Industrial Optimization


 Shana Montgomery
 2 years ago
 Views:
Transcription
1 Industrial Optimization Lessons learned from Optimization in Practice Marco Lübbecke Chair of Operations Research RWTH Aachen University, Germany SICS Stockholm Feb 11, 2013
2 Discrete Optimization: Some Applications vehicle routing container logistics course timetabling production planning materials stacking patient scheduling
3 Steel Production
4 Coil Coating
5 Coil Coating: Local Cost
6 Coil Coating: Global Cost
7 Coil Coating: A Sequencing Problem? A sequencing problem... oven finish coater oven primer coater finish coater chem coater
8 Coil Coating: A Sequencing Problem? A sequencing problem... oven test runs finish coater temperature di erences oven many more... primer coater finish coater color changes +rollerchanges height/width/... di erences chem coater roller changes width di erence over threshold? +specialcoating with a very complicated cost function.
9 Shuttle Coaters
10 Tank Assignment Problem Given a fixed sequence of coils
11 Tank Assignment Problem Given a fixed sequence of coils Setup work necessary if
12 Tank Assignment Problem Given a fixed sequence of coils Setup work necessary if I color changes ; cleaning
13 Tank Assignment Problem Given a fixed sequence of coils cleaning cleaning cleaning cleaning Setup work necessary if I color changes ; cleaning
14 Tank Assignment Problem Given a fixed sequence of coils cleaning cleaning cleaning cleaning Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
15 Tank Assignment Problem Given a fixed sequence of coils roller change roller change cleaning &roller change cleaning cleaning cleaning Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
16 Tank Assignment Problem Given a fixed sequence of coils roller change roller change cleaning &roller change cleaning cleaning cleaning Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
17 Tank Assignment Problem Given a fixed sequence of coils 1 2 roller change roller change cleaning &roller change cleaning cleaning cleaning Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
18 Tank Assignment Problem Given a fixed sequence of coils 1 roller change roller change cleaning &roller change cleaning cleaning cleaning 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
19 Tank Assignment Problem Given a fixed sequence of coils tank 1 1 tank 2 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
20 Tank Assignment Problem Given a fixed sequence of coils tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
21 Tank Assignment Problem Given a fixed sequence of coils, use shuttle to minimize idle time ( tank assignment ) tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
22 Tank Assignment Problem Given a fixed sequence of coils, use shuttle to minimize idle time ( tank assignment ) tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change
23 Tank Assignment Problem Given a fixed sequence of coils, use shuttle to minimize idle time ( tank assignment ) tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change! avoiding setup work saves time
24 Tank Assignment Problem Given a fixed sequence of coils, use shuttle to minimize idle time ( tank assignment ) tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change! avoiding setup work saves time
25 Tank Assignment Problem Given a fixed sequence of coils, use shuttle to minimize idle time ( tank assignment ) tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change! avoiding setup work saves time
26 Tank Assignment Problem Given a fixed sequence of coils, use shuttle to minimize idle time ( tank assignment ) tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change! avoiding setup work saves time! concurrent setup work on idle tank saves time
27 Tank Assignment Problem Given a fixed sequence of coils, use shuttle to minimize idle time ( tank assignment ) tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change! avoiding setup work saves time! concurrent setup work on idle tank saves time
28 Tank Assignment Problem Given a fixed sequence of coils, use shuttle to minimize idle time ( tank assignment ) tank 1 tank 2 Setup work necessary if I color changes ; cleaning I coil has larger width than predecessor(s) ; roller change! avoiding setup work saves time! concurrent setup work on idle tank saves time
29 Tank Assignment for Several Coaters I coating line has multiple coaters oven finish coater oven primer coater finish coater chem coater
30 Tank Assignment for Several Coaters I coating line has multiple coaters tank 1 tank 2 tank 1 tank 2 k shuttle coaters tank 1 tank 2
31 Tank Assignment for Several Coaters I coating line has multiple coaters tank 1 tank 2 tank 1 tank 2 k shuttle coaters tank 1 tank 2 I limited resources ; no parallel concurrent setup
32 Tank Assignment for Several Coaters I coating line has multiple coaters tank 1 tank 2 tank 1 tank 2 k shuttle coaters tank 1 tank 2 I limited resources ; no parallel concurrent setup
33 Tank Assignment for Several Coaters I coating line has multiple coaters tank 1 tank 2 tank 1 tank 2 k shuttle coaters tank 1 tank 2 I limited resources ; no parallel concurrent setup
34 Tank Assignment for Several Coaters I coating line has multiple coaters tank 1 tank 2 tank 1 tank 2 k shuttle coaters tank 1 tank 2 I limited resources ; no parallel concurrent setup
35 Tank Assignment: Interval Model I subsequence run on same tank interval of coils tank 1 tank 2
36 Tank Assignment: Interval Model I subsequence run on same tank interval of coils tank 1 tank 2 I I weight(i) = time saved due to setup work avoided (vs. no shuttle) i.e. setup setup I I
37 Tank Assignment: Interval Model I subsequence run on same tank interval of coils tank 1 tank 2 I I weight(i) = time saved due to setup work avoided (vs. no shuttle) i.e. setup setup I + saved time from concurrent setup (if possible) I i.e. setup concurrent setup I I
38 Tank Assignment Optimization Special case: one shuttle coater! select most profitable, nonoverlapping intervals! optimum tank assignment max weight independent set in interval graph! can be solved in polynomial time
39 Tank Assignment Optimization Special case: one shuttle coater! select most profitable, nonoverlapping intervals! optimum tank assignment max weight independent set in interval graph! can be solved in polynomial time General case: k shuttle coaters! need generalized intervals due to concurrent setup! special class of 2union graphs! optimum tank assignment max weight independent set in special 2union graph! NPhard! polynomial time dynamic program for fixed k
40 Tank Assignment Heuristic Practice Tank Assignment Problem with k coaters e new ideas for cient algorithm far too slow, even for small instances Theory Max Weight Indep. Set in special 2union graphs polynomialtime algorithm for fixed k ; dynamic programming strongly NPhard
41 Visualization/Verification of Solutions At a glance: Sequence, tank assignment, and cleaning schedule +adetailedexcelsheet
42 Quality of Solutions I How good are our heuristic coating plans?
43 Integer Program: Variables
44 Integer Program: Variables z s : for each possible subsequence s (global cost) z s
45 Integer Program: Variables y i, j z s : y i, j : for each possible subsequence s (global cost) between subseq.s (local cost) z s
46 Integer Program: Variables x p, j y i, j z s : y i, j : x p, j : for each possible subsequence s (global cost) between subseq.s (local cost) decide whether job j is at position p z s
47 Integer Program: The Master Problem min X s c sz s + X i,j2j c i,jy i,j X x p,j 1 j 2 J p2p X x p,j apple 1 p 2 P j2j X s3j: p(s,j)=p z s = x p,j p 2 P, j 2 J x last(t),i + x first(t+1),j apple 1+y i,j t =1,...,T 1 x p,j 2 {0, 1} p 2 P, j 2 J y i,j 2 {0, 1} i, j 2 J z s 2 {0, 1} s 2 S I solved by branchandprice
48 Results
49 Results I Reduction of idle times by about 30%! solutions verified in practice I Optimization potential for the makespan below 10%! probably less I Our schedules taught practitioners about their machines! OR/maths brings up solutions never thought of before I Went live in 2010! finally, after countless feedback cycles
50 Letter of Appreciation
51 Letter of Appreciation
52 Why (Mathematical) Optimization? I almost every process shows some improvement potential I active decision support in complex situations is rare I need relief from routine tasks, concentrate on essential I need constant/reliable quality over di erent shifts
53 Two Worlds: Views, Motivations, Interests academia/research I interesting problem! I every " counts I the problem instances may be infeasible I research takes time I clean, welldefined world industry/services I we need a solution! I we do not care about 2% I we need a solution, no matter what! I results due yesterday I nasty constraints
54 Tailormade vs. Standard Software academic solution I projectspecific support I your problem is our problem I our solution fits your process I optimization algorithms I active planning suggestions I too cheap standard software I longterm support I your problem means cash I your process fits their solution I heuristics at best I passive visualization I too expensive
55 Complementary Competences I ideal configuration may take three partners I problem owner I software/it provider I academia/research institution
56 Data
57 Are you creative? What would you improve? I objectives may be hard to formulate I don t talk to consultants (too much) I talk to mathematicians computer scientists, programmers!
58 We have many Constraints, or have we? I we have been doing this for 20 years! I distinguish habits from real constraints I mathematical solutions may look di erent from human plans I be open to the unknown
59 Humans don t know how to optimize! I don t feel bad about it! I optimization is made for computers, not humans!
60 Acceptance I talk to everybody involved I convince local expert I if possible: demonstrate potential early I convince management I improve in rounds I usually: optimization supports sta, not replaces them I your task is not easy, why should the solution be?
61 Summary and Conclusion I optimization may bring your business to the next level I academia o ers more and less I be open!
5 INTEGER LINEAR PROGRAMMING (ILP) E. Amaldi Fondamenti di R.O. Politecnico di Milano 1
5 INTEGER LINEAR PROGRAMMING (ILP) E. Amaldi Fondamenti di R.O. Politecnico di Milano 1 General Integer Linear Program: (ILP) min c T x Ax b x 0 integer Assumption: A, b integer The integrality condition
More informationClassification  Examples
Lecture 2 Scheduling 1 Classification  Examples 1 r j C max given: n jobs with processing times p 1,...,p n and release dates r 1,...,r n jobs have to be scheduled without preemption on one machine taking
More informationApproximation Algorithms. Scheduling. Approximation algorithms. Scheduling jobs on a single machine
Approximation algorithms Approximation Algorithms Fast. Cheap. Reliable. Choose two. NPhard problems: choose 2 of optimal polynomial time all instances Approximation algorithms. Tradeoff between time
More informationResource Allocation and Scheduling
Lesson 3: Resource Allocation and Scheduling DEIS, University of Bologna Outline Main Objective: joint resource allocation and scheduling problems In particular, an overview of: Part 1: Introduction and
More informationClassification  Examples 1 1 r j C max given: n jobs with processing times p 1,..., p n and release dates
Lecture 2 Scheduling 1 Classification  Examples 11 r j C max given: n jobs with processing times p 1,..., p n and release dates r 1,..., r n jobs have to be scheduled without preemption on one machine
More informationMinimum Makespan Scheduling
Minimum Makespan Scheduling Minimum makespan scheduling: Definition and variants Factor 2 algorithm for identical machines PTAS for identical machines Factor 2 algorithm for unrelated machines Martin Zachariasen,
More informationResearch Article Batch Scheduling on TwoMachine Flowshop with MachineDependent Setup Times
Hindawi Publishing Corporation Advances in Operations Research Volume 2009, Article ID 153910, 10 pages doi:10.1155/2009/153910 Research Article Batch Scheduling on TwoMachine Flowshop with MachineDependent
More informationNPcompleteness and the real world. NP completeness. NPcompleteness and the real world (2) NPcompleteness and the real world
completeness and the real world completeness Course Discrete Biological Models (Modelli Biologici Discreti) Zsuzsanna Lipták Imagine you are working for a biotech company. One day your boss calls you
More informationReal Time Scheduling Basic Concepts. Radek Pelánek
Real Time Scheduling Basic Concepts Radek Pelánek Basic Elements Model of RT System abstraction focus only on timing constraints idealization (e.g., zero switching time) Basic Elements Basic Notions task
More informationBranchandPrice Approach to the Vehicle Routing Problem with Time Windows
TECHNISCHE UNIVERSITEIT EINDHOVEN BranchandPrice Approach to the Vehicle Routing Problem with Time Windows Lloyd A. Fasting May 2014 Supervisors: dr. M. Firat dr.ir. M.A.A. Boon J. van Twist MSc. Contents
More informationA Genetic Algorithm Approach for Solving a Flexible Job Shop Scheduling Problem
A Genetic Algorithm Approach for Solving a Flexible Job Shop Scheduling Problem Sayedmohammadreza Vaghefinezhad 1, Kuan Yew Wong 2 1 Department of Manufacturing & Industrial Engineering, Faculty of Mechanical
More informationDiscrete Optimization
Discrete Optimization [Chen, Batson, Dang: Applied integer Programming] Chapter 3 and 4.14.3 by Johan Högdahl and Victoria Svedberg Seminar 2, 20150331 Todays presentation Chapter 3 Transforms using
More informationScheduling and (Integer) Linear Programming
Scheduling and (Integer) Linear Programming Christian Artigues LAAS  CNRS & Université de Toulouse, France artigues@laas.fr Master Class CPAIOR 2012  Nantes Christian Artigues Scheduling and (Integer)
More informationNPcomplete? NPhard? Some Foundations of Complexity. Prof. Sven Hartmann Clausthal University of Technology Department of Informatics
NPcomplete? NPhard? Some Foundations of Complexity Prof. Sven Hartmann Clausthal University of Technology Department of Informatics Tractability of Problems Some problems are undecidable: no computer
More informationScheduling Shop Scheduling. Tim Nieberg
Scheduling Shop Scheduling Tim Nieberg Shop models: General Introduction Remark: Consider non preemptive problems with regular objectives Notation Shop Problems: m machines, n jobs 1,..., n operations
More informationApproximation Algorithms
Approximation Algorithms or: How I Learned to Stop Worrying and Deal with NPCompleteness Ong Jit Sheng, Jonathan (A0073924B) March, 2012 Overview Key Results (I) General techniques: Greedy algorithms
More informationOptimal Scheduling for Dependent Details Processing Using MS Excel Solver
BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 8, No 2 Sofia 2008 Optimal Scheduling for Dependent Details Processing Using MS Excel Solver Daniela Borissova Institute of
More informationDuplicating and its Applications in Batch Scheduling
Duplicating and its Applications in Batch Scheduling Yuzhong Zhang 1 Chunsong Bai 1 Shouyang Wang 2 1 College of Operations Research and Management Sciences Qufu Normal University, Shandong 276826, China
More information2.3 Scheduling jobs on identical parallel machines
2.3 Scheduling jobs on identical parallel machines There are jobs to be processed, and there are identical machines (running in parallel) to which each job may be assigned Each job = 1,,, must be processed
More informationSimultaneous Scheduling of Machines and Material Handling System in an FMS
Simultaneous Scheduling of Machines and Material Handling System in an FMS B. Siva Prasad Reddy* and C.S.P. Rao** *Department of Mech. Engg., KITS, Warangal5 5 (A.P) INDIA. **Department of Mech. Engg.,
More information1 st year / 20142015/ Principles of Industrial Eng. Chapter 3 / Dr. May G. Kassir. Chapter Three
Chapter Three Scheduling, Sequencing and Dispatching 31 SCHEDULING Scheduling can be defined as prescribing of when and where each operation necessary to manufacture the product is to be performed. It
More informationAutomated Scheduling, School of Computer Science and IT, University of Nottingham 1. Job Shop Scheduling. Disjunctive Graph.
Job hop cheduling Contents 1. Problem tatement 2. Disjunctive Graph. he hifting Bottleneck Heuristic and the Makespan Literature: 1. cheduling, heory, Algorithms, and ystems, Michael Pinedo, Prentice Hall,
More informationvii TABLE OF CONTENTS CHAPTER TITLE PAGE DECLARATION DEDICATION ACKNOWLEDGEMENT ABSTRACT ABSTRAK
vii TABLE OF CONTENTS CHAPTER TITLE PAGE DECLARATION DEDICATION ACKNOWLEDGEMENT ABSTRACT ABSTRAK TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF ABBREVIATIONS LIST OF SYMBOLS LIST OF APPENDICES
More informationComplexity Theory. IE 661: Scheduling Theory Fall 2003 Satyaki Ghosh Dastidar
Complexity Theory IE 661: Scheduling Theory Fall 2003 Satyaki Ghosh Dastidar Outline Goals Computation of Problems Concepts and Definitions Complexity Classes and Problems Polynomial Time Reductions Examples
More informationCHAPTER 1. Basic Concepts on Planning and Scheduling
CHAPTER 1 Basic Concepts on Planning and Scheduling Scheduling, FEUP/PRODEI /MIEIC 1 Planning and Scheduling: Processes of Decision Making regarding the selection and ordering of activities as well as
More informationPlanning and Scheduling in the Digital Factory
Institute for Computer Science and Control Hungarian Academy of Sciences Berlin, May 7, 2014 1 Why "digital"? 2 Some Planning and Scheduling problems 3 Planning for "oneofakind" products 4 Scheduling
More informationSingle machine parallel batch scheduling with unbounded capacity
Workshop on Combinatorics and Graph Theory 21th, April, 2006 Nankai University Single machine parallel batch scheduling with unbounded capacity Yuan Jinjiang Department of mathematics, Zhengzhou University
More informationChapter 1, Operations Research (OR)
Chapter 1, Operations Research (OR) Kent Andersen February 7, 2007 The term Operations Research refers to research on operations. In other words, the study of how to operate something in the best possible
More informationAlgorithm Design and Analysis
Algorithm Design and Analysis LECTURE 27 Approximation Algorithms Load Balancing Weighted Vertex Cover Reminder: Fill out SRTEs online Don t forget to click submit Sofya Raskhodnikova 12/6/2011 S. Raskhodnikova;
More informationCharles Fleurent Director  Optimization algorithms
Software Tools for Transit Scheduling and Routing at GIRO Charles Fleurent Director  Optimization algorithms Objectives Provide an overview of software tools and optimization algorithms offered by GIRO
More informationJUSTINTIME SCHEDULING WITH PERIODIC TIME SLOTS. Received December May 12, 2003; revised February 5, 2004
Scientiae Mathematicae Japonicae Online, Vol. 10, (2004), 431 437 431 JUSTINTIME SCHEDULING WITH PERIODIC TIME SLOTS Ondřej Čepeka and Shao Chin Sung b Received December May 12, 2003; revised February
More informationA Hybrid Heuristic Rule for Constrained Resource Allocation in PERT Type Networks
World Applied Sciences Journal 7 (10): 13241330, 2009 ISSN 18184952 IDOSI Publications, 2009 A Hybrid Heuristic Rule for Constrained Resource Allocation in PERT Type Networks Siamak Baradaran and S.M.T.
More informationPlanning and Scheduling in Manufacturing and Services
Michael L. Pinedo Planning and Scheduling in Manufacturing and Services Second edition 4y Springer Preface Contents of CDROM vii xvii Part I Preliminaries 1 Introduction 3 1.1 Planning and Scheduling:
More informationDynamic programming formulation
1.24 Lecture 14 Dynamic programming: Job scheduling Dynamic programming formulation To formulate a problem as a dynamic program: Sort by a criterion that will allow infeasible combinations to be eli minated
More informationBatch Splitting in an Assembly Scheduling Environment
Batch Splitting in an Assembly Scheduling Environment Satyaki Ghosh Dastidar Rakesh Nagi 1 420 Bell Hall, Department of Industrial Engineering, University at Buffalo (SUNY), Buffalo, NY 14260, USA. This
More informationFactors to Describe Job Shop Scheduling Problem
Job Shop Scheduling Job Shop A work location in which a number of general purpose work stations exist and are used to perform a variety of jobs Example: Car repair each operator (mechanic) evaluates plus
More informationMIPBased Approaches for Solving Scheduling Problems with Batch Processing Machines
The Eighth International Symposium on Operations Research and Its Applications (ISORA 09) Zhangjiajie, China, September 20 22, 2009 Copyright 2009 ORSC & APORC, pp. 132 139 MIPBased Approaches for Solving
More informationIntroducción a Calendarización en Sistemas Paralelas, Grids y Nubes
CICESE Research Center Ensenada, Baja California Mexico Introducción a Calendarización en Sistemas Paralelas, Grids y Nubes Dr. Andrei Tchernykh CICESE Centro de Investigación Científica y de Educación
More informationRonald Graham: Laying the Foundations of Online Optimization
Documenta Math. 239 Ronald Graham: Laying the Foundations of Online Optimization Susanne Albers Abstract. This chapter highlights fundamental contributions made by Ron Graham in the area of online optimization.
More informationHighMix LowVolume Flow Shop Manufacturing System Scheduling
Proceedings of the 14th IAC Symposium on Information Control Problems in Manufacturing, May 2325, 2012 HighMix LowVolume low Shop Manufacturing System Scheduling Juraj Svancara, Zdenka Kralova Institute
More informationIntroduction to production scheduling. Industrial Management Group School of Engineering University of Seville
Introduction to production scheduling Industrial Management Group School of Engineering University of Seville 1 Introduction to production scheduling Scheduling Production scheduling Gantt Chart Scheduling
More informationAn improved online algorithm for scheduling on two unrestrictive parallel batch processing machines
This is the PrePublished Version. An improved online algorithm for scheduling on two unrestrictive parallel batch processing machines Q.Q. Nong, T.C.E. Cheng, C.T. Ng Department of Mathematics, Ocean
More informationHomogeneity Learners grouped in one kind of educational institution are perceived to be similar and therefore get the same treatment. Heterogeneity Learners are perceived to be di erent. Adjustments are
More information! Solve problem to optimality. ! Solve problem in polytime. ! Solve arbitrary instances of the problem. #approximation algorithm.
Approximation Algorithms 11 Approximation Algorithms Q Suppose I need to solve an NPhard problem What should I do? A Theory says you're unlikely to find a polytime algorithm Must sacrifice one of three
More informationAbstract Title: Planned Preemption for Flexible Resource Constrained Project Scheduling
Abstract number: 0150551 Abstract Title: Planned Preemption for Flexible Resource Constrained Project Scheduling Karuna Jain and Kanchan Joshi Shailesh J. Mehta School of Management, Indian Institute
More informationDuration Must be Job (weeks) Preceeded by
1. Project Scheduling. This problem deals with the creation of a project schedule; specifically, the project of building a house. The project has been divided into a set of jobs. The problem is to schedule
More informationSimulating Optimum Design of Handling Service Center System Based on WITNESS
Advances in Natural Science Vol. 6, No. 4, 2013, pp. 6468 DOI:10.3968/j.ans.1715787020130604.2958 ISSN 17157862 [PRINT] ISSN 17157870 [ONLINE] www.cscanada.net www.cscanada.org Simulating Optimum Design
More informationThe problem with waiting time
The problem with waiting time Why the only way to real optimization of any process requires discrete event simulation Bill Nordgren, MS CIM, FlexSim Software Products Over the years there have been many
More informationSIMS 255 Foundations of Software Design. Complexity and NPcompleteness
SIMS 255 Foundations of Software Design Complexity and NPcompleteness Matt Welsh November 29, 2001 mdw@cs.berkeley.edu 1 Outline Complexity of algorithms Space and time complexity ``Big O'' notation Complexity
More informationChapter 11. 11.1 Load Balancing. Approximation Algorithms. Load Balancing. Load Balancing on 2 Machines. Load Balancing: Greedy Scheduling
Approximation Algorithms Chapter Approximation Algorithms Q. Suppose I need to solve an NPhard problem. What should I do? A. Theory says you're unlikely to find a polytime algorithm. Must sacrifice one
More informationImproved Algorithms for Data Migration
Improved Algorithms for Data Migration Samir Khuller 1, YooAh Kim, and Azarakhsh Malekian 1 Department of Computer Science, University of Maryland, College Park, MD 20742. Research supported by NSF Award
More information5 Scheduling. Operations Planning and Control
5 Scheduling Operations Planning and Control Some Background Machines (resources) are Machines process jobs (molding machine, x ray machine, server in a restaurant, computer ) Machine Environment Single
More informationScheduling Single Machine Scheduling. Tim Nieberg
Scheduling Single Machine Scheduling Tim Nieberg Single machine models Observation: for nonpreemptive problems and regular objectives, a sequence in which the jobs are processed is sufficient to describe
More informationProgram Monday, June 22, 2009
Program Monday, June 22, 2009 9:00 Welcome and Introduction 9:20 George Nemhauser (Georgia Institute of Technology): A Maritime Inventory Routing Problem 10:05 Coffee Break 10:20 Jens Baudach (TU Dortmund)
More informationOptimization Modeling for Mining Engineers
Optimization Modeling for Mining Engineers Alexandra M. Newman Division of Economics and Business Slide 1 Colorado School of Mines Seminar Outline Linear Programming Integer Linear Programming Slide 2
More informationOptimization Challenges
Optimization Challenges 1 Agenda Agenda Optimization Challenge prelude Quintiq Introduction Optimization Challenge Question and Answers 2 Optimization Challenge What? A friendly competition to see who
More informationIntroduction to Design Optimization
Introduction to Design Optimization Various Design Objectives Minimum Weight (under Allowable Stress) A PEM Fuel Cell Stack with Even Compression over Active Area (Minimum Stress Difference) Minimum Maximum
More information! Solve problem to optimality. ! Solve problem in polytime. ! Solve arbitrary instances of the problem. !approximation algorithm.
Approximation Algorithms Chapter Approximation Algorithms Q Suppose I need to solve an NPhard problem What should I do? A Theory says you're unlikely to find a polytime algorithm Must sacrifice one of
More informationScheduling Parallel Jobs with Linear Speedup
Scheduling Parallel Jobs with Linear Speedup Alexander Grigoriev and Marc Uetz Maastricht University, Quantitative Economics, P.O.Box 616, 6200 MD Maastricht, The Netherlands. Email: {a.grigoriev,m.uetz}@ke.unimaas.nl
More information11. APPROXIMATION ALGORITHMS
11. APPROXIMATION ALGORITHMS load balancing center selection pricing method: vertex cover LP rounding: vertex cover generalized load balancing knapsack problem Lecture slides by Kevin Wayne Copyright 2005
More informationScheduling Algorithm with Optimization of Employee Satisfaction
Washington University in St. Louis Scheduling Algorithm with Optimization of Employee Satisfaction by Philip I. Thomas Senior Design Project http : //students.cec.wustl.edu/ pit1/ Advised By Associate
More informationApplied Algorithm Design Lecture 5
Applied Algorithm Design Lecture 5 Pietro Michiardi Eurecom Pietro Michiardi (Eurecom) Applied Algorithm Design Lecture 5 1 / 86 Approximation Algorithms Pietro Michiardi (Eurecom) Applied Algorithm Design
More informationScheduling Parallel Jobs with Monotone Speedup 1
Scheduling Parallel Jobs with Monotone Speedup 1 Alexander Grigoriev, Marc Uetz Maastricht University, Quantitative Economics, P.O.Box 616, 6200 MD Maastricht, The Netherlands, {a.grigoriev@ke.unimaas.nl,
More informationMinimizing Cycle Time for PCB Assembly Lines: An Integer Programming Model and a BranchandBound Approach
Information and Management Sciences Volume 19, Number 2, pp. 237243, 2008 Minimizing Cycle Time for PCB Assembly Lines: An Integer Programming Model and a BranchandBound Approach P. Ji Y. F. Wan Hong
More informationResource Optimization of Spatial TDMA in Ad Hoc Radio Networks: A Column Generation Approach
Resource Optimization of Spatial TDMA in Ad Hoc Radio Networks: A Column Generation Approach Patrik Björklund, Peter Värbrand and Di Yuan Department of Science and Technology, Linköping University SE601
More informationScheduling Parallel Machine Scheduling. Tim Nieberg
Scheduling Parallel Machine Scheduling Tim Nieberg Problem P C max : m machines n jobs with processing times p 1,..., p n Problem P C max : m machines n jobs with processing times p 1,..., p { n 1 if job
More informationCOURSE SYLLABUS INMT1317 INDUSTRIAL AUTOMATION
COURSE SYLLABUS INMT1317 INDUSTRIAL AUTOMATION Catalog Description: A study of the applications of industrial automation systems, including identification of system requirements, equipment integration,
More informationChapter 12 Making Meaning in Algebra Examining Students Understandings and Misconceptions
Assessing Mathematical Proficiency MSRI Publications Volume 53, 2007 Chapter 12 Making Meaning in Algebra Examining Students Understandings and Misconceptions DAVID FOSTER Students often get confused and
More informationTRANSPORT PLANNING IN CONDITIONS OF DIFFERENT TRANSPORT TARIFFS APPLICATION OF INTEGER PROGRAMMING
TOTAL LOGISTIC MANAGEMENT No. 1 2008 PP. 25 31 Paweł HANCZAR TRANSPORT PLANNING IN CONDITIONS OF DIFFERENT TRANSPORT TARIFFS APPLICATION OF INTEGER PROGRAMMING Abstract: This paper presents the application
More informationOptimization of the physical distribution of furniture. Sergey Victorovich Noskov
Optimization of the physical distribution of furniture Sergey Victorovich Noskov Samara State University of Economics, Soviet Army Street, 141, Samara, 443090, Russian Federation Abstract. Revealed a significant
More informationChapter 2 Allocation of Virtual Machines
Chapter 2 Allocation of Virtual Machines In this chapter, we introduce a solution to the problem of costeffective VM allocation and reallocation. Unlike traditional solutions, which typically reallocate
More informationLINEAR PROGRAMMING PROBLEM: A GEOMETRIC APPROACH
59 LINEAR PRGRAMMING PRBLEM: A GEMETRIC APPRACH 59.1 INTRDUCTIN Let us consider a simple problem in two variables x and y. Find x and y which satisfy the following equations x + y = 4 3x + 4y = 14 Solving
More informationINTEGRATED OPTIMIZATION OF SAFETY STOCK
INTEGRATED OPTIMIZATION OF SAFETY STOCK AND TRANSPORTATION CAPACITY Horst Tempelmeier Department of Production Management University of Cologne AlbertusMagnusPlatz D50932 Koeln, Germany http://www.spw.unikoeln.de/
More informationOptimising Patient Transportation in Hospitals
Optimising Patient Transportation in Hospitals Thomas Hanne 1 Fraunhofer Institute for Industrial Mathematics (ITWM), FraunhoferPlatz 1, 67663 Kaiserslautern, Germany, hanne@itwm.fhg.de 1 Introduction
More informationM. Sugumaran / (IJCSIT) International Journal of Computer Science and Information Technologies, Vol. 2 (3), 2011, 10011006
A Design of Centralized Meeting Scheduler with Distance Metrics M. Sugumaran Department of Computer Science and Engineering,Pondicherry Engineering College, Puducherry, India. Abstract Meeting scheduling
More informationAnalysis of Approximation Algorithms for kset Cover using FactorRevealing Linear Programs
Analysis of Approximation Algorithms for kset Cover using FactorRevealing Linear Programs Stavros Athanassopoulos, Ioannis Caragiannis, and Christos Kaklamanis Research Academic Computer Technology Institute
More informationLinear Programming is the branch of applied mathematics that deals with solving
Chapter 2 LINEAR PROGRAMMING PROBLEMS 2.1 Introduction Linear Programming is the branch of applied mathematics that deals with solving optimization problems of a particular functional form. A linear programming
More informationPriori ty ... ... ...
.Maintenance Scheduling Maintenance scheduling is the process by which jobs are matched with resources (crafts) and sequenced to be executed at certain points in time. The maintenance schedule can be prepared
More informationTHROUGHPUT OPTIMIZATION IN ROBOTIC CELLS
Contents Preface xv 1. ROBOTIC CELLS IN PRACTICE 1 1.1 Cellular Manufacturing 2 1.2 Robotic Cell Flowshops 3 1.3 Throughput Optimization 7 1.4 Historical Overview 9 1.5 Applications 11 2. A CLASSIFICATION
More informationVENDOR MANAGED INVENTORY
VENDOR MANAGED INVENTORY Martin Savelsbergh School of Industrial and Systems Engineering Georgia Institute of Technology Joint work with Ann Campbell, Anton Kleywegt, and Vijay Nori Distribution Systems:
More informationAdvanced Planning and Scheduling
Taylor Scheduler Welcome! Taylor Scheduler is our advanced planning and production scheduling software. Its many features allow Taylor Scheduler to be able to handle just about any manufacturing scheduling
More informationSport Timetabling. Outline DM87 SCHEDULING, TIMETABLING AND ROUTING. Outline. Lecture 15. 1. Problem Definitions
Outline DM87 SCHEDULING, TIMETABLING AND ROUTING Lecture 15 Sport Timetabling 1. Problem Definitions Marco Chiarandini DM87 Scheduling, Timetabling and Routing 2 Problems we treat: single and double roundrobin
More informationThe truck scheduling problem at crossdocking terminals
The truck scheduling problem at crossdocking terminals Lotte Berghman,, Roel Leus, Pierre Lopez To cite this version: Lotte Berghman,, Roel Leus, Pierre Lopez. The truck scheduling problem at crossdocking
More informationFive High Order Thinking Skills
Five High Order Introduction The high technology like computers and calculators has profoundly changed the world of mathematics education. It is not only what aspects of mathematics are essential for learning,
More informationJob Scheduling Techniques for Distributed Systems with Heterogeneous Processor Cardinality
Job Scheduling Techniques for Distributed Systems with Heterogeneous Processor Cardinality HungJui Chang JanJan Wu Department of Computer Science and Information Engineering Institute of Information
More informationDynamic programming. Doctoral course Optimization on graphs  Lecture 4.1. Giovanni Righini. January 17 th, 2013
Dynamic programming Doctoral course Optimization on graphs  Lecture.1 Giovanni Righini January 1 th, 201 Implicit enumeration Combinatorial optimization problems are in general NPhard and we usually
More informationOptimal Cheque Production: A Case Study
Blo UNIVERSITÀ DI SALERNO Dipartimento di Matematica e Informatica D.M.I. Via Ponte don Melillo 84084 Fisciano (SA) Italy Optimal Cheque Production: A Case Study Raffaele Cerulli, Renato De Leone, Monica
More informationModels of a Vending Machine Business
Math Models: Sample lesson Tom Hughes, 1999 Models of a Vending Machine Business Lesson Overview Students take on different roles in simulating starting a vending machine business in their school that
More information5.1 Bipartite Matching
CS787: Advanced Algorithms Lecture 5: Applications of Network Flow In the last lecture, we looked at the problem of finding the maximum flow in a graph, and how it can be efficiently solved using the FordFulkerson
More informationSingle machine models: Maximum Lateness 12 Approximation ratio for EDD for problem 1 r j,d j < 0 L max. structure of a schedule Q...
Lecture 4 Scheduling 1 Single machine models: Maximum Lateness 12 Approximation ratio for EDD for problem 1 r j,d j < 0 L max structure of a schedule 0 Q 1100 11 00 11 000 111 0 0 1 1 00 11 00 11 00
More informationModels for Incorporating Block Scheduling in Blood Drive Staffing Problems
University of Arkansas, Fayetteville ScholarWorks@UARK Industrial Engineering Undergraduate Honors Theses Industrial Engineering 52014 Models for Incorporating Block Scheduling in Blood Drive Staffing
More informationGraphical method. plane. (for max) and down (for min) until it touches the set of feasible solutions. Graphical method
The graphical method of solving linear programming problems can be applied to models with two decision variables. This method consists of two steps (see also the first lecture): 1 Draw the set of feasible
More informationOn Orchestrating Virtual Network Functions
On Orchestrating Virtual Network Functions Presented @ CNSM 2015 Md. Faizul Bari, Shihabur Rahman Chowdhury, and Reaz Ahmed, and Raouf Boutaba David R. Cheriton School of Computer science University of
More informationApproximability of TwoMachine NoWait Flowshop Scheduling with Availability Constraints
Approximability of TwoMachine NoWait Flowshop Scheduling with Availability Constraints T.C. Edwin Cheng 1, and Zhaohui Liu 1,2 1 Department of Management, The Hong Kong Polytechnic University Kowloon,
More informationSteel stacking. A problem in inventory management in the steel industry. João Pedro Pedroso
A problem in inventory management in the steel industry International Symposium on Mathematics of Logistics TUMSAT, Japan, November 2011 Part of the presentation concerns joint work with Rui Rei and Mikio
More informationA Robust Formulation of the Uncertain Set Covering Problem
A Robust Formulation of the Uncertain Set Covering Problem Dirk Degel Pascal Lutter Chair of Management, especially Operations Research RuhrUniversity Bochum Universitaetsstrasse 150, 44801 Bochum, Germany
More informationParallel machines scheduling with applications to Internet adslot placement
UNLV Theses/Dissertations/Professional Papers/Capstones 122011 Parallel machines scheduling with applications to Internet adslot placement Shaista Lubna University of Nevada, Las Vegas Follow this and
More informationA new BranchandPrice Algorithm for the Traveling Tournament Problem (TTP) Column Generation 2008, Aussois, France
A new BranchandPrice Algorithm for the Traveling Tournament Problem (TTP) Column Generation 2008, Aussois, France Stefan Irnich 1 sirnich@or.rwthaachen.de RWTH Aachen University Deutsche Post Endowed
More informationprinceton univ. F 13 cos 521: Advanced Algorithm Design Lecture 6: Provable Approximation via Linear Programming Lecturer: Sanjeev Arora
princeton univ. F 13 cos 521: Advanced Algorithm Design Lecture 6: Provable Approximation via Linear Programming Lecturer: Sanjeev Arora Scribe: One of the running themes in this course is the notion of
More informationScheduling Programming Activities and Johnson's Algorithm
Scheduling Programming Activities and Johnson's Algorithm Allan Glaser and Meenal Sinha Octagon Research Solutions, Inc. Abstract Scheduling is important. Much of our daily work requires us to juggle multiple
More information