DantzigWolfe bound and DantzigWolfe cookbook


 Austen Glenn
 3 years ago
 Views:
Transcription
1 DantzigWolfe bound and DantzigWolfe cookbook DTUManagement Technical University of Denmark 1
2 Outline LP strength of the DantzigWolfe The exercise from last week... The DantzigWolfe cookbook 2
3 DantzigWolfe bound strength I have previously stated that the main reason for using DZ is speed. This is not entirely true: The LP bound can be strengthened using DantzigWolfe! 3
4 Example from last time 4 Objective 3 2 A1 A
5 Example from last time: MIP version 4 Objective 3 2 A1 A2 1 Optimum
6 Example from last time: MIP version 4 LP optimum IP optimum Objective 3 2 A1 A2 1 Convex hull optimum
7 Condition for bound improvement So, besides improving the speed of LP solution, we can get an improved bound if: The subproblem (A 2 ) has nonintegral solution property So we have to solve an integer problem which is hard in the subproblem... We may need specialized algorithms... We may be able to improve solution speed if a number of smaller subproblems are created. 7
8 Job planning under budget constraint i: Jobs to perform j: Persons to perform job C i,j : Cost if person j performs job i T i,j : Training cost to train j for job i 8
9 Direct model Min: s.t.: i,j C i,j x i,j i,j x i,j = 1 j i j x i,j = 1 i T i,j x i,j 18 x i,j [0, 1] 9
10 The possibilities of decomposition Which constraint should be removed? The assignment constraints? The subproblem creates full schedules assigning all jobs to all persons The master problem selects combinations of the schedules. The budget constraint??? 10
11 1 Subproblem (only the constraints) Min: c r s =??? s.t.: x i,j = 1 j i x i,j {0,1} Notice: α 0 and β R j x i,j = 1 i 11
12 1 Master problem Min: C s y s s.t.: T s y s 18 (α 0) s s y s = 1 (β R) s y s [0, 1] 12
13 1 Subproblem Min: c r s = i,j C i,j x i,j α i,j T i,j x i,j β = i,j (C i,j α T i,j )x i,j β s.t.: x i,j = 1 j i j x i,j {0,1} x i,j = 1 i Notice: α 0 and β R 13
14 2 decomposition The budget constraint: The schedules are now job selections which obeys the training budget constraint. The master problem job is then to mix (fractionally) the different schedules The subproblem is then a knapsack problem... 14
15 2 Subproblem (without objective function) Min: c i,j =??? s.t.: T i,j x i,j 18 i,j x i,j {0,1} Notice: α j R and β i R 15
16 2 Master problem Min: C s y s s.t.: A s jy s = 1 j (α j R) s s s B s iy s = 1 i (β i R) y s = 1 (γ R) s y s [0, 1] 16
17 2 Subproblem Min: c i,j = C i,j x i,j i,j j α j β i x i,j γ x i,j i i j = i,j (C i,j α j β i )x i,j γ s.t.: T i,j x i,j 18 i,j x i,j {0,1} Notice: α j R and β i R 17
18 DantzigWolfe cookbook Write up the original MIP problem (carefully!) Write up dual variables for each type of constraints and set dual variable bounds Move set of constraints (A 2 ) to subproblem (ignore the subproblem objective for now). WHAT IS THE SUBPROBLEM INTUITIVELY??? What does one solution correspond to? 18
19 DantzigWolfe cookbook Write up the master problem, with the new variables, both constraints and objective function Finally, write up the subproblem objective: minc red =(c π A 1 )x α, i.e. the original cost minus the column times the dual variables. Open question: How should the subproblem be solved? 19
Optimization Theory for Large Systems
Optimization Theory for Large Systems LEON S. LASDON CASE WESTERN RESERVE UNIVERSITY THE MACMILLAN COMPANY COLLIERMACMILLAN LIMITED, LONDON Contents 1. Linear and Nonlinear Programming 1 1.1 Unconstrained
More informationTutorial: Operations Research in Constraint Programming
Tutorial: Operations Research in Constraint Programming John Hooker Carnegie Mellon University May 2009 Revised June 2009 May 2009 Slide 1 Motivation Benders decomposition allows us to apply CP and OR
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 informationLoad Balancing of Telecommunication Networks based on Multiple Spanning Trees
Load Balancing of Telecommunication Networks based on Multiple Spanning Trees Dorabella Santos Amaro de Sousa Filipe Alvelos Instituto de Telecomunicações 3810193 Aveiro, Portugal dorabella@av.it.pt Instituto
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 informationScheduling Home Health Care with Separating Benders Cuts in Decision Diagrams
Scheduling Home Health Care with Separating Benders Cuts in Decision Diagrams André Ciré University of Toronto John Hooker Carnegie Mellon University INFORMS 2014 Home Health Care Home health care delivery
More informationOperations Research for Telecommunication Linear Programming and Network Routing
Operations Research for Telecommunication Linear Programming and Network Routing tks@imm.dtu.dk Informatics and Mathematical Modeling Technical University of Denmark 1 Operations Research (OR) OR: Mathematics
More informationNoncommercial Software for MixedInteger Linear Programming
Noncommercial Software for MixedInteger Linear Programming J. T. Linderoth T. K. Ralphs December, 2004. Revised: January, 2005. Abstract We present an overview of noncommercial software tools for the
More informationSolving Integer Programming with BranchandBound Technique
Solving Integer Programming with BranchandBound Technique This is the divide and conquer method. We divide a large problem into a few smaller ones. (This is the branch part.) The conquering part is done
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 informationBranch and Cut for TSP
Branch and Cut for TSP jla,jc@imm.dtu.dk Informatics and Mathematical Modelling Technical University of Denmark 1 BranchandCut for TSP BranchandCut is a general technique applicable e.g. to solve symmetric
More informationEfficient and Robust Allocation Algorithms in Clouds under Memory Constraints
Efficient and Robust Allocation Algorithms in Clouds under Memory Constraints Olivier Beaumont,, Paul RenaudGoud Inria & University of Bordeaux Bordeaux, France 9th Scheduling for Large Scale Systems
More information4.6 Linear Programming duality
4.6 Linear Programming duality To any minimization (maximization) LP we can associate a closely related maximization (minimization) LP. Different spaces and objective functions but in general same optimal
More informationLiner Shipping Revenue Management with Respositioning of Empty Containers
Liner Shipping Revenue Management with Respositioning of Empty Containers Berit Løfstedt David Pisinger Simon Spoorendonk Technical Report no. 0815 ISSN: 01078283 Dept. of Computer Science University
More informationSome representability and duality results for convex mixedinteger programs.
Some representability and duality results for convex mixedinteger programs. Santanu S. Dey Joint work with Diego Morán and Juan Pablo Vielma December 17, 2012. Introduction About Motivation Mixed integer
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 informationSchedulAir. Airline planning & airline scheduling with Unified Optimization. decisal. Copyright 2014 Decisal Ltd. All rights reserved.
Copyright 2014 Decisal Ltd. All rights reserved. Airline planning & airline scheduling with Unified Optimization SchedulAir Overview Unified Optimization Benders decomposition Airline planning & scheduling
More informationDantzigWolfe and Lagrangian decompositions in integer linear programming
DantzigWolfe and Lagrangian decompositions in integer linear programming Lucas Létocart, Nora Touati Moungla, Anass Nagih To cite this version: Lucas Létocart, Nora Touati Moungla, Anass Nagih. DantzigWolfe
More informationInverse Optimization by James Orlin
Inverse Optimization by James Orlin based on research that is joint with Ravi Ahuja Jeopardy 000  the Math Programming Edition The category is linear objective functions The answer: When you maximize
More informationLecture 3: Linear Programming Relaxations and Rounding
Lecture 3: Linear Programming Relaxations and Rounding 1 Approximation Algorithms and Linear Relaxations For the time being, suppose we have a minimization problem. Many times, the problem at hand can
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 informationRecovery of primal solutions from dual subgradient methods for mixed binary linear programming; a branchandbound approach
MASTER S THESIS Recovery of primal solutions from dual subgradient methods for mixed binary linear programming; a branchandbound approach PAULINE ALDENVIK MIRJAM SCHIERSCHER Department of Mathematical
More informationBig Data Optimization at SAS
Big Data Optimization at SAS Imre Pólik et al. SAS Institute Cary, NC, USA Edinburgh, 2013 Outline 1 Optimization at SAS 2 Big Data Optimization at SAS The SAS HPA architecture Support vector machines
More informationMinimize subject to. x S R
Chapter 12 Lagrangian Relaxation This chapter is mostly inspired by Chapter 16 of [1]. In the previous chapters, we have succeeded to find efficient algorithms to solve several important problems such
More informationOptimization in R n Introduction
Optimization in R n Introduction Rudi Pendavingh Eindhoven Technical University Optimization in R n, lecture Rudi Pendavingh (TUE) Optimization in R n Introduction ORN / 4 Some optimization problems designing
More informationDefinition of a Linear Program
Definition of a Linear Program Definition: A function f(x 1, x,..., x n ) of x 1, x,..., x n is a linear function if and only if for some set of constants c 1, c,..., c n, f(x 1, x,..., x n ) = c 1 x 1
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 informationSolving NP Hard problems in practice lessons from Computer Vision and Computational Biology
Solving NP Hard problems in practice lessons from Computer Vision and Computational Biology Yair Weiss School of Computer Science and Engineering The Hebrew University of Jerusalem www.cs.huji.ac.il/ yweiss
More informationOptimization models for targeted offers in direct marketing: exact and heuristic algorithms
Optimization models for targeted offers in direct marketing: exact and heuristic algorithms Fabrice Talla Nobibon, Roel Leus and Frits C.R. Spieksma {Fabrice.TallaNobibon; Roel.Leus; Frits.Spieksma}@econ.kuleuven.be
More informationInteger Programming Formulation
Integer Programming Formulation 1 Integer Programming Introduction When we introduced linear programs in Chapter 1, we mentioned divisibility as one of the LP assumptions. Divisibility allowed us to consider
More informationSome Optimization Fundamentals
ISyE 3133B Engineering Optimization Some Optimization Fundamentals Shabbir Ahmed Email: sahmed@isye.gatech.edu Homepage: www.isye.gatech.edu/~sahmed Basic Building Blocks min or max s.t. objective as
More informationMinimizing costs for transport buyers using integer programming and column generation. Eser Esirgen
MASTER STHESIS Minimizing costs for transport buyers using integer programming and column generation Eser Esirgen DepartmentofMathematicalSciences CHALMERS UNIVERSITY OF TECHNOLOGY UNIVERSITY OF GOTHENBURG
More informationIEOR 4404 Homework #2 Intro OR: Deterministic Models February 14, 2011 Prof. Jay Sethuraman Page 1 of 5. Homework #2
IEOR 4404 Homework # Intro OR: Deterministic Models February 14, 011 Prof. Jay Sethuraman Page 1 of 5 Homework #.1 (a) What is the optimal solution of this problem? Let us consider that x 1, x and x 3
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 informationA stochastic programming approach for supply chain network design under uncertainty
A stochastic programming approach for supply chain network design under uncertainty Tjendera Santoso, Shabbir Ahmed, Marc Goetschalckx, Alexander Shapiro School of Industrial & Systems Engineering, Georgia
More informationLine Planning with Minimal Traveling Time
Line Planning with Minimal Traveling Time Anita Schöbel and Susanne Scholl Institut für Numerische und Angewandte Mathematik, GeorgAugustUniversität Göttingen Lotzestrasse 1618, 37083 Göttingen, Germany
More informationCHAPTER 9. Integer Programming
CHAPTER 9 Integer Programming An integer linear program (ILP) is, by definition, a linear program with the additional constraint that all variables take integer values: (9.1) max c T x s t Ax b and x integral
More informationA Column Generation Model for Truck Routing in the Chilean Forest Industry
A Column Generation Model for Truck Routing in the Chilean Forest Industry Pablo A. Rey Escuela de Ingeniería Industrial, Facultad de Ingeniería, Universidad Diego Portales, Santiago, Chile, email: pablo.rey@udp.cl
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 informationA ColumnGeneration and BranchandCut Approach to the BandwidthPacking Problem
[J. Res. Natl. Inst. Stand. Technol. 111, 161185 (2006)] A ColumnGeneration and BranchandCut Approach to the BandwidthPacking Problem Volume 111 Number 2 MarchApril 2006 Christine Villa and Karla
More informationLecture 11: 01 Quadratic Program and Lower Bounds
Lecture :  Quadratic Program and Lower Bounds (3 units) Outline Problem formulations Reformulation: Linearization & continuous relaxation Branch & Bound Method framework Simple bounds, LP bound and semidefinite
More informationOptimized Scheduling in RealTime Environments with Column Generation
JG U JOHANNES GUTENBERG UNIVERSITAT 1^2 Optimized Scheduling in RealTime Environments with Column Generation Dissertation zur Erlangung des Grades,.Doktor der Naturwissenschaften" am Fachbereich Physik,
More information1 Introduction. Linear Programming. Questions. A general optimization problem is of the form: choose x to. max f(x) subject to x S. where.
Introduction Linear Programming Neil Laws TT 00 A general optimization problem is of the form: choose x to maximise f(x) subject to x S where x = (x,..., x n ) T, f : R n R is the objective function, S
More informationRoute optimization applied to school transports A method combining column generation with greedy heuristics
PREPRINT Route optimization applied to school transports A method combining column generation with greedy heuristics Mikael Andersson Peter Lindroth Department of Mathematics CHALMERS UNIVERSITY OF TECHNOLOGY
More informationProximal mapping via network optimization
L. Vandenberghe EE236C (Spring 234) Proximal mapping via network optimization minimum cut and maximum flow problems parametric minimum cut problem application to proximal mapping Introduction this lecture:
More informationQoS optimization for an. ondemand transportation system via a fractional linear objective function
QoS optimization for an Load charge ratio ondemand transportation system via a fractional linear objective function Thierry Garaix, University of Avignon (France) Column Generation 2008 QoS optimization
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 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 informationLecture 7: Approximation via Randomized Rounding
Lecture 7: Approximation via Randomized Rounding Often LPs return a fractional solution where the solution x, which is supposed to be in {0, } n, is in [0, ] n instead. There is a generic way of obtaining
More informationGENERALIZED INTEGER PROGRAMMING
Professor S. S. CHADHA, PhD University of Wisconsin, Eau Claire, USA Email: schadha@uwec.edu Professor Veena CHADHA University of Wisconsin, Eau Claire, USA Email: chadhav@uwec.edu GENERALIZED INTEGER
More information3. Linear Programming and Polyhedral Combinatorics
Massachusetts Institute of Technology Handout 6 18.433: Combinatorial Optimization February 20th, 2009 Michel X. Goemans 3. Linear Programming and Polyhedral Combinatorics Summary of what was seen in the
More informationLecture 3. Linear Programming. 3B1B Optimization Michaelmas 2015 A. Zisserman. Extreme solutions. Simplex method. Interior point method
Lecture 3 3B1B Optimization Michaelmas 2015 A. Zisserman Linear Programming Extreme solutions Simplex method Interior point method Integer programming and relaxation The Optimization Tree Linear Programming
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 informationINTEGER PROGRAMMING. Integer Programming. Prototype example. BIP model. BIP models
Integer Programming INTEGER PROGRAMMING In many problems the decision variables must have integer values. Example: assign people, machines, and vehicles to activities in integer quantities. If this is
More informationMathematical finance and linear programming (optimization)
Mathematical finance and linear programming (optimization) Geir Dahl September 15, 2009 1 Introduction The purpose of this short note is to explain how linear programming (LP) (=linear optimization) may
More informationRegression Using Support Vector Machines: Basic Foundations
Regression Using Support Vector Machines: Basic Foundations Technical Report December 2004 Aly Farag and Refaat M Mohamed Computer Vision and Image Processing Laboratory Electrical and Computer Engineering
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 informationNew Exact Solution Approaches for the Split Delivery Vehicle Routing Problem
New Exact Solution Approaches for the Split Delivery Vehicle Routing Problem Gizem Ozbaygin, Oya Karasan and Hande Yaman Department of Industrial Engineering, Bilkent University, Ankara, Turkey ozbaygin,
More informationMultiperiod and stochastic formulations for a closed loop supply chain with incentives
Multiperiod and stochastic formulations for a closed loop supply chain with incentives L. G. HernándezLanda, 1, I. Litvinchev, 1 Y. A. RiosSolis, 1 and D. Özdemir2, 1 Graduate Program in Systems Engineering,
More informationOptimal Allocation of renewable Energy Parks: A Two Stage Optimization Model. Mohammad Atef, Carmen Gervet German University in Cairo, EGYPT
Optimal Allocation of renewable Energy Parks: A Two Stage Optimization Model Mohammad Atef, Carmen Gervet German University in Cairo, EGYPT JFPC 2012 1 Overview Egypt & Renewable Energy Prospects Case
More informationAn interval linear programming contractor
An interval linear programming contractor Introduction Milan Hladík Abstract. We consider linear programming with interval data. One of the most challenging problems in this topic is to determine or tight
More informationMixed Integer Programming in Production Planning with Billofmaterials Structures: Modeling and Algorithms
Submitted to manuscript (Please, provide the mansucript number!) Mixed Integer Programming in Production Planning with Billofmaterials Structures: Modeling and Algorithms Tao Wu,, Leyuan Shi, Kerem Akartunalı
More informationMinimizing the Number of Machines in a UnitTime Scheduling Problem
Minimizing the Number of Machines in a UnitTime Scheduling Problem Svetlana A. Kravchenko 1 United Institute of Informatics Problems, Surganova St. 6, 220012 Minsk, Belarus kravch@newman.basnet.by Frank
More informationInteger Programming: Algorithms  3
Week 9 Integer Programming: Algorithms  3 OPR 992 Applied Mathematical Programming OPR 992  Applied Mathematical Programming  p. 1/12 DantzigWolfe Reformulation Example Strength of the Linear Programming
More informationScheduling inbound calls in call centers
Iowa State University Digital Repository @ Iowa State University Graduate Theses and Dissertations Graduate College 2009 Scheduling inbound calls in call centers Somchan Vuthipadadon Iowa State University
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 informationMODELS AND ALGORITHMS FOR WORKFORCE ALLOCATION AND UTILIZATION
MODELS AND ALGORITHMS FOR WORKFORCE ALLOCATION AND UTILIZATION by Ada Yetunde Barlatt A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Industrial
More informationarxiv:cs/0106002v2 [cs.dm] 21 Aug 2001
Solving Assembly Line Balancing Problems by Combining IP and CP Alexander Bockmayr and Nicolai Pisaruk arxiv:cs/0106002v2 [cs.dm] 21 Aug 2001 Université Henri Poincaré, LORIA B.P. 239, F54506 VandœuvrelèsNancy,
More informationFinal Report. to the. Center for Multimodal Solutions for Congestion Mitigation (CMS) CMS Project Number: 2010018
Final Report to the Center for Multimodal Solutions for Congestion Mitigation (CMS) CMS Project Number: 2010018 CMS Project Title: Impacts of Efficient Transportation Capacity Utilization via MultiProduct
More informationReconnect 04 Solving Integer Programs with Branch and Bound (and Branch and Cut)
Sandia is a ultiprogra laboratory operated by Sandia Corporation, a Lockheed Martin Copany, Reconnect 04 Solving Integer Progras with Branch and Bound (and Branch and Cut) Cynthia Phillips (Sandia National
More informationGAMS, Condor and the Grid: Solving Hard Optimization Models in Parallel. Michael C. Ferris University of Wisconsin
GAMS, Condor and the Grid: Solving Hard Optimization Models in Parallel Michael C. Ferris University of Wisconsin Parallel Optimization Aid search for global solutions (typically in nonconvex or discrete)
More informationA Stochastic Programming Model for Scheduling Call Centers with Global Service Level Agreements
A Stochastic Programming Model for Scheduling Call Centers with Global Service Level Agreements Working Paper Thomas R. Robbins Terry P. Harrison Department of Supply Chain and Information Systems, Smeal
More informationChapter 13: Binary and MixedInteger Programming
Chapter 3: Binary and MixedInteger Programming The general branch and bound approach described in the previous chapter can be customized for special situations. This chapter addresses two special situations:
More informationWarshall s Algorithm: Transitive Closure
CS 0 Theory of Algorithms / CS 68 Algorithms in Bioinformaticsi Dynamic Programming Part II. Warshall s Algorithm: Transitive Closure Computes the transitive closure of a relation (Alternatively: all paths
More informationSBB: A New Solver for Mixed Integer Nonlinear Programming
SBB: A New Solver for Mixed Integer Nonlinear Programming Michael R. Bussieck GAMS Development Corp. Arne S. Drud ARKI Consulting & Development A/S OR2001, Duisburg Overview! SBB = Simple Branch & Bound!
More informationLecture 10 Scheduling 1
Lecture 10 Scheduling 1 Transportation Models 1 large variety of models due to the many modes of transportation roads railroad shipping airlines as a consequence different type of equipment and resources
More informationChapter 3 INTEGER PROGRAMMING 3.1 INTRODUCTION. Robert Bosch. Michael Trick
Chapter 3 INTEGER PROGRAMMING Robert Bosch Oberlin College Oberlin OH, USA Michael Trick Carnegie Mellon University Pittsburgh PA, USA 3.1 INTRODUCTION Over the last 20 years, the combination of faster
More informationIntroduction to Stochastic Optimization in Supply Chain and Logistic Optimization
Introduction to Stochastic Optimization in Supply Chain and Logistic Optimization John R. Birge Northwestern University IMA Tutorial, Stochastic Optimization, September 00 1 Outline Overview Part I  Models
More informationMultilayer MPLS Network Design: the Impact of Statistical Multiplexing
Multilayer MPLS Network Design: the Impact of Statistical Multiplexing Pietro Belotti, Antonio Capone, Giuliana Carello, Federico Malucelli Tepper School of Business, Carnegie Mellon University, Pittsburgh
More informationAn Expressive Auction Design for Online Display Advertising. AUTHORS: Sébastien Lahaie, David C. Parkes, David M. Pennock
An Expressive Auction Design for Online Display Advertising AUTHORS: Sébastien Lahaie, David C. Parkes, David M. Pennock Li PU & Tong ZHANG Motivation Online advertisement allow advertisers to specify
More informationStrategic planning in LTL logistics increasing the capacity utilization of trucks
Strategic planning in LTL logistics increasing the capacity utilization of trucks J. Fabian Meier 1,2 Institute of Transport Logistics TU Dortmund, Germany Uwe Clausen 3 Fraunhofer Institute for Material
More informationA Constraint Programming based Column Generation Approach to Nurse Rostering Problems
Abstract A Constraint Programming based Column Generation Approach to Nurse Rostering Problems Fang He and Rong Qu The Automated Scheduling, Optimisation and Planning (ASAP) Group School of Computer Science,
More informationCloud Branching. Timo Berthold. joint work with Domenico Salvagnin (Università degli Studi di Padova)
Cloud Branching Timo Berthold Zuse Institute Berlin joint work with Domenico Salvagnin (Università degli Studi di Padova) DFG Research Center MATHEON Mathematics for key technologies 21/May/13, CPAIOR
More informationWater networks security: A twostage mixedinteger stochastic program for sensor placement under uncertainty
Computers and Chemical Engineering 31 (2007) 565 573 Water networks security: A twostage mixedinteger stochastic program for sensor placement under uncertainty Vicente RicoRamirez a,, Sergio FraustoHernandez
More informationCombining (Integer) Linear Programming Techniques and Metaheuristics for Combinatorial Optimization
Combining (Integer) Linear Programming Techniques and Metaheuristics for Combinatorial Optimization Günther R. Raidl 1 and Jakob Puchinger 2 1 Institute of Computer Graphics and Algorithms, Vienna University
More informationModels in Transportation. Tim Nieberg
Models in Transportation Tim Nieberg Transportation Models large variety of models due to the many modes of transportation roads railroad shipping airlines as a consequence different type of equipment
More informationIntroduction to Support Vector Machines. Colin Campbell, Bristol University
Introduction to Support Vector Machines Colin Campbell, Bristol University 1 Outline of talk. Part 1. An Introduction to SVMs 1.1. SVMs for binary classification. 1.2. Soft margins and multiclass classification.
More informationDistributed and Scalable QoS Optimization for Dynamic Web Service Composition
Distributed and Scalable QoS Optimization for Dynamic Web Service Composition Mohammad Alrifai L3S Research Center Leibniz University of Hannover, Germany alrifai@l3s.de Supervised by: Prof. Dr. tech.
More informationWeek 5 Integral Polyhedra
Week 5 Integral Polyhedra We have seen some examples 1 of linear programming formulation that are integral, meaning that every basic feasible solution is an integral vector. This week we develop a theory
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 informationOptimizing Call Center Staffing using Simulation and Analytic Center Cutting Plane Methods
Submitted to Management Science manuscript MS009982004.R1 Optimizing Call Center Staffing using Simulation and Analytic Center Cutting Plane Methods Júlíus Atlason, Marina A. Epelman Department of Industrial
More informationIn this paper we present a branchandcut algorithm for
SOLVING A TRUCK DISPATCHING SCHEDULING PROBLEM USING BRANCHANDCUT ROBERT E. BIXBY Rice University, Houston, Texas EVA K. LEE Georgia Institute of Technology, Atlanta, Georgia (Received September 1994;
More informationBranch, Cut, and Price: Sequential and Parallel
Branch, Cut, and Price: Sequential and Parallel T.K. Ralphs 1, L. Ladányi 2, and L.E. Trotter, Jr. 3 1 Department of Industrial and Manufacturing Systems Engineering, Lehigh University, Bethlehem, PA 18017,
More informationA Branch and Bound Algorithm for Solving the Binary Bilevel Linear Programming Problem
A Branch and Bound Algorithm for Solving the Binary Bilevel Linear Programming Problem John Karlof and Peter Hocking Mathematics and Statistics Department University of North Carolina Wilmington Wilmington,
More informationLarge Neighborhood Search beyond MIP
KonradZuseZentrum für Informationstechnik Berlin Takustraße 7 D14195 BerlinDahlem Germany TIMO BERTHOLD, STEFAN HEINZ, MARC E. PFETSCH 1, STEFAN VIGERSKE 2, Large Neighborhood Search beyond MIP 1 2
More informationOptimal Bandwidth Sharing in MultiSwarm MultiParty P2P Video Conferencing Systems
1 Optimal Bandwidth Sharing in MultiSwarm MultiParty P2P Video Conferencing Systems Chao Liang, Student Member, IEEE, Miao Zhao, Member, IEEE, and Yong Liu, Member, IEEE Abstract In a multiparty video
More information6.231 Dynamic Programming and Stochastic Control Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 6.231 Dynamic Programming and Stochastic Control Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 6.231
More informationCOMP 250 Fall 2012 lecture 2 binary representations Sept. 11, 2012
Binary numbers The reason humans represent numbers using decimal (the ten digits from 0,1,... 9) is that we have ten fingers. There is no other reason than that. There is nothing special otherwise about
More informationModeling Integer and Combinatorial Programs
Contents 7 Modeling Integer and Combinatorial Programs 287 7.1 Types of Integer Programs, an Example Puzzle Problem, andaclassicalsolutionmethod... 287 7.2 TheKnapsackProblems... 296 7.3 Set Covering,
More informationDynamic Programming. Applies when the following Principle of Optimality
Dynamic Programming Applies when the following Principle of Optimality holds: In an optimal sequence of decisions or choices, each subsequence must be optimal. Translation: There s a recursive solution.
More information