QoS optimization for an. ondemand transportation system via a fractional linear objective function


 Antony Elwin Goodman
 2 years ago
 Views:
Transcription
1 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 for an ondemand transportation system via a fractional linear objective function p. 1
2 Plan Ondemand transportation system (DARP) Load charge ratio Column generation for the DARP Maximization of the loading rate Computational results and observations QoS optimization for an ondemand transportation system via a fractional linear objective function p. 2
3 Dialaride Problem (DARP) PickUp & Delivery with Time Windows + QoS constraints A roadnetwork: travel times, distances... Introduction DARP Classical method QoS Load charge ratio R requests r pickup r +, dropoff r points load F r, time windows [T inf r, T sup r ] K vehicles type k depots k +, k, quantity K k, capacity F k, km cost, speed 10: :55 9: :00 10:00 8: :25 13:00 9: :10 11:50 12:00 QoS optimization for an ondemand transportation system via a fractional linear objective function p. 3
4 Master problem min ω Ω C ω λ ω Introduction DARP Classical method QoS Load charge ratio subject to λ ω ρ ωr = 1 ω Ω λ ω K k ω Ω k λ ω integer r = 1,..., R k = 1,..., K ω Ω Ω k : feasible routes with vehicle type k, Ω = K k=1 Ω k Objective function minimizes total inconvenience ρ ωr {0,1} : request r is in route ω QoS optimization for an ondemand transportation system via a fractional linear objective function p. 4
5 Introduction DARP Classical method QoS Load charge ratio Slave problems RC ω = C ω = (i,j) ω (i,j) ω C ij (C ij π ij ) ω: arcs of ω, π ij : well defined dual cost We model slave problem as an ESPPRC solved by dynamic programming Label L is a partial path ending in v L at time T L with open requests O L, closed requests that are still time reachable S L and a cost C L Dominance rule: v L = v M, T L T M, O L O M and S L S M O M T M and C L C M ; T M are time reachable requests for M QoS optimization for an ondemand transportation system via a fractional linear objective function p. 5
6 Quality of service We develop an algorithm using robust accelerations (LDS, heuristic... ). We solve instances with 100 requests Introduction DARP Classical method QoS Load charge ratio Adaptation to new QoS criteria? time lost for inbound and outbound requests Cost resource extension fonction is not nondecreasing distance Working network is a pgraph of nondominated (distance/time) paths loading rate Fractional linear objective function QoS optimization for an ondemand transportation system via a fractional linear objective function p. 6
7 Loading rate Definition Iterative method Loading rate: number of passengers times their travel time divided by the total travel time of vehicles max P P ω Ω N ωλ ω ω Ω D ωλ ω = N(λ) D(λ) f ij (variables): passenger flow N ω = (i,j) ω f ijt ij D ω = (i,j) ω T ij T ij (data): travel time. We exclude waiting times Practical interests: Good indicator for local authorities, that prefer fullloaded vehicles on road A social impact QoS optimization for an ondemand transportation system via a fractional linear objective function p. 7
8 Direct algorithm CharnesCooper (62) Change of variable x = 1/ ω Ω D ωλ ω : max x ω Ω N ωλ ω Direct method Iterative method s.t. x ω Ω λ ωρ ωr = x, r = 1,..., R x ω Ω k λ ω xk k x ω Ω D ωλ ω = 1 xλ ω 0 x 0, k = 1,..., K, ω Ω λ ω xλ ω : max ω Ω N ωλ ω s.t. ω Ω λ ωρ ωr = x, r = 1,..., R ω Ω k λ ω xk k, k = 1,..., K ω Ω D ωλ ω = 1 λ ω 0, ω Ω x 0 QoS optimization for an ondemand transportation system via a fractional linear objective function p. 8
9 Direct algorithm slave problem ESPPRC: min ω Ω N ωλ ω Direct method Iterative method C ω = (i,j) ω f it ij RC ω = C ω (i,j) ω (π ij + µt ij ) New dominance rule: v L = v M, T L T M, O L O M C L C M and S L S M O M T L become C L C M + r O M \O L det(r, T M ) + r S L \(S M O M T M ) min{det(r+, T M ) + det(r, T M ),0} QoS optimization for an ondemand transportation system via a fractional linear objective function p. 9
10 Direct algorithm slave problem Lower bounds on detours by vertex v Direct method Iterative method Compare each feasible arc (u, w) with path (u, v, w) det(v, t) = min u,w V ( µ f u )(T uv + T vu T uw ) F v T vw π uv Durations observe triangular inequality Prepreprocessing max f u depending on u,v and w type, since other values are constant at each iteration QoS optimization for an ondemand transportation system via a fractional linear objective function p. 10
11 Iterative algorithm Dinkelbach(67) P = {λ R + : ω Ω λ ωρ ωr = 1 r = 1,..., R; ω Ω k λ ω K k k = 1,..., K} Iterative method MP: max λ P q(λ) = N(λ)/D(λ) Introduce F(x) = max λ P N(λ) xd(λ) Propertie: λ is optimal for MP F(q(λ )) = 0 Find λ n s.t. q(λ ) q(λ n ) < δ, δ > 0 Find λ n s.t. F(q(λ n )) < ε, ε > 0 Since F(x) is decreasing and F(q(λ )) = 0 Proof: q(λ 0 ) = N(λ 0 )/D(λ 0 ) F(q(λ 0 )) 0 F(q(λ 0 )) = 0 0 > N(λ) q(λ 0 )D(λ), λ q(λ 0 ) = max λ P N(λ)/D(λ) QoS optimization for an ondemand transportation system via a fractional linear objective function p. 11
12 Iterative algorithm Iterative method Sequence (λ n ): λ n+1 is defined as the optimal solution of F(q(λ n )) = max λ P N(λ) q(λ n )D(λ) Sequence (q n ) = q(λ n ) = N(λ n 1 )/D(λ n 1 ) increases and converges Algorithm builds (λ n ) and stops when F(q n ) < ε Two schemes integrate column generation (CG): Apply Dinkelbach algorithm on MP Apply Dinkelbach algorithm on each RMP BranchandBound scheme is based on q n values QoS optimization for an ondemand transportation system via a fractional linear objective function p. 12
13 Iterative algorithm λ 0 = λ 1 Ω {λ i } Ω {λ i } λ 0 = λ 1 Iterative method Solve LP F(q 0 ) = max λ P N(λ) q 0 D(λ) q 1 = N(λ 1 )/D(λ 1 ) F(q 0 ) = N(λ 1 ) q 0 D(λ 1 ) Solve LP F(q 0 ) = max λ P N(λ) q 0 D(λ) q 1 = N(λ 1 )/D(λ 1 ) F(q 0 ) = N(λ 1 ) q 0 D(λ 1 ) λ i with positive reduced cost? no yes F(q 0 ) ε? no yes yes F(q 0 ) ε? no yes λ i with positive reduced cost? no STOP STOP QoS optimization for an ondemand transportation system via a fractional linear objective function p. 13
14 Iterative algorithm slave problem ESPPRC: min F(q 0 ) = q 0 D(λ) N(λ) Iterative method C ω = (i,j) ω q0 T ij f i T ij RC ω = C ω (i,j) ω π ij Same remarks as for the direct algorithm and lower bounds on detours: det(v, t) = min u,w V (q 0 f u )(T uv + T vu + T uw ) F v T vw π uv Prepreprocessing max f u QoS optimization for an ondemand transportation system via a fractional linear objective function p. 14
15 Instances Iterative method Two benchmarks Li and Lim ( 50 requests) from Solomon s Cordeau (from 16 to 96 requests) One vehicle type Modifications We compute new tight time windows T sup T inf = 1.5T r r + r + r QoS optimization for an ondemand transportation system via a fractional linear objective function p. 15
16 Results on random Li & Lim s Iterative method instance loading rate cpu sec. name min D(λ) max N(λ)/D(λ) direct iterative r r r r r r r r r r r r QoS optimization for an ondemand transportation system via a fractional linear objective function p. 16
17 Results on cluster Li & Lim s Iterative method instance loading rate cpu sec. name min D(λ) max N(λ)/D(λ) direct iterative c c c c c c c c c QoS optimization for an ondemand transportation system via a fractional linear objective function p. 17
18 Results on random/cluster Li & Lim s Iterative method instance loading rate cpu sec. name min D(λ) max N(λ)/D(λ) direct iterative rc rc rc rc rc rc rc rc QoS optimization for an ondemand transportation system via a fractional linear objective function p. 18
19 Iterative method Results on Cordeau s instance loading rate cpu sec. name min D(λ) max N(λ)/D(λ) direct iterative b b b b b b b b b b b b b b b b b b b b b b b b QoS optimization for an ondemand transportation system via a fractional linear objective function p. 19
20 Conclusions Iterative method Generic schemes managing fractional linear objective function with column generation They succeed in solving our problem Travel time minimization also (almost) optimizes loading rate We could implement many of classical acceleration methods in the proposed algorithm have to be carried out with less bounded numerator and denominator in order to test the convergence speed QoS optimization for an ondemand transportation system via a fractional linear objective function p. 20
BranchandPrice 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 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 informationVehicle routing problems with alternative paths: an application to ondemand transportation
Vehicle routing problems with alternative paths: an application to ondemand transportation Thierry Garaix, Christian Artigues, Dominique Feillet, Didier Josselin To cite this version: Thierry Garaix,
More informationA hierarchical multicriteria routing model with traffic splitting for MPLS networks
A hierarchical multicriteria routing model with traffic splitting for MPLS networks João Clímaco, José Craveirinha, Marta Pascoal jclimaco@inesccpt, jcrav@deecucpt, marta@matucpt University of Coimbra
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 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 informationBranchandPrice for the Truck and Trailer Routing Problem with Time Windows
BranchandPrice for the Truck and Trailer Routing Problem with Time Windows Sophie N. Parragh JeanFrançois Cordeau October 2015 BranchandPrice for the Truck and Trailer Routing Problem with Time Windows
More informationTwo objective functions for a real life Split Delivery Vehicle Routing Problem
International Conference on Industrial Engineering and Systems Management IESM 2011 May 25  May 27 METZ  FRANCE Two objective functions for a real life Split Delivery Vehicle Routing Problem Marc Uldry
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 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 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 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 informationOptimal Vehicle Routing and Scheduling with Precedence Constraints and Location Choice
Optimal Vehicle Routing and Scheduling with Precedence Constraints and Location Choice G. Ayorkor Korsah, Anthony Stentz, M. Bernardine Dias, and Imran Fanaswala Abstract To realize the vision of intelligent
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 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 informationDantzigWolfe bound and DantzigWolfe cookbook
DantzigWolfe bound and DantzigWolfe cookbook thst@man.dtu.dk DTUManagement Technical University of Denmark 1 Outline LP strength of the DantzigWolfe The exercise from last week... The DantzigWolfe
More information2.3 Convex Constrained Optimization Problems
42 CHAPTER 2. FUNDAMENTAL CONCEPTS IN CONVEX OPTIMIZATION Theorem 15 Let f : R n R and h : R R. Consider g(x) = h(f(x)) for all x R n. The function g is convex if either of the following two conditions
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 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 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 informationSolving the Vehicle Routing Problem with Multiple Trips by Adaptive Memory Programming
Solving the Vehicle Routing Problem with Multiple Trips by Adaptive Memory Programming Alfredo Olivera and Omar Viera Universidad de la República Montevideo, Uruguay ICIL 05, Montevideo, Uruguay, February
More informationColumn Generation for the Pickup and Delivery Problem with Time Windows
Column Generation for the Pickup and Delivery Problem with Time Windows Kombinatorisk optimering 1. april 2005 Stefan Røpke Joint work with JeanFrançois Cordeau Work in progress! Literature, homework
More informationModeling and solving vehicle routing problems with many available vehicle types
MASTER S THESIS Modeling and solving vehicle routing problems with many available vehicle types SANDRA ERIKSSON BARMAN Department of Mathematical Sciences Division of Mathematics CHALMERS UNIVERSITY OF
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 informationThe vehicle routing problem with time windows is a hard combinatorial optimization problem that has
TRANSPORTATION SCIENCE Vol. 38, No. 4, November 2004, pp. 515 530 issn 00411655 eissn 15265447 04 3804 0515 informs doi 10.1287/trsc.1030.0049 2004 INFORMS A TwoStage Hybrid Local Search for the Vehicle
More information1 Norms and Vector Spaces
008.10.07.01 1 Norms and Vector Spaces Suppose we have a complex vector space V. A norm is a function f : V R which satisfies (i) f(x) 0 for all x V (ii) f(x + y) f(x) + f(y) for all x,y V (iii) f(λx)
More informationA Service Design Problem for a Railway Network
A Service Design Problem for a Railway Network Alberto Caprara Enrico Malaguti Paolo Toth Dipartimento di Elettronica, Informatica e Sistemistica, University of Bologna Viale Risorgimento, 240136  Bologna
More informationDecision Mathematics D1 Advanced/Advanced Subsidiary. Tuesday 5 June 2007 Afternoon Time: 1 hour 30 minutes
Paper Reference(s) 6689/01 Edexcel GCE Decision Mathematics D1 Advanced/Advanced Subsidiary Tuesday 5 June 2007 Afternoon Time: 1 hour 30 minutes Materials required for examination Nil Items included with
More informationDave Sly, PhD, MBA, PE Iowa State University
Dave Sly, PhD, MBA, PE Iowa State University Tuggers deliver to multiple locations on one trip, where Unit Load deliveries involve only one location per trip. Tugger deliveries are more complex since the
More informationModeling and Solving the Capacitated Vehicle Routing Problem on Trees
in The Vehicle Routing Problem: Latest Advances and New Challenges Modeling and Solving the Capacitated Vehicle Routing Problem on Trees Bala Chandran 1 and S. Raghavan 2 1 Department of Industrial Engineering
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 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 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 informationHet inplannen van besteld ambulancevervoer (Engelse titel: Scheduling elected ambulance transportation)
Technische Universiteit Delft Faculteit Elektrotechniek, Wiskunde en Informatica Delft Institute of Applied Mathematics Het inplannen van besteld ambulancevervoer (Engelse titel: Scheduling elected ambulance
More informationOn the Technician Routing and Scheduling Problem
On the Technician Routing and Scheduling Problem July 25, 2011 Victor Pillac *, Christelle Guéret *, Andrés Medaglia * Equipe Systèmes Logistiques et de Production (SLP), IRCCyN Ecole des Mines de Nantes,
More informationThe Trip Scheduling Problem
The Trip Scheduling Problem Claudia Archetti Department of Quantitative Methods, University of Brescia Contrada Santa Chiara 50, 25122 Brescia, Italy Martin Savelsbergh School of Industrial and Systems
More informationLecture 15 An Arithmetic Circuit Lowerbound and Flows in Graphs
CSE599s: Extremal Combinatorics November 21, 2011 Lecture 15 An Arithmetic Circuit Lowerbound and Flows in Graphs Lecturer: Anup Rao 1 An Arithmetic Circuit Lower Bound An arithmetic circuit is just like
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 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 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 informationOptimizing departure times in vehicle routes
Optimizing departure times in vehicle routes A.L. Kok, E.W. Hans, J.M.J. Schutten Operational Methods for Production and Logistics, University of Twente, P.O. Box 217, 7500AE, Enschede, Netherlands Abstract
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 informationHybrid Heterogeneous Electric Fleet Routing Problem with City Center Restrictions
Hybrid Heterogeneous Electric Fleet Routing Problem with City Center Restrictions Gerhard Hiermann 1, Richard Hartl 2, Jakob Puchinger 1, Thibaut Vidal 3 1 AIT Austrian Institute of Technology 2 University
More informationRandomization Approaches for Network Revenue Management with Customer Choice Behavior
Randomization Approaches for Network Revenue Management with Customer Choice Behavior Sumit Kunnumkal Indian School of Business, Gachibowli, Hyderabad, 500032, India sumit kunnumkal@isb.edu March 9, 2011
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 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 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 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 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 informationIntegrating Benders decomposition within Constraint Programming
Integrating Benders decomposition within Constraint Programming Hadrien Cambazard, Narendra Jussien email: {hcambaza,jussien}@emn.fr École des Mines de Nantes, LINA CNRS FRE 2729 4 rue Alfred Kastler BP
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 informationConvex Programming Tools for Disjunctive Programs
Convex Programming Tools for Disjunctive Programs João Soares, Departamento de Matemática, Universidade de Coimbra, Portugal Abstract A Disjunctive Program (DP) is a mathematical program whose feasible
More informationCollaborative transportation planning of lessthantruckload freight
OR Spectrum DOI 10.1007/s002910130331x REGULAR ARTICLE Collaborative transportation planning of lessthantruckload freight A routebased request exchange mechanism Xin Wang Herbert Kopfer SpringerVerlag
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 informationResearch Paper Business Analytics. Applications for the Vehicle Routing Problem. Jelmer Blok
Research Paper Business Analytics Applications for the Vehicle Routing Problem Jelmer Blok Applications for the Vehicle Routing Problem Jelmer Blok Research Paper Vrije Universiteit Amsterdam Faculteit
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 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 informationRouting and Scheduling in Tramp Shipping  Integrating Bunker Optimization Technical report
Downloaded from orbit.dtu.dk on: Jul 04, 2016 Routing and Scheduling in Tramp Shipping  Integrating Bunker Optimization Technical report Vilhelmsen, Charlotte; Lusby, Richard Martin ; Larsen, Jesper Publication
More informationOn a Railway Maintenance Scheduling Problem with Customer Costs and MultiDepots
Als Manuskript gedruckt Technische Universität Dresden Herausgeber: Der Rektor On a Railway Maintenance Scheduling Problem with Customer Costs and MultiDepots F. Heinicke (1), A. Simroth (1), G. Scheithauer
More informationA hybrid approach for solving realworld nurse rostering problems
Presentation at CP 2011: A hybrid approach for solving realworld nurse rostering problems Martin Stølevik (martin.stolevik@sintef.no) Tomas Eric Nordlander (tomas.nordlander@sintef.no) Atle Riise (atle.riise@sintef.no)
More informationGenOpt (R) Generic Optimization Program User Manual Version 3.0.0β1
(R) User Manual Environmental Energy Technologies Division Berkeley, CA 94720 http://simulationresearch.lbl.gov Michael Wetter MWetter@lbl.gov February 20, 2009 Notice: This work was supported by the U.S.
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 informationEigenvalues and eigenvectors of a matrix
Eigenvalues and eigenvectors of a matrix Definition: If A is an n n matrix and there exists a real number λ and a nonzero column vector V such that AV = λv then λ is called an eigenvalue of A and V is
More informationApproximation Algorithms: LP Relaxation, Rounding, and Randomized Rounding Techniques. My T. Thai
Approximation Algorithms: LP Relaxation, Rounding, and Randomized Rounding Techniques My T. Thai 1 Overview An overview of LP relaxation and rounding method is as follows: 1. Formulate an optimization
More informationA Network Flow Approach in Cloud Computing
1 A Network Flow Approach in Cloud Computing Soheil Feizi, Amy Zhang, Muriel Médard RLE at MIT Abstract In this paper, by using network flow principles, we propose algorithms to address various challenges
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 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 informationLinear Programming for Optimization. Mark A. Schulze, Ph.D. Perceptive Scientific Instruments, Inc.
1. Introduction Linear Programming for Optimization Mark A. Schulze, Ph.D. Perceptive Scientific Instruments, Inc. 1.1 Definition Linear programming is the name of a branch of applied mathematics that
More informationOnline vehicle routing and scheduling with continuous vehicle tracking
Online vehicle routing and scheduling with continuous vehicle tracking Jean Respen, Nicolas Zufferey, JeanYves Potvin To cite this version: Jean Respen, Nicolas Zufferey, JeanYves Potvin. Online vehicle
More informationRouting in Line Planning for Public Transport
KonradZuseZentrum für Informationstechnik Berlin Takustraße 7 D14195 BerlinDahlem Germany MARC E. PFETSCH RALF BORNDÖRFER Routing in Line Planning for Public Transport Supported by the DFG Research
More informationA Linear Programming Based Method for Job Shop Scheduling
A Linear Programming Based Method for Job Shop Scheduling Kerem Bülbül Sabancı University, Manufacturing Systems and Industrial Engineering, OrhanlıTuzla, 34956 Istanbul, Turkey bulbul@sabanciuniv.edu
More informationFurther Study on Strong Lagrangian Duality Property for Invex Programs via Penalty Functions 1
Further Study on Strong Lagrangian Duality Property for Invex Programs via Penalty Functions 1 J. Zhang Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing
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 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 informationPUBLIC TRANSPORT ON DEMAND
MASTER S THESIS SUMMARY PUBLIC TRANSPORT ON DEMAND A better match between passenger demand and capacity M.H. Matena C o n n e x x i o n L a a p e r s v e l d 7 5 1213 BV Hilversum PUBLIC TRANSPORT ON
More informationError Bound for Classes of Polynomial Systems and its Applications: A Variational Analysis Approach
Outline Error Bound for Classes of Polynomial Systems and its Applications: A Variational Analysis Approach The University of New South Wales SPOM 2013 Joint work with V. Jeyakumar, B.S. Mordukhovich and
More informationNew Benchmark Instances for the Capacitated Vehicle Routing Problem
New Benchmark Instances for the Capacitated Vehicle Routing Problem Eduardo Uchoa* 1, Diego Pecin 2, Artur Pessoa 1, Marcus Poggi 2, Anand Subramanian 3, Thibaut Vidal 2 1 Universidade Federal Fluminense,
More informationThe Goldberg Rao Algorithm for the Maximum Flow Problem
The Goldberg Rao Algorithm for the Maximum Flow Problem COS 528 class notes October 18, 2006 Scribe: Dávid Papp Main idea: use of the blocking flow paradigm to achieve essentially O(min{m 2/3, n 1/2 }
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 informationOptimizing the Placement of Integration Points in Multihop Wireless Networks
Optimizing the Placement of Integration Points in Multihop Wireless Networks Ranveer Chandra, Lili Qiu, Kamal Jain, Mohammad Mahdian Cornell University Microsoft Research Abstract Efficient integration
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 informationOn the effect of forwarding table size on SDN network utilization
IBM Haifa Research Lab On the effect of forwarding table size on SDN network utilization Rami Cohen IBM Haifa Research Lab Liane Lewin Eytan Yahoo Research, Haifa Seffi Naor CS Technion, Israel Danny Raz
More informationComputer Algorithms. NPComplete Problems. CISC 4080 Yanjun Li
Computer Algorithms NPComplete Problems NPcompleteness The quest for efficient algorithms is about finding clever ways to bypass the process of exhaustive search, using clues from the input in order
More informationOffline sorting buffers on Line
Offline sorting buffers on Line Rohit Khandekar 1 and Vinayaka Pandit 2 1 University of Waterloo, ON, Canada. email: rkhandekar@gmail.com 2 IBM India Research Lab, New Delhi. email: pvinayak@in.ibm.com
More informationChap 4 The Simplex Method
The Essence of the Simplex Method Recall the Wyndor problem Max Z = 3x 1 + 5x 2 S.T. x 1 4 2x 2 12 3x 1 + 2x 2 18 x 1, x 2 0 Chap 4 The Simplex Method 8 corner point solutions. 5 out of them are CPF solutions.
More informationAdaptive Memory Programming for the Vehicle Routing Problem with Multiple Trips
Adaptive Memory Programming for the Vehicle Routing Problem with Multiple Trips Alfredo Olivera, Omar Viera Instituto de Computación, Facultad de Ingeniería, Universidad de la República, Herrera y Reissig
More informationBeyond the Stars: Revisiting Virtual Cluster Embeddings
Beyond the Stars: Revisiting Virtual Cluster Embeddings Matthias Rost Technische Universität Berlin September 7th, 2015, TélécomParisTech Joint work with Carlo Fuerst, Stefan Schmid Published in ACM SIGCOMM
More informationDynamic Vehicle Routing in MATSim
Poznan University of Technology Department of Motor Vehicles and Road Transport ZPSiTD Dynamic Vehicle Routing in MATSim Simulation and Optimization Michal Maciejewski michal.maciejewski@put.poznan.pl
More informationNumerical Analysis Lecture Notes
Numerical Analysis Lecture Notes Peter J. Olver 5. Inner Products and Norms The norm of a vector is a measure of its size. Besides the familiar Euclidean norm based on the dot product, there are a number
More informationCOORDINATION PRODUCTION AND TRANSPORTATION SCHEDULING IN THE SUPPLY CHAIN ABSTRACT
Technical Report #98T010, Department of Industrial & Mfg. Systems Egnieering, Lehigh Univerisity (1998) COORDINATION PRODUCTION AND TRANSPORTATION SCHEDULING IN THE SUPPLY CHAIN Kadir Ertogral, S. David
More informationGuessing Game: NPComplete?
Guessing Game: NPComplete? 1. LONGESTPATH: Given a graph G = (V, E), does there exists a simple path of length at least k edges? YES 2. SHORTESTPATH: Given a graph G = (V, E), does there exists a simple
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 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 informationA Method for Scheduling Integrated Transit Service
A Method for Scheduling Integrated Transit Service Mark Hickman Department of Civil Engineering and Engineering Mechanics The University of Arizona P.O. Box 210072 Tucson, AZ 857210072 USA Phone: (520)
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 informationMartin Savelsbergh. Georgia Institute of Technology. Joint work with Alan Erera, Mike Hewitt, Yang Zhang
Dynamic Load Planning for LessThanTruckload Carriers Schneider Professor Georgia Institute of Technology Joint work with Alan Erera, Mike Hewitt, Yang Zhang TRANSLOG, December 10, 2009 Part I: Advances
More informationCost Models for Vehicle Routing Problems. 8850 Stanford Boulevard, Suite 260 R. H. Smith School of Business
0769514359/02 $17.00 (c) 2002 IEEE 1 Cost Models for Vehicle Routing Problems John Sniezek Lawerence Bodin RouteSmart Technologies Decision and Information Technologies 8850 Stanford Boulevard, Suite
More informationNonlinear Optimization: Algorithms 3: Interiorpoint methods
Nonlinear Optimization: Algorithms 3: Interiorpoint methods INSEAD, Spring 2006 JeanPhilippe Vert Ecole des Mines de Paris JeanPhilippe.Vert@mines.org Nonlinear optimization c 2006 JeanPhilippe Vert,
More information