods for production scheduling. Section 2 presents two chapters about flow shop scheduling. Section 3 describes heuristic and metaheuristic methods for treating the scheduling problem in an efficient manner. In addition, two test cases are presented in Section 4. The first uses simulation, while the second shows a real implementation of a production scheduling system. Finally, Section 5 presents some modeling strategies for building production scheduling systems. This book will be of interest to those working in the decision-making branches of production, in various operational research areas, as well as computational methods design. People from a diverse background ranging from academia and research to those working in industry, can take advantage of this volume

A Platform for Scalable Low-Latency Analytics using MapReduce

Today, the ability to process big data has become crucial to the information needs of many enterprise businesses, scientific applications, and governments. Recently, there have been increasing needs of processing data that is not only big but also fast . Here fast data refers to high-speed real-time and near real-time data streams, such as Twitter feeds, search query streams, click streams, impressions, and system logs. To handle both historical data and real-time data, many companies have to maintain multiple systems. However, recent real-world case studies show that maintaining multiple systems cause not only code duplication, but also intensive manual work to partition the analytics workloads and determine which data is processed by which system. These issues point to the need for a general, unified data processing framework to support analytical queries with different latency requirements. This thesis takes a further step towards building a general, unified system for big and fast data analytics. In order to build such a system, I propose to build on existing solutions on data parallelism and extend them with two new features: incremental processing and stream processing with latency constraints. This thesis starts with Hadoop, the most popular open-source MapReduce implementation, which provides proven scalability based on data parallelism. I answer the following questions: (1) Is Hadoop able to support incremental processing? (2) What are the necessary architecture changes in order to support incremental processing? (3) What are the additional design features needed to support stream processing with latency constraints? The thesis includes three parts that answer each of the questions. The first part of the thesis validates whether the existing MapReduce implementations can support incremental processing. Incremental processing means that computation is performed as soon as the relevant data becomes available. My extensive benchmark study of Hadoop-based MapReduce systems shows that the widely-used sort-merge implementation for partitioning and parallel processing poses a fundamental barrier to incremental computation. I further propose a cost model, and optimize the Hadoop system configuration based on the model. The benchmark results over the optimized system verify that the barrier to incremental computation is intrinsic, and cannot be removed by tuning system parameters. In the second part of the thesis, I employ various purely hash-based techniques to enable fast in-memory incremental processing in MapReduce, and frequent key based techniques to extend such processing to workloads that require memory more than available. I evaluate my Hadoop-based prototype equipped with all proposed techniques. The results show that the hash techniques allow the reduce progress to keep up with the map progress with up to 3 orders of magnitude reduction of internal disk spills, and enable results to be returned early. The third part of the thesis aims to support stream processing with latency constraints based on the incremental processing platform resulted from the second part. I perform a benchmark study to understand the sources of latency. I then propose a number of necessary architecture changes to support stream processing, and augment the platform with new latency-aware model-driven resource planning and latency-aware runtime scheduling techniques to meet user-specified latency constraints while maximizing throughput. Experiments using real-world workloads show that the techniques reduce the latency from tens or hundreds of seconds to sub-second, with 2x-5x increase in throughput. The new platform offers 1-2 orders of magnitude improvements over Storm, a commercial-grade distributed stream system, and Spark Streaming, a state-of-the-art academic prototype, when considering both latency and throughput

Chi: a scalable and programmable control plane for distributed stream processing systems

Stream-processing workloads and modern shared cluster environments exhibit high variability and unpredictability. Combined with the large parameter space and the diverse set of user SLOs, this makes modern streaming systems very challenging to statically configure and tune. To address these issues, in this paper we investigate a novel control-plane design, Chi, which supports continuous monitoring and feedback, and enables dynamic re-configuration. Chi leverages the key insight of embedding control-plane messages in the data-plane channels to achieve a low-latency and flexible control plane for stream-processing systems. Chi introduces a new reactive programming model and design mechanisms to asynchronously execute control policies, thus avoiding global synchronization. We show how this allows us to easily implement a wide spectrum of control policies targeting different use cases observed in production. Large-scale experiments using production workloads from a popular cloud provider demonstrate the flexibility and efficiency of our approach

A Survey on the Evolution of Stream Processing Systems

Stream processing has been an active research field for more than 20 years, but it is now witnessing its prime time due to recent successful efforts by the research community and numerous worldwide open-source communities. This survey provides a comprehensive overview of fundamental aspects of stream processing systems and their evolution in the functional areas of out-of-order data management, state management, fault tolerance, high availability, load management, elasticity, and reconfiguration. We review noteworthy past research findings, outline the similarities and differences between early ('00-'10) and modern ('11-'18) streaming systems, and discuss recent trends and open problems.Comment: 34 pages, 15 figures, 5 table

Scheduling Problems

Scheduling is defined as the process of assigning operations to resources over time to optimize a criterion. Problems with scheduling comprise both a set of resources and a set of a consumers. As such, managing scheduling problems involves managing the use of resources by several consumers. This book presents some new applications and trends related to task and data scheduling. In particular, chapters focus on data science, big data, high-performance computing, and Cloud computing environments. In addition, this book presents novel algorithms and literature reviews that will guide current and new researchers who work with load balancing, scheduling, and allocation problems

A PROCRUSTEAN APPROACH TO STREAM PROCESSING

The increasing demand for real-time data processing and the constantly growing data volume have contributed to the rapid evolution of Stream Processing Engines (SPEs), which are designed to continuously process data as it arrives. Low operational cost and timely delivery of results are both objectives of paramount importance for SPEs. Given the volatile and uncharted nature of data streams, achieving the aforementioned goals under fixed resources is a challenge. This calls for adaptable SPEs, which can react to fluctuations in processing demands. In the past, three techniques have been developed for improving an SPE’s ability to adapt. Those techniques are classified based on applications’ requirements on exact or approximate results: stream partitioning, and re-partitioning target exact, and load shedding targets approximate processing. Stream partitioning strives to balance load among processors, and previous techniques neglected hidden costs of distributed execution. Load Shedding lowers the accuracy of results by dropping part of the input, and previous techniques did not cope with evolving streams. Stream re-partitioning is used to reconfigure execution while processing takes place, and previous techniques did not fully utilize window semantics. In this dissertation, we put stream processing in a procrustean bed, in terms of the manner and the degree that processing takes place. To this end, we present new approaches, for window-based aggregate operators, which are applicable to both exact and approximate stream processing in modern SPEs. Our stream partitioning, re-partitioning, and load shedding solutions offer improvements in performance and accuracy on real-world data by exploiting the semantics of both data and operations. In addition, we present SPEAr, the design of an SPE that accelerates processing by delivering approximate results with accuracy guarantees and avoiding unnecessary load. Finally, we contribute a hybrid technique, ShedPart, which can further improve load balance and performance of an SPE

Performance analysis and scheduling strategies for ambulatory surgical facilities

Ambulatory surgery is a procedure that does not require an overnight hospital stay and is cost effective and efficient. The goal of this research is to develop an ASF operational model which allows management to make key decisions. This research develops and utilizes the simulation software ARENA based model to accommodate: (a) Time related uncertainties – Three system uncertainties characterize the problem (ii) Surgery time variance (ii) Physician arrival delay and (iii) Patient arrival delay; (b) Resource Capture Complexities – Patient flows vary significantly and capture/utilize both staffing and/or physical resources at different points and varying levels; and (c) Processing Time Differences – Patient care activities and surgical operation times vary by type and have a high level of variance between patient acuity within the same surgery type. A multi-dimensional ASF non-clinical performance objective is formulated and includes: (i) Fixed Labor Costs – regular time staffing costs for two nurse groups and medical/tech assistants, (i i) Overtime Labor Costs – staffing costs beyond the regular schedule, (i i i) Patient Delay Penalty – Imputed costs of waiting time experienced patients, and (iv) Physician Delay Penalty – Imputed costs of physicians having to delay surgical procedures due to ASF causes (limited staffing, patient delays, blocked OR, etc.). Three ASF decision problems are studied: (i) Optimize Staffing Resources Levels - Variations in staffing levels though are inversely related to patient waiting times and physician delays. The decision variable is the number of staff for three resource groups, for a given physician assignment and surgery profile. The results show that the decision space is convex, but decision robustness varies by problem type. For the problems studied the optimal levels provided 9% to 28% improvements relative to the baseline staffing level. The convergence rate is highest for less than optimal levels of Nurse-A. The problem is thus amenable to a gradient based search. (ii) Physician Block Assignment - The decision variables are the block assignments and the patient arrivals by type in each block. Five block assignment heuristics are developed and evaluated. Heuristic #4 which utilizes robust activity estimates (75% likelihood) and generates an asymmetrical resource utilization schedule, is found to be statistically better or equivalent to all other heuristics for 9 out of the 10 problems and (iii) Patient Arrival Schedule – Three decision variables in the patient arrival control (a) Arrival time of first patient in a block (b) The distribution and sequence of patients for each surgery type within the assigned windows and (c) The inter arrival time between patients, which could be constant or varying. Seven scheduling heuristics were developed and tested. Two heuristics one based on Palmers Rule and the other based on the SPT (Shortest Processing Time) Rule gave very strong results