5 Scheduling. Operations Planning and Control


 Corey Walker
 1 years ago
 Views:
Transcription
1 5 Scheduling Operations Planning and Control
2 Some Background Machines (resources) are Machines process jobs (molding machine, x ray machine, server in a restaurant, computer ) Machine Environment Single Machine Parallel Machines (identical vs. different) Flow Shops: different machines (e.g. assembly lines) Each job must be processed by each machine exactly once All jobs have the same routing A job cannot begin processing on the second machine until it has completed processing on the first Job Shops Each job may have its own routing Open Shops (e.g. car repair shop) Jobs have no specific routing 2
3 Scheduling Algorithms Instance: particular set of data for the model Exact algorithm: Optimum solution for every instance why Heuristic algorithm: a good solution, we hope, optimal or close to optimal for every instance 3
4 Measures Completion time of job i, Ci Flow time of Job i: Fi=Ci ri, ri as release date Lateness of job i: Li=Ci di, di as due date Tardiness of job i: Ti = max {0;Li}, Li>0 Earliness of job i: Ei=max{0, Li} Number of tardy jobs: Ni 4
5 Some Application Gantt Charts Developed by Henry Gantt (1911) Consider the following four job, three machine jobshop scheduling problem Assume the following sequences: on M on M on M3 5
6 Some Application Gantt Charts (cont.): Example The Gantt Chart oriented towards machines is: Last operation of job 1 is on machine 3 and is completed at time 14. So, completion time, Ci : C 1 = 14 (on machine 3) Also: C 2 = 11 (on machine 3); C 3 = 13 (on machine 1) and C 4 = 10 (on machine 1) 6
7 Some Background Gantt Charts (cont.): Example The makespan is: Since F i = C i r i but r i = 0 in this example for all i, then flowtime and completion time are the same. Total flowtime is: Min 7
8 Some Background Gantt Charts (cont.): Example The lateness and tardiness of a job The total lateness is Number of tardy jobs is (δ i = 1) The total tardiness is The maximum tardiness is 8
9 Common Sequencing Rules FCFS. First Come First Served. Jobs processed in the order they come to the shop SPT. Shortest Processing Time. Jobs with the shortest processing time are scheduled first EDD. Earliest Due Date. Jobs are sequenced according to their due dates CR. Critical Ratio. Schedule the next job with the shortest CR value. Compute the ratio of remaining time until the due date and processing time of the job
10 Common Sequencing Rules A machining center in a job shop for a local fabrication company has 5 unprocessed jobs (1 to 5). Given the processing times and due dates, apply the sequencing rules to determine scheduling options Mean Flow time, Average Tardiness and # tardy jobs Job Number Processing Time Due Date
11 Single Machine Scheduling Introduction Applicability Single Machine Aggregated Machines Bottleneck Machines Methods Simple Methods Target on performance measures Optimization procedures (heuristic, optimal) Sequence dependent setup times Static vs. Dynamic scheduling 11
12 Single Machine Scheduling Minimizing Flow time What if your in process inventory costs dominate? Minimize total flow time tends to minimize total holding costs Example Proposed sequence: Total flowtime (F)=? F = p 1 + (p 1 +p 2 ) + (p 1 +p 2 +p 3 )+...+(p 1 +p p n ) F = n p 1 + (n 1) p p n For this problem F = High value P and delivers asap
13 Single Machine Scheduling Minimizing Flow time Shortest Processing Time (SPT) Sequence of jobs ordered from the smallest to largest processing times Is this optimal? Theorem. SPT sequencing minimizes total flowtime on a single machine with zero release times. Proof. We assume an optimal schedule is not an SPT sequence. S is optimal sequence (assumed) with iand then j S is a schedule where j comes before I The set of jobs B comes before i/j or j/i and A comes after p i > p j TF(S) = TF(B) + (t+p i ) + (t+p i +p j ) + TF(A) TF(S ) = TF(B) + (t+ p j ) + (t+ p j +p i ) + TF(A) TF(S) TF(S )= p i p j > 0» t is the completion of the last job in B, TF(A) and TF(B) are total flowtimes of jobs in A and B 13
14 Single Machine Scheduling Minimizing Flow time Example (cont.) Optimal Schedule is Completion times C 1 = 11, C 2 = 2, C 3 = 7, C 4 = 4 and C 5 =15 Total Flow time = Total Completion Time = 39 Remarks on the SPT Rule Minimizes total time jobs spend in the system (because all release times are 0) Minimizes the mean number of jobs waiting to be processed (mean work in progress) Also minimizes Total Lateness (Li=Ci di). Why? 14 Professor penalty Parkinson Law
15 Single Machine Scheduling Maximal Tardiness and Maximal Lateness Due date oriented measure Earliest due date sequence (EDD) Minimizes the Maximal Tardiness (T max ), T max =max{0;li} Minimizes the Maximal Lateness (L max ), Li=Ci di Example EDD sequence is Tardiness of the jobs is (0, 0, 2, 1, 0) 15 Customer satisfaction Minmax
16 Single Machine Scheduling Number of Tardy Jobs EDD may have several jobs somewhat tardy If the fixed cost component of jobs being tardy dominates we wish to have the most of them on time Moore s Algorithm Step1. Compute the tardiness for each job in the EDD sequence. Set N T =0, and let k be the first position containing a tardy job. If no job is tardy go to step 4. Step 2. Find the job with the largest processing time in positions 1 to k. Step 3. Remove job j* from the sequence, set N T =N T+1, and repeat Step1. Step 4. Place the removed N T jobs in any order at the end of the sequence. This sequence minimizes the number of tardy jobs 16
17 Single Machine Scheduling Number of Tardy Jobs Example EDD sequence Step 1: The tardiness is (0, 0, 2, 1, 0) Job 4 in the third position is the first tardy job; Step 2: The processing times for jobs 5, 3 and 4 are 4, 3, 2, respectively; largest processing time for job 5 Step 3: Remove job 5, go to step 1 Step 1: EDD sequence is ; completion times (3, 5, 7, 11) and tardiness (0, 0, 0, 0) Go to step 4. Step 4: schedule that minimizes the number of tardy jobs is / and has 1 tardy job: Jobs 5 17
18 Single Machine Scheduling Precedence Constraints: Lawler s Algorithm Objective function g i is a non decreasing function of the flow time F i Examples = minimizing maximum lateness ;0 minimizing maximum tardiness 18
19 Single Machine Scheduling Precedence Constraints: Lawler s Algorithm Concept Back scheduling At each step determine the set of jobs V not required to precede any other Among V choose job k that satisfies and corresponds to the processing time of the current sequence Job k is scheduled last Determine again V and is reduced by 19
20 Lawler s Algorithm Example An automotive painting and repair has 6 cars waiting to repairs. Three (1,2,3) from car rental and he agreed to finish these cars based on the due dates. Cars 4,5,6 from a retailer dealer, he agreed that car 4 be completed first (customer is waiting). The processing times and due dates are available for each job. How should be the schedule to minimize the maximum tardiness? Job Pi Due Date
21 Single Machine Scheduling Minimizing Set up Times Sequence dependent set up times The time to change from one product to another may be significant and may depend on the previous part produced p ij = time to process job j if it immediately follows job i Examples: Electronics industry Paint shops Injection molding Minimizes makespan, since it also considers set up Problem is equivalent to the traveling salesman problem (TSP) Plastic Tops 21
22 Single Machine Scheduling Minimizing Set up Times SST = Shortest Set up Time Heuristic A metal products manufacturer has contracted to ship metal braces each day for four customers. Each brace requires a different set up on the rolling mill: *Job C cannot follow job D, because of quality problems SST heuristic:» Step 1 starting arbitrarily by choosing one Job: A» Step 2 B has the smallest set up time following A; A B» Step 3 C has the smallest set up time of all the remaining jobs following B; A B C» Step 4 D is the last remaining job; A B C D A with a makespan of =14 Starting point 22
23 Single Machine Scheduling Minimizing Set up Times A regret based algorithm A regret is a penalty for a decision that was not made Each job must be included once: at least one element from each row Pick the smallest element in each row and their sum is the lower bound on makespan Reduced matrix Row reduction Column reduction Sum of reduced coef = lower bound Find the reduced matrix! Has a 0 in each column and each row 23
24 Single Machine Scheduling Minimizing Set up Times A regret based algorithm (cont.) The reduced matrix is 1 2 If job B does not follow (come after) job A, some other job must follow A» C adds no set up time (is already in the lower bound) Some job must precede B: D has 0 set up» Thus, we have 0 regret not to chose B to follow A A B, A?;? B; 24
25 Single Machine Scheduling Minimizing Set up Times A regret based algorithm (cont.) The reduced matrix is (cont.) 1 2 Zero cell C D» If C does not precede D then we must select other job to precede D (? D)» A can precede D : A D with a regret of 1 time unit» C? : C A with zero regret time unit» Select the jobs pair based on the highest regret value 25
26 Single Machine Scheduling Minimizing Set up Times A regret based algorithm (cont.) Find the cycle sequence that minimizes the set up time Data p ij element of the set up time matrix (even if reduced) R ij regret for element ij, where p ij = 0 C max makespan of the partial sequence L iteration n jobs 26
27 Single Machine Scheduling Minimizing Set up Times A regret based algorithm (cont.) Step 0: C(max) = 0 and L = 1 Step 1: Reduce the Matrix 3 27
28 Single Machine Scheduling Minimizing Set up Times A regret based algorithm (cont.) Step 2: Calculate the regret 3 Step 3 Choose the largest regret : 17 Step 4 Assign a job pair: Job 2 immediately follows job 5 (5 2) L = 1+1; We prohibit
29 Single Machine Scheduling Minimizing Set up Times A regret based algorithm (cont.) New Matrix Step 1: reduce the matrix C(max) = = 24 29
30 Single Machine Scheduling Minimizing Set up Times A regret based algorithm (cont.) Step 2 Calculate the regret Step 3 Chose the largest regret: 9 Step 4 Assign a job pair: 3 1 Prohibit 1 3 Step 1 Reduce the matrix: not possible 30
31 Single Machine Scheduling Minimizing Set up Times A regret based algorithm (cont.) Step 2 Calculate regret Step 3 Choose the largest regret: 3 Step 4 Assign job pair : 1 4; Partial sequence: 5 2, Prohibit 4 1 and 4 3 (to keep from being chosen) Final Matrix Choose 2 3 and 4 5 > sequence The total set up time is 24 31
32 Parallel Machines Introduction A job can be processed in any of the machines The time to process a job is the same on any machine A job consists of a single operation Decision Which machine processes the job? In what order? 32
33 Parallel Machines Introduction List Schedule Sequence of all jobs Assign the next job on the list to the machine with the smallest amount of work assigned Procedure Step 0. Let H i =0, i=1,2,...,m be the assigned workload on machine i, L=([1],[2],...,[n]) the ordered list sequence, C j =0, j=1,2,...,n, and k=1 Step 1. Let j*= L k and H i* =mini =1,m {Hi}; Assign job j* to be processed on machine i*, C j* =H i* +p j*,hi*=h i* +p j* Step 2. Set k=k+1, if k>n, stop. Otherwise go to step 1. 33
34 Parallel Machines Flow Time Consider a facility with 3 identical machines and 15 jobs that need to be done as soon as possible; Processing times(after SPT): 34
35 Parallel Machines Makespan Use the longest processing time list (LPT) Truck Assign the next job on the list to the machine with the least total processing time assigned (heuristic) 35
36 Flow Shops Introduction Jobs processed sequentially on multiple machines All jobs processed in the same order Makespan on a Two Machine Flow Shop Johnson s Algorithm Example Machines Jobs Total Time
37 Flow Shops Makespan on a Two Machine Flow Shop Johnson s Algorithm Example (cont.) Natural schedule for example has a total makespan of 22 h Sequence : makespan of 17» Is this optimal? The makespan must be as large as the sum of the processing times on either machine Makespan must account for unavoidable idle times» For each machine, add the minimum processing time of a job in the other machine» Example: the bound becomes 17, so is optimal 37
38 Flow Shops Makespan on a Two Machine Flow Shop Johnson s Algorithm Step 1» Select the job with the lowest processing time on each machine from the schedulable job list» If the list is empty, the procedure is finished» If the processing time of the job selected is from machine 1, go to step 2, otherwise, go to step 3 Step 2» Schedule the job in the earliest position of the sequence and remove it from the schedulable job list» Return to step 1 Step 3» Schedule the job in the latest position of the sequence and remove it from the schedulable job list» Return to step 1 Johnson s algorithm provides the optimal solution 38
39 Flow Shops Heuristics CDS Heuristic Convert a m machine problem into a two machine problem. How? Procedure Start with: k=1 and l=m; then k=2 and l=m 1; until: k=m 1 and l=2 m 1 schedules are generated Use the best of these m 1 schedules 39
40 Flow Shops Heuristics CDS Heuristic Data Use the CDS to solve the problem First use the Johnson s algorithm for machines 1 and 4 40
41 Flow Shops Heuristics CDS Heuristic Second combine M1 with M2 to pseudomachine 1 and M3 with M4 to pseudomachine 2 Finally combine M1+M2+M3 into pseudomachine 1 and M2+M3+M4 into pseudomachine 2 41
42 Flow Shops Heuristics CDS Heuristic Gantt Chart for CDS schedule 42
43 Job Shops Introduction Different routings for different jobs Difficult to schedule precedence constraints (n!) m possible schedules 43
44 Job Shops Two Machine Job Shops Jackson (1956) adapted the Johnson s algorithm to minimize makespan Job Sets with Machines A and B Machine A: {AB}, {A}, {BA} Machine B: {BA}, {B}, {AB} Why in this order? The order of jobs within the set is to be determined Procedure Machine A: {AB} jobs ordered by Johnson s Algorithm, then {A} in any Shortest Processing Time {BA} jobs in reverse Johnsons order Machine B: {BA} jobs reverse Johnsons order, then {B} in SPT {AB} jobs in ordered by Johnson s Algorithm 44
45 Job Shops Two Machine Job Shops Jackson (1956) adapted the Johnson s algorithm to minimize makespan Example 45
46 Job Shops Two Machine Job Shops Jackson (1956) adapted the Johnson s algorithm to minimize makespan Example 46
47 Stochastic Scheduling: Static Case Single machine case. Suppose that processing times are random variables. If the objective is to minimize average weighted flow time, jobs are sequenced according to expected weighted SPT. That is, if job times are t 1, t 2,..., and the respective weights are u 1, u 2,... then job i precedes job i+1 if E(t i )/u i < E(t i+1 )/u i+1.
48 Stochastic Scheduling: Static Case (continued) Multiple Machines. Requires the assumption that the distribution of job times is exponential, (memoryless property). Assume two parallel machines processing n jobs. Then the optimal sequence is to schedule the jobs according to LEPT (longest expected processing time first). Johnsons algorithm for scheduling n jobs on two machines (flow shop) in the deterministic case has a natural extension to the stochastic case as long as the job times are exponentially distributed.
Factors 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 informationOPERATIONS SCHEDULING. Operations Management Dr. Ron Lembke
OPERATIONS SCHEDULING Operations Management Dr. Ron Lembke Kinds of Scheduling Job shop scheduling Personnel scheduling Facilities scheduling Vehicle scheduling Vendor scheduling Project scheduling Dynamic
More informationChapter 8. Operations Scheduling
Chapter 8 Operations Scheduling Buffer Soldering Visual Inspection Special Stations Buffer workforce Production Management 161 Scheduling is the process of organizing, choosing and timing resource usage
More informationMANUFACTURING MODELS
MANUFACTURING MODELS Manufacturing models In manufacturing models: Resource is called a machine Task is called as job A job may be a single operation or a collection of operations to be done in several
More informationΣΧΕΔΙΑΣΜΟΣ ΚΑΙ ΠΡΟΓΡΑΜ ΜΑΤΙΣΜΟΣ ΠΑΡΑΓΩΓΗΣ Βραχυχρόνιος Προγραμματισμός Παραγωγής
ΣΧΕΔΙΑΣΜΟΣ ΚΑΙ ΠΡΟΓΡΑΜ ΜΑΤΙΣΜΟΣ ΠΑΡΑΓΩΓΗΣ Βραχυχρόνιος Προγραμματισμός Παραγωγής Γιώργος Λυμπερόπουλος Πανεπιστήμιο Θεσσαλίας Τμήμα Μηχανολόγων Μηχανικών 1 PRODUCTION PLANNING AND SCHEDULING ShortTerm
More informationModule 7 Sequencing and scheduling
Module 7 Sequencing and scheduling 1. Define sequencing and scheduling? Sequence refers to the order of carrying out activities. Scheduling is the timing (or timetable) to carry out the activities 2. Classify
More informationCHAPTER 15: SHORTTERM SCHEDULING
TRUE/FALSE CHAPTER 15: SHORTTERM SCHEDULING 1. Delta uses mathematical shortterm scheduling techniques and a hightech nerve center to manage the rapid rescheduling necessary to cope with weather delays
More informationLinear Programming Applications. Assignment Problem
Linear Programming Applications Assignment Problem 1 Introduction Assignment problem is a particular class of transportation linear programming problems Supplies and demands will be integers (often 1)
More informationOperations Management
151 Scheduling Operations Management William J. Stevenson 8 th edition 152 Scheduling CHAPTER 15 Scheduling McGrawHill/Irwin Operations Management, Eighth Edition, by William J. Stevenson Copyright
More informationFlow Shop Scheduling CHAPTER CONTENTS
4 Flow Shop Scheduling CHPTER CONTENTS 4.1 Introduction 4.2 Minimization of makespan using Johnson s Rule for (F 2 C max ) Problem 4.3 Minimization of Makespan for (F 3 C max ) Problem 4.4 Minimization
More informationCopyright 2009 by The McGrawHill Companies, Inc. All Rights Reserved.
Chapter 16 McGrawHill/Irwin Copyright 2009 by The McGrawHill Companies, Inc. All Rights Reserved. : Establishing the timing of the use of equipment, facilities and human activities in an organization
More informationA MODIFIED GIFFLER AND THOMPSON ALGORITHM COMBINED WITH DYNAMIC SLACK TIME FOR SOLVING DYNAMIC SCHEDULE PROBLEMS
A MODIFIED GIFFLER AND THOMPSON ALGORITHM COMBINED WITH DYNAMIC SLACK TIME FOR SOLVING DYNAMIC SCHEDULE PROBLEMS Tanti Octavia Lecturer of Industrial Technology Faculty, Industrial Engineering Department
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 informationPERT 09 Penjadwalan Jangka Pendek (2) Assignment Method Pengurutan Pekerjaan Teori Keterbatasan
PERT 09 Penjadwalan Jangka Pendek (2) Assignment Method Pengurutan Pekerjaan Teori Keterbatasan Assignment Method Assigns tasks or jobs to resources Type of linear programming model Objective Minimize
More informationFlow Shop. 1. Example of a flow shop problem
Flow Shop In a flow shop problem, there are m machines that should process n jobs. All jobs have the same processing order through the machines. The order of the jobs on each machine can be different.
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 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 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 information1. The total amount of time required to complete a schedule is called what? 3. Do deadlines determine the timing in forward or backward scheduling?
1. The total amount of time required to complete a schedule is called what? 2. Line balancing is a technique for scheduling for a system that produces at what level of volume? 3. Do deadlines determine
More informationOperations Scheduling
Operations Scheduling Content Different kinds of scheduling operations Different shop loading methods Develop a schedule using priority rules Calculate scheduling for multiple workstations Develop a schedule
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 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 informationOperations Management
Operations Management ShortTerm Scheduling Chapter 15 151 Outline GLOAL COMPANY PROFILE: DELTA AIRLINES THE STRATEGIC IMPORTANCE OF SHORT TERM SCHEDULING SCHEDULING ISSUES Forward and ackward Scheduling
More informationDynamic Programming.S1 Sequencing Problems
Dynamic Programming.S1 Sequencing Problems Operations Research Models and Methods Paul A. Jensen and Jonathan F. Bard Many operational problems in manufacturing, service and distribution require the sequencing
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 informationShortTerm Scheduling. Outline
ShortTerm Scheduling 15 Outline Global Company Profile: Delta Air Lines The Importance of ShortTerm Scheduling Scheduling Issues Scheduling ProcessFocused Facilities 1 Outline  Continued Loading s
More informationPRODUCTION PLANNING AND SCHEDULING Part 1
PRODUCTION PLANNING AND SCHEDULING Part Andrew Kusiak 9 Seamans Center Iowa City, Iowa  7 Tel: 99 Fax: 9669 andrewkusiak@uiowa.edu http://www.icaen.uiowa.edu/~ankusiak Forecasting Planning Hierarchy
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 informationComparison of simulationbased schedule generation methodologies for semiconductor manufacturing
University of Arkansas, Fayetteville ScholarWorks@UARK Industrial Engineering Undergraduate Honors Theses Industrial Engineering 52007 Comparison of simulationbased schedule generation methodologies
More informationSpecial layout models
Special layout models Chapter 7 (Warehouse Operations) Chapter 10 (Facility Planning Models) Machine layout model Storage layout planning Warehouse layout model Machine Layout Models Objective: To arrange
More information56:272 Integer Programming & Network Flows Final Exam  Fall 99
56:272 Integer Programming & Network Flows Final Exam  Fall 99 Write your name on the first page, and initial the other pages. Answer all the multiplechoice questions and X of the remaining questions.
More informationPLANNING AND SCHEDULING
PLANNING AND SCHEDULING Andrew Kusiak 2139 Seamans Center Iowa City, Iowa 522421527 Tel: 319335 5934 Fax: 319335 5669 andrewkusiak@uiowa.edu http://www.icaen.uiowa.edu/~ankusiak Forecasting Balancing
More informationLOGISTIQUE ET PRODUCTION SUPPLY CHAIN & OPERATIONS MANAGEMENT
LOGISTIQUE ET PRODUCTION SUPPLY CHAIN & OPERATIONS MANAGEMENT CURSUS CONTENTS 1) Introduction 2) Human resources functions 3) A new factory 4) Products 5) Services management 6) Methods 7) Planification
More informationMinimizing Sum of Completion Times and Makespan in MasterSlave Systems
1 Minimizing Sum of Completion Times and Makespan in MasterSlave Systems Joseph YT. Leung, Senior Member, IEEE, and Hairong Zhao, Member, IEEE Abstract We consider scheduling problems in the masterslave
More informationBA OPERATIONS MANAGEMENT
Project Management Scheduling Techniques, PERT, CPM; Scheduling  work centers nature, importance; Priority rules and techniques, shop floor control; Flow shop scheduling Johnson s Algorithm Gantt charts;
More informationVEHICLE ROUTING PROBLEM
VEHICLE ROUTING PROBLEM Readings: E&M 0 Topics: versus TSP Solution methods Decision support systems for Relationship between TSP and Vehicle routing problem () is similar to the Traveling salesman problem
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 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 informationOperations Research 2
Operations Research 2 Lecturer: David Ramsey Room B2026 david.ramsey@ul.ie www.ul.ie/ramsey August 31, 2011 1 / 80 Recommended Text Operations Research An Introduction. Hamdy A. Taha (003/TAH) The 7th
More informationLPT rule: Whenever a machine becomes free for assignment, assign that job whose. processing time is the largest among those jobs not yet assigned.
LPT rule Whenever a machine becomes free for assignment, assign that job whose processing time is the largest among those jobs not yet assigned. Example m1 m2 m3 J3 Ji J1 J2 J3 J4 J5 J6 6 5 3 3 2 1 3 5
More informationA new optimal algorithm for a timedependent scheduling problem
A new optimal algorithm for a timedependent scheduling problem Marek Kubale, Krzysztof M. Ocetkiewicz Department of Algorithms and System Modeling Gdańsk University of Technology, Gdańsk ul. Gabriela
More informationSEQUENCEDEPENDENT SETUP AND CLEANUP TIMES IN A TWOMACHINE JOBSHOP WITH MINIMIZING MAKESPAN. Yuri N. Sotskov Frank Werner
SEQUENCEDEPENDENT SETUP AND CLEANUP TIMES IN A TWOMACHINE JOBSHOP WITH MINIMIZING MAKESPAN Yuri N. Sotskov Frank Werner United Institute of Informatics Problems, National Academy of Sciences of Belarus,
More informationHeuristic approach to Nonpreemptive Open Shop Scheduling to Minimize Number of Late Jobs nt
Heuristic approach to Nonpreemptive Open Shop Scheduling to Minimize Number of Late Jobs nt Eric A. Siy Department of Industrial Engineering De La Salle University 2401 Taft Avenue, Manila, Philippines
More informationOperations research (OR) is concerned
PERFORMANCE EXCELLENCE IN THE WOOD PRODUCTS INDUSTRY EM 8779 June 02 $3.50 Transportation Problem: A Special Case for Linear Programming Problems J. Reeb and S. Leavengood A key problem managers face is
More information5 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 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 informationShortTerm Scheduling
Strategic Implications of By scheduling effectively, companies use assets more effectively and create greater capacity per dollar invested, which, in turn, lowers cost This added capacity and related flexibility
More informationImproved MILP models for twomachine flowshop with batch processing machines
Mathematical and Computer Modelling 48 (2008) 1254 1264 www.elsevier.com/locate/mcm Improved MILP models for twomachine flowshop with batch processing machines ChingJong Liao a,, LiMan Liao b a Department
More informationPriority Algorithms. Sashka Davis University of California, San Diego June 2, 2003
Priority Algorithms Sashka Davis University of California, San Diego sdavis@cs.ucsd.edu June 2, 2003 Abstract This paper reviews the recent development of the formal framework of priority algorithms for
More information56:272 Integer Programming & Network Flows Final Exam Solutions  Fall 99
56:272 Integer Programming & Network Flows Final Exam Solutions  Fall 99 Write your name on the first page, and initial the other pages. Answer all the multiplechoice questions and X of the remaining
More informationII.7 PARALLEL MACHINES
II.7 PARALLEL MACHINES 1. SPT Rule for minimizing Mean Flow Time 2. LPT Rule for reducing Makespan 3. EDD Rule for reducing Maximum Tardiness 4. Slack Rule for reducing Tardiness 5. Wilkerson Irwin Rule
More information5 TRAVELING SALESMAN PROBLEM
5 TRAVELING SALESMAN PROBLEM PROBLEM DEFINITION AND EXAMPLES TRAVELING SALESMAN PROBLEM, TSP: Find a Hamiltonian cycle of minimum length in a given complete weighted graph G=(V,E) with weights c ij =distance
More informationScheduling Interval Scheduling, Reservations, and Timetabling. Tim Nieberg
Scheduling Interval Scheduling, Reservations, and Timetabling Tim Nieberg Service Models activities, which are restricted by time windows, have to be assigned to resources often activities use several
More informationApproximation Algorithms
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 desired features. Solve
More informationSCHEDULING WITH NONRENEWABLE RESOURCES
SCHEDULING WITH NONRENEWABLE RESOURCES by Péter Györgyi Supervisor: Tamás Kis Operations Research Department Eötvös Loránd University Budapest, 2013. Contents Acknowledgement 2 Notations 3 1 Introduction
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 informationMinimizing the number of late jobs in case of stochastic processing times with minimum success probabilities
Minimizing the number of late jobs in case of stochastic processing times with minimum success probabilities Marjan van den Akker Han Hoogeveen institute of information and computing sciences, utrecht
More informationChapter 8 Network Models
Chapter 8 Network Models to accompany Introduction to Mathematical Programming: Operations Research, Volume th edition, by Wayne L. Winston and Munirpallam Venkataramanan Presentation by: H. Sarper Description
More informationChapter 11. Approximation Algorithms. Slides by Kevin Wayne PearsonAddison Wesley. All rights reserved.
Chapter 11 Approximation Algorithms Slides by Kevin Wayne. Copyright @ 2005 PearsonAddison Wesley. All rights reserved. 1 Approximation Algorithms Q. Suppose I need to solve an NPhard problem. What should
More informationAdvanced Operation Research Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras
Advanced Operation Research Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology, Madras Lecture No. # 01 Introduction and Linear Programming We begin this lecture series
More informationGeneral Idea of the Problem. Allocation of Resources Allocation of Time Slots Constraints Optimisation
Scheduling Problems General Idea of the Problem Allocation of Resources Allocation of Time Slots Constraints Optimisation Definition of the Problem J = {J 1,..., J n } M = {M 1,..., M m } Schedule Mapping
More informationIntegrated support system for planning and scheduling... 2003/4/24 page 75 #101. Chapter 5 Sequencing and assignment Strategies
Integrated support system for planning and scheduling... 2003/4/24 page 75 #101 Chapter 5 Sequencing and assignment Strategies 5.1 Overview This chapter is dedicated to the methodologies used in this work
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 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 informationOPERATIONS MANAGEMENT (MSIS 301) STUDY GUIDE EXAM 2
OPERATIONS MANAGEMENT (MSIS 301) STUDY GUIDE EXAM 2 Project Management MULTIPLE CHOICE 1. Which of the following statements regarding Bechtel is true? a. Its competitive advantage is project management.
More information2006 Prentice Hall, Inc. 15 2. 2006 Prentice Hall, Inc. 15 3. 2006 Prentice Hall, Inc. 15 4
Operations Management hapter 5 ShortTerm Scheduling Outline The Strategic Importance Of Short Term Scheduling Scheduling Issues Forward and ackward Scheduling Scheduling riteria PowerPoint presentation
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 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 informationThis supplement focuses on operations
OPERATIONS SCHEDULING SUPPLEMENT J J1 J OPERATIONS SCHEDULING LEARNING GOALS After reading this supplement, you should be able to: 1. Define new performance measures (beyond flow time and past due) for
More informationTHE purpose of this paper is to solve the lot streaming
An Integer Programming Formulation for the Lot Streaming Problem in a Job Shop Environment with Setups Udo Buscher and Liji Shen Abstract This paper aims at solving the lot streaming problem in a job shop
More informationPart II: Location problems and the design of transportation networks
Transportation Logistics Part II: Location problems and the design of transportation networks c R.F. Hartl, S.N. Parragh 1/68 Location problems Production sites PS1 PS2 PS3 PS4 Full truck load transportation
More informationImproved Heuristics for Manufacturing Scheduling
Improved Heuristics for Manufacturing Scheduling A Thesis Submitted In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Engineering By SAPKAL SAGAR ULHAS Under the Supervision
More informationCHAPTER  1 BASICS, DEVELOPMENT AND BRIEF SURVEY OF SCHEDULING THEORY Background of Operation Research
CHAPTER  1 BASICS, DEVELOPMENT AND BRIEF SURVEY OF SCHEDULING THEORY 1.1. Background of Operation Research Any problem that requires a positive decision to be made can be classified as an Operation Research
More informationNEURAL NETWORK MODELING AND SIMULATION OF THE SCHEDULING
25 NEURAL NETWORK MODELING AND SIMULATION OF THE SCHEDULING Ricardo Lorenzo Avila Rondon Facultad de Ingeniería, Universidad de Holguín, Cuba. ricardo@cadcam.uho.edu.cu Adriano da Silva Carvalho Facultade
More informationMULTIPLE CHOICE QUESTIONS DECISION SCIENCE
MULTIPLE CHOICE QUESTIONS DECISION SCIENCE 1. Decision Science approach is a. Multidisciplinary b. Scientific c. Intuitive 2. For analyzing a problem, decisionmakers should study a. Its qualitative aspects
More informationWORSTCASE PERFORMANCE ANALYSIS OF SOME APPROXIMATION ALGORITHMS FOR MINIMIZING MAKESPAN AND FLOWTIME
WORSTCASE PERFORMANCE ANALYSIS OF SOME APPROXIMATION ALGORITHMS FOR MINIMIZING MAKESPAN AND FLOWTIME PERUVEMBA SUNDARAM RAVI, LEVENT TUNÇEL, MICHAEL HUANG Abstract. In 1976, Coffman and Sethi conjectured
More informationLINEAR PROGRAMMING LECTURE NOTES FOR QTM PAPER OF BBE (H), DELHI UNIVERSITY ( ) LINEAR PROGRAMMING
LINEAR PROGRAMMING All organizations, whether large or small, need optimal utilization of their scarce or limited resources to achieve certain objectives. Scarce resources may be money, manpower, material,
More informationCS261: A Second Course in Algorithms Lecture #13: Online Scheduling and Online Steiner Tree
CS6: A Second Course in Algorithms Lecture #3: Online Scheduling and Online Steiner Tree Tim Roughgarden February 6, 06 Preamble Last week we began our study of online algorithms with the multiplicative
More informationLecture Notes 12: Scheduling  Cont.
Online Algorithms 18.1.2012 Professor: Yossi Azar Lecture Notes 12: Scheduling  Cont. Scribe:Inna Kalp 1 Introduction In this Lecture we discuss 2 scheduling models. We review the scheduling over time
More information11. APPROXIMATION ALGORITHMS
Coping with NPcompleteness 11. APPROXIMATION ALGORITHMS load balancing center selection pricing method: vertex cover LP rounding: vertex cover generalized load balancing knapsack problem Q. Suppose I
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 informationChapter 2. Job Shop Scheduling  Formulation and Modeling. 2.1 Problem Structure
Chapter Job Shop Scheduling  Formulation and Modeling Machine scheduling problems arise in different structures and settings. In order to obtain a clear comprehension of the contents in this thesis, the
More informationRealTime Scheduling (Part 1) (Working Draft) RealTime System Example
RealTime Scheduling (Part 1) (Working Draft) Insup Lee Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania www.cis.upenn.edu/~lee/ CIS 41,
More informationSTABILITY OF OPTIMAL LINE BALANCE WITH GIVEN STATION SET
Chapter 10 STABILITY OF OPTIMAL LINE BALANCE WITH GIVEN STATION SET Yuri N. Sotskov, Alexandre Dolgui, Nadezhda Sotskova, Frank Werner Abstract: Key words: We consider the simple assembly line balancing
More information3.1 Simplex Method for Problems in Feasible Canonical Form
Chapter SIMPLEX METHOD In this chapter, we put the theory developed in the last to practice We develop the simplex method algorithm for LP problems given in feasible canonical form and standard form We
More informationCHAPTER 5 A NEW ALTERNATE METHOD OF ASSIGNMENT PROBLEM
69 CHAPTER 5 A NEW ALTERNATE METHOD OF ASSIGNMENT PROBLEM 5.1 Introduction An assignment problem is a particular case of transportation problem where the objective is to assign a number of resources to
More informationIII. Beyond Linear Optimization
Optimization Models Draft of August 26, 2005 III. Beyond Linear Optimization Robert Fourer Department of Industrial Engineering and Management Sciences Northwestern University Evanston, Illinois 602083119,
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 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 informationMultiObjective Resource Constrained Project Scheduling Using Critical Chain Project Management Approach
MultiObjective Resource Constrained Project Scheduling Using Critical Chain Project Management Approach CH. Lakshmi Tulasi 1, Dr. A. Ramakrishna Rao 2 1 Research Scholar, Dept. of Mech. Engg., S. V. U.
More information4.9 Markov matrices. DEFINITION 4.3 A real n n matrix A = [a ij ] is called a Markov matrix, or row stochastic matrix if. (i) a ij 0 for 1 i, j n;
49 Markov matrices DEFINITION 43 A real n n matrix A = [a ij ] is called a Markov matrix, or row stochastic matrix if (i) a ij 0 for 1 i, j n; (ii) a ij = 1 for 1 i n Remark: (ii) is equivalent to AJ n
More informationAlgorithms Using List Scheduling and Greedy Strategies for Scheduling in the Flowshop with Resource Constraints. Ewa Figielska *
Zeszyty Naukowe WWSI, No. 11, Vol. 8, 2014, pp. 2939 Algorithms Using List Scheduling and Greedy Strategies for Scheduling in the Flowshop with Resource Constraints Ewa Figielska * Warsaw School of Computer
More informationGESTION DE LA PRODUCTION ET DES OPERATIONS PICASSO EXERCICE INTEGRE
ECAP 21 / PROD2100 GESTION DE LA PRODUCTION ET DES OPERATIONS PICASSO EXERCICE INTEGRE 20042005 Prof : Pierre Semal : semal@poms.ucl.ac.be Assistants : Eléonore de le Court : delecourt@poms.ucl.ac.be
More informationCompletion Time Scheduling and the WSRPT Algorithm
Completion Time Scheduling and the WSRPT Algorithm Bo Xiong, Christine Chung Department of Computer Science, Connecticut College, New London, CT {bxiong,cchung}@conncoll.edu Abstract. We consider the online
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 information56:171 Operations Research Final Examination Solution Fall 2001
56:171 Operations Research Final Examination Solution Fall 2001 Write your name on the first page, and initial the other pages. Answer both Parts A and B, and select any 4 (out of 5) problems from Part
More informationA SIMULATION STUDY FOR DYNAMIC FLEXIBLE JOB SHOP SCHEDULING WITH SEQUENCEDEPENDENT SETUP TIMES
A SIMULATION STUDY FOR DYNAMIC FLEXIBLE JOB SHOP SCHEDULING WITH SEQUENCEDEPENDENT SETUP TIMES by Zakaria Yahia Abdelrasol Abdelgawad A Thesis Submitted to the Faculty of Engineering at Cairo University
More informationCS 583: Approximation Algorithms Lecture date: February 3, 2016 Instructor: Chandra Chekuri
CS 583: Approximation Algorithms Lecture date: February 3, 2016 Instructor: Chandra Chekuri Scribe: CC Notes updated from Spring 2011. In the previous lecture we discussed the Knapsack problem. In this
More informationFundamentals of probability /15.085
Fundamentals of probability. 6.436/15.085 LECTURE 23 Markov chains 23.1. Introduction Recall a model we considered earlier: random walk. We have X n = Be(p), i.i.d. Then S n = 1 j n X j was defined to
More informationCSC Linear Programming and Combinatorial Optimization Lecture 7: von Neumann minimax theorem, Yao s minimax Principle, Ellipsoid Algorithm
D CSC2411  Linear Programming and Combinatorial Optimization Lecture : von Neumann minimax theorem, Yao s minimax Principle, Ellipsoid Algorithm Notes taken by Xuming He March 4, 200 Summary: In this
More information