Outline Outline Complexity Hierarchy Complexity Hierarchy DMP204 - PDF document

Course Introduction Course Introduction Scheduling Scheduling Outline Outline Complexity Hierarchy Complexity Hierarchy DMP204 SCHEDULING, TIMETABLING AND ROUTING 1. Course Introduction 1. Course Introduction Lecture 1 Introduction to Scheduling: Terminology, 2. Scheduling 2. Scheduling Problem Classification Problem Classification Classification 3. Complexity Hierarchy 3. Complexity Hierarchy Marco Chiarandini 2 3 Course Introduction Course Introduction Course Introduction Scheduling Scheduling Scheduling Course Presentation Evaluation Complexity Hierarchy Complexity Hierarchy Complexity Hierarchy Communication media Black Board (BB). What we use: Mail Final Assessment (10 ECTS) Schedule Announcements Oral exam: 30 minutes + 5 minutes defense project meant to assess the base knowledge Course Documents (for Photocopies) Third quarter 2008 Fourth quarter 2008 Group project: Tuesday 10:15-12:00 Wednesday 12:15-14:00 Blog – Students’ Lecture Diary free choice of a case study among few proposed ones Friday 8:15-10:00 Friday 10:15-12:00 Electronic hand in of the exam project Deliverables: program + report meant to assess the ability to apply Web-site http://www.imada.sdu.dk/~marco/DM204/ ∼ 27 lectures Schedule: Project hand in deadline + oral exam in June Lecture plan and slides Literature and Links Exam documents 4 5 6 Course Introduction Course Introduction Course Introduction Scheduling Scheduling Scheduling Course Content Course Material Course Goals and Project Plan Complexity Hierarchy Complexity Hierarchy Complexity Hierarchy General Optimization Methods Mathematical Programming, How to Tackle Real-life Optimization Problems: Constraint Programming, Formulate (mathematically) the problem Heuristics Literature Model the problem and recognize possible similar problems Problem Specific Algorithms (Dynamic Programming, Branch and Bound) B1 Pinedo, M. Planning and Scheduling in Manufacturing and Services Search in the literature (or in the Internet) for: Springer Verlag, 2005 Scheduling complexity results (is the problem NP -hard?) B2 Pinedo, M. Scheduling: Theory, Algorithms, and Systems Springer Single and Parallel Machine Models solution algorithms for original problem New York, 2008 Flow Shops and Flexible Flow Shops solution algorithms for simplified problem B3 Toth, P. & Vigo, D. (ed.) The Vehicle Routing Problem SIAM Job Shops Design solution algorithms Monographs on Discrete Mathematics and Applications, 2002 Resource-Constrained Project Scheduling Test experimentally with the goals of: Timetabling Slides Interval Scheduling, Reservations Class exercises (participatory) configuring Educational Timetabling tuning parameters Workforce and Employee Timetabling comparing Transportation Timetabling studying the behavior (prediction of scaling and deviation from Vehicle Routing optimum) Capacited Vehicle Routing Vehicle Routing with Time Windows 7 8 9 Course Introduction Course Introduction Course Introduction Scheduling Scheduling Problem Classification Scheduling Problem Classification The problem Solving Cycle Outline Scheduling Complexity Hierarchy Complexity Hierarchy Complexity Hierarchy The real problem Manufacturing 1. Course Introduction Project planning Modelling Experimental Single, parallel machine and job shop systems Analysis Flexible assembly systems 2. Scheduling Mathematical Automated material handling (conveyor system) Model Quick Solution: Problem Classification Lot sizing Heuristics Supply chain planning Services Algorithm 3. Complexity Hierarchy Implementation ⇒ different algorithms Mathematical Design of Theory good Solution Algorithms 10 11 12 Course Introduction Course Introduction Scheduling Problem Classification Scheduling Problem Classification Problem Definition Visualization Complexity Hierarchy Complexity Hierarchy Constraints Scheduling are represented by Gantt charts Activities Resources machine-oriented Objectives M 1 J 1 J 2 J 3 J 4 J 5 Problem Definition Given: a set of jobs J = { J 1 , . . . , J n } that have to be processed M 2 J 1 J 2 J 3 J 4 J 5 by a set of machines M = { M 1 , . . . , M m } Find: a schedule , M 3 J 1 J 2 J 3 J 4 J 5 i.e. , a mapping of jobs to machines and processing times time subject to feasibility and optimization constraints. 0 5 10 15 20 or job-oriented Notation: ... n, j, k jobs m, i, h machines 14 15 Course Introduction Course Introduction Course Introduction Scheduling Problem Classification Scheduling Problem Classification Scheduling Problem Classification Data Associated to Jobs Problem Classification α | β | γ Classification Scheme Complexity Hierarchy Complexity Hierarchy Complexity Hierarchy Machine Environment α 1 α 2 α 1 α 2 α 1 α 2 | β 1 . . . β 13 | γ Processing time p ij Release date r j single machine/multi-machine ( α 1 = α 2 = 1 or α 2 = m ) A scheduling problem is described by a triplet α | β | γ . parallel machines: identical ( α 1 = P ), uniform p j /v i ( α 1 = Q ), Due date d j (called deadline, if strict) α machine environment (one or two entries) unrelated p j /v ij ( α 1 = R ) Weight w j β job characteristics (none or multiple entry) multi operations models: Flow Shop ( α 1 = F ), Open Shop γ objective to be minimized (one entry) ( α 1 = O ), Job Shop ( α 1 = J ), Mixed (or Group) Shop ( α 1 = X ) A job J j may also consist of a number n j of operations O j 1 , O j 2 , . . . , O jn j and data for each operation. Associated to each operation a set of machines µ jl ⊆ M Single Machine Flexible Flow Shop Open, Job, Mixed Shop [R.L. Graham, E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan (1979): ( α = FFc ) Optimization and approximation in deterministic sequencing and scheduling: a survey, Ann. Discrete Math. 4, 287-326.] Data that depend on the schedule (dynamic) Starting times S ij Completion time C ij , C j 17 18 19