On step fixed-charge hub location problem
|
|
- Amberly Miller
- 5 years ago
- Views:
Transcription
1 On step fixed-charge hub location problem Marcos Roberto Silva DEOP - Departamento de Engenharia Operacional Patrus Transportes Urgentes Ltda , Guarulhos, SP marcos.roberto.silva@uol.com.br Keywords: mathematical modeling, hub location, fixed-charge, step function, tabu search Abstract: In this paper we introduce the on step fixed-charge hub location problem. We believe that this problem was never studied before, where the hub location problem has a step objective function, and fixed cost is imposed for every arc of the hub-and-spoke network. A mathematical model, and a solution approach based on tabu search heuristic is proposed, showing promising results, considering the potential of practical application in different areas, such as transportation and telecommunication network design. 1 Introduction In this paper we study the problem of configuring a hub-and-spoke network where fixed cost is incurred for every arc that is used in the network. The step fixed-charge hub location problem is a variation of the hub location problem, where the fixed cost is in the form of a step function dependent on the load in a given route. Hubs are special facilities that serve as switching, transshipment and sorting points in manyto-many distribution systems. Instead of serving each origin-destination pair directly, hub facilities concentrate flows in order to take advantage of economies of scale. Flows from the same origin with different destinations are consolidated on their route to the hub and are combined with flows that have different origins but the same destination. The consolidation is on the route from the origin to the hub and from the hub to the destination as well as between hubs [1]. A recent survey of hub location problems is presented in [6]. The Uncapacitated Single Allocation p-hub Median Problem (USApHMP), first introduced by [13], was chosen to be used as a case study in this paper, with the inclusion of fixed costs in the arcs of the hub-and-spoke network. The USApHMP was largely studied in the literature with more than 20 papers published until 2008 [1], with exact and heuristic solution methods proposed, including branch-and-bound [4], tabu search [16], simulated annealing [3], Lagrangean relaxation heuristic [14], local search [10], to name a few. We believe that this is the first work that studies the fixed-charge hub location problem where the objetive function is a step function. This problem has various application areas in transportation (air passenger, cargo) and telecommunication network design. In less-than-truckload (LTL) trucking transportation, when a route between terminals is opened, it is necessary to define the kind of vehicle to use, depending on the flow, incurring on different fixed costs for different models of vehicles. In the telecommunications industry, it represents the design of private networks that use digital transmission facilities (called T1 circuits) to carry voice and data traffic between locations. Given an organization s forecast for data and voice traffic between its various locations, the 660
2 problem consists of defining the configuration of transmission facilities between the locations (nodes) providing the necessary link capacities to carry this traffic at minimum cost [12]. In Section 2 we present the mathematical formulation of the problem. In Section 3 the computational results are presented, and in Section 4 the conclusions and some further directions are outlined. 2 Mathematical formulation The on step fixed-charge hub location problem was formulated based on the approach used by [5] for the capacitated single allocation hub location problem (CSAHLP) and in [11] for the on step fixed-charge transportation problem. Let N be the set of nodes, C ij be the transportation cost per unit flow between nodes i and j, and W ij be the amount of flow from origin i to destination j. The path from an origin spoke node i to a destination spoke node j includes three components: collection from spoke node i to its designated hub k, transfer between hubs k and l, and distribution from hub l to destination spoke j. The cost per unit flow along this route (i k l j) is given by χc ik + αc kl + δc lj, where χ, α and δ denote cost multipliers on the collection, transfer and distribution, respectively. Usually α is much smaller than χ and δ due to volume discount on inter-hub links. A factor α < 1 was originally proposed by [13] to represent an economy of scale on the transportation cost between hubs; the two other factors, χ and δ, were later introduced by [3] to properly represent the reality of postal services costs, especially different modes that can be used in mail collection and distribution. We define the variable Ykl i as the total amount of flow of commodity i (i.e. traffic emanating from node i) that is routed between hubs k and l. The variable Z ik equals one if node i is assigned to hub k and zero otherwise. The amount of flow from origin i to destination j is given by W ij, while O i, D i represents the total amount of flow originated and destined at node i, respectively. Thus, the on step fixed charge hub location problem can be formulated as the following mathematical programming problem: min Z = ( ) C ik Z ik χo i + δd i i N k N + αc kl Ykl i i N k N l N + Z ik U ik + N kl V kl i N k N k N l N (1) Subject to: where l N Z ik = 1, i N (2) k N Z kk = p, (3) k N Z ik Z kk, i N, k N (4) Ykl i Ylk i l N = O i Z ik W ij Z jk, j N i N, k N (5) Z ik {0, 1}, i N, k N (6) Ykl i 0, i N, k N, l N (7) 661
3 N kl = { 1 : if Ylk i > 0, i N, k N, l N 0 : otherwise Formulation of U ik : Assume that a fixed cost to open a route from i to k is u ik,1 if the flow is less than or equal to A ik, and u ik,2 when the flow is higher than A ik. Thus, U ik which is the total fixed charge associated with the route from spoke node i, i N, to the hub k, k N, is: where U ik = b ik,1 u ik,1 + b ik,2 u ik,2 (8) b ik,1 = 1 if Z ik = 1, = 0 otherwise; b ik,2 = 1 if max {O i, D i }Z ik > A ik, = 0 otherwise. Similarly, V kl is the total fixed charge associated with the route between hubs k and l, k N, l N, having two levels of fixed costs: v kl,1 and v kl,2. where V kl = e kl,1 v kl,1 + e kl,2 v kl,2 (9) e kl,1 = 1 if Ykl i i N = 0 otherwise; e kl,2 = 1 if Ykl i kl, i N = 0 otherwise; In the above formulation, constraints (2) impose that each node i is assigned to exactly one hub, while constraints (3) ensure that exactly p hubs needs to be opened. Constrains (4) ensure that no node is assigned to a location unless a hub is opened at that site. Constraints (5) represent the divergence equations for each commodity i at node k in a complete graph, where the demand and supply at the nodes is determined by the allocation variables Z ik. Note that U ik and V kl are step functions, which in this special case has two steps. It could have multiple steps, depending on the problem structure. 3 Preliminary computational experiments Given the nature and complexity of the problem, we opted to develop a tabu search heuristic based on [15] and [16] to solve the on step fixed-charge hub location problem. In both the works, the tabu search heuristic was shown to be effective in solving the hub location problems, being capable of finding the optimal solution in all problems tested. The problem solved in [16] was the USApHMP, and in [15] the uncapacitated single allocation hub location problem (USAHLP). Tabu search (TS) is a local search procedure that uses memory structures to guide the movements from one feasible solution to another, aiming to explore regions of the search space that would be otherwise left unexplored in order to escape local optima. After a move is made, it is classified as tabu (i.e., forbidden) for a certain number of iterations in order to prevent cycling. The fundamental principles underlying TS are fully explained in [7], [8] and in [9]. 662
4 The data used for the computational experiments was the CAB (Civil Aeronautics Board) data set, first introduced by [13], and this set has been extensively used in the literature as a benchmark for evaluating algorithms for different hub location problems. This data set is based on the airline passenger interactions between 25 US cities in 1970 evaluated by the Civil Aeronautics Board (CAB). The CAB data set is available in the OR Library [2]. We solved problems of four different sizes: the first 10 nodes, the first 15, the first 20 and the full CAB data set with 25 nodes. The number of hubs to be located was tested with p = {2, 3, 4}, and with the discount factor α = {0.2, 0.4, 0.6, 0.8, 1.0}, resulting in 60 problems solved. Since there is no fixed-charge costs provided in the CAB data set, we arbitrarily defined values for U ik and V kl : u ik,1 = 1.0, i N, k N; u ik,2 = 2.0, i N, k N; v kl,1 = 1.0, k N, l N; v kl,2 = 2.0, k N, l N. The values of A ik and F kl were also defined arbitrarily, based on the flow values of the problem at hand. These values are presented in Table 1. The values of A ik were defined as the same for all i N and for all k N, and named only as A for short. The same for F kl, with only one value for all k N and for all l N, also named as F for short. The F value was also defined in function of the number of hubs to be located (p). F n A p = 2 p = 3 p = Table 1: Values used for A ik and F kl for the experiments with the CAB data set All the experiments were performed on a laptop equipped with 2.4 GHz Intel Core i5 processor (only one processor was used for the experiments), with 4GB of RAM, running under Mac OS X , and the tabu search heuristic was coded using Fortran programming language. We implemented the tabu search method only with short-term memory. The tabu tenure and the maximum number of iterations was set to five and ten respectively, for both the locational and allocational part of the problem, regardless of their sizes. These values are the same used in [15]. In Table 2 we present the results obtained with tabu search heuristic on solving the set of problems with n = 25 nodes. As can be seen in this table, the CPU time increases as the number of hubs increases (column CPUt(s) ), and the objective function value (column Obj.func. ) decreases because of the lower variable costs. 4 Conclusions and further research In this paper we introduced the on step fixed-charge hub location problem and we proposed a mathematical model for the special case when the objective function has two steps, and the hub location problem chosen as a case study was the uncapacitated single allocation p-hub median problem (USApHMP). We believe that this is the first work that has studied the fixed-charge hub location problem where the objetive function is a step function, imposing fixed costs at every arc in the hub-and-spoke network. We developed a tabu search heuristic to solve a set 663
5 n p α Obj.func. CPUt(s) n p α Obj.func. CPUt(s) Table 2: Results for the CAB data set of problems created using the CAB (Civil Aeronautics Board) data set. The results obtained showed that this approach can be useful in solving step fixed-charge hub location problems. Real world hub location problems are much larger than those presented in this paper. So, further research must concentrate on solving larger problems, and also on modeling and developing new solution methods to solve different variations of hub location problems. References [1] Alumur, S., and Kara, B. Y. Network hub location problems: The state of the art. European Journal of Operational Research 190, 1 (2008), [2] Beasley, J. E. OR-Library: Distributing test problems by electronic mail. Journal of the Operational Research Society 41 (1990), [3] Ernst, A. T., and Krishnamoorthy, M. Efficient algorithms for the uncapacitated single allocation p-hub median problem. Location Science 4, 3 (1996), Hub Location. [4] Ernst, A. T., and Krishnamoorthy, M. Exact and heuristic algorithms for the uncapacitated multiple allocation p-hub median problem. European Journal of Operational Research 104, 1 (1998),
6 [5] Ernst, A. T., and Krishnamoorthy, M. Solution algorithms for the capacitated single allocation hub location problem. Annals of Operations Research 86 (1999), [6] Farahani, R. Z., Hekmatfar, M., Arabani, A. B., and Nikbakhsh, E. Hub location problems: A review of models, classification, solution techniques, and applications. Computers & Industrial Engineering 64, 4 (2013), [7] Glover, F. Future paths for integer programming and links to artificial intelligence. Computers & Operations Research 13, 5 (1986), [8] Glover, F. Tabu search, part I. ORSA Journal on Computing 1, 3 (Summer 1989), [9] Glover, F. Tabu search, part II. ORSA Journal on Computing 2, 1 (Winter 1990), [10] Klincewicz, J. G. Heuristics for the p-hub location problem. European Journal of Operational Research 53, 1 (1991), [11] Kowalski, K., and Lev, B. On step fixed-charge transportation problem. Omega 36, 1 (2008), [12] Magnanti, T. L., Mirchandani, P., and Vachani, R. The convex hull of two core capacitated network design problems. Mathematical Programming 60 (1993), [13] O Kelly, M. E. A quadratic integer program for the location of interacting hub facilities. European Journal of Operational Research 32, 3 (December 1987), [14] Pirkul, H., and Schilling, D. A. An efficient procedure for designing single allocation hub and spoke systems. Management Science 42, 12 (1998), [15] Silva, M. R., and Cunha, C. B. New simple and efficient heuristics for the uncapacitated single allocation hub location problem. Computers & Operations Research 36, 12 (2009), [16] Skorin-Kapov, D., and Skorin-Kapov, J. On tabu search for the location of interacting hub facilities. European Journal of Operational Research 73, 3 (March 1994),
Solving the Capacitated Single Allocation Hub Location Problem Using Genetic Algorithm
Solving the Capacitated Single Allocation Hub Location Problem Using Genetic Algorithm Faculty of Mathematics University of Belgrade Studentski trg 16/IV 11 000, Belgrade, Serbia (e-mail: zoricast@matf.bg.ac.yu)
More informationUsing Decomposition Techniques for Solving Large-Scale Capacitated Hub Location Problems with Single Assignment
Using Decomposition Techniques for Solving Large-Scale Capacitated Hub Location Problems with Single Assignment Ivan Contreras*, Elena Fernández Department of Statistics and Operations Research Technical
More informationSolving Large Aircraft Landing Problems on Multiple Runways by Applying a Constraint Programming Approach
Solving Large Aircraft Landing Problems on Multiple Runways by Applying a Constraint Programming Approach Amir Salehipour School of Mathematical and Physical Sciences, The University of Newcastle, Australia
More informationLOCATING HUBS IN TRANSPORT NETWORKS: AN ARTIFICIAL INTELLIGENCE APPROACH
DOI: http://dx.doi.org/10.7708/ijtte.2014.4(3).04 UDC: 656.022.5 LOCATING HUBS IN TRANSPORT NETWORKS: AN ARTIFICIAL INTELLIGENCE APPROACH Dušan Teodorović 1, Milica Šelmić 21, Ivana Vukićević 3 1, 2, 3
More informationComplete / Incomplete Hierarchical Hub Center Single Assignment Network Problem
Journal of Optimization in Industrial Engineering 14 (2014) 1-12 Complete / Incomplete Hierarchical Hub Center Single Assignment Network Problem Alireza Arshadi Khamseh a,*, Mohammad Doost Mohamadi b a
More informationOn the Computational Behavior of a Dual Network Exterior Point Simplex Algorithm for the Minimum Cost Network Flow Problem
On the Computational Behavior of a Dual Network Exterior Point Simplex Algorithm for the Minimum Cost Network Flow Problem George Geranis, Konstantinos Paparrizos, Angelo Sifaleras Department of Applied
More informationSolving Capacitated P-Median Problem by Hybrid K-Means Clustering and Fixed Neighborhood Search algorithm
Proceedings of the 2010 International Conference on Industrial Engineering and Operations Management Dhaka, Bangladesh, January 9 10, 2010 Solving Capacitated P-Median Problem by Hybrid K-Means Clustering
More informationCapacitated Single-Assignment Hub Covering Location Problem under Fuzzy Environment
Capacitated Single-Assignment Hub Covering Location Problem under Fuzzy Environment Abbas Mirakhorli Abstract- This paper studies capacitated single-allocation hub covering location problem with fuzzy
More informationBranch-and-Price for Large-Scale Capacitated Hub Location Problems with Single Assignment
Branch-and-Price for Large-Scale Capacitated Hub Location Problems with Single Assignment Ivan Contreras 1, Juan A. Díaz 2, Elena Fernández 1 1 Dpt. d Estadística i Investigació Operativa, Universitat
More informationCLUSTER-BASED OPTIMIZATION OF URBAN TRANSIT HUB LOCATIONS: METHODOLOGY AND CASE STUDY IN CHINA
Yu, Liu, Chang and Yang 1 CLUSTER-BASED OPTIMIZATION OF URBAN TRANSIT HUB LOCATIONS: METHODOLOGY AND CASE STUDY IN CHINA Jie Yu Department of Civil Engineering The University of Maryland, College Par,
More informationFundamentals of Integer Programming
Fundamentals of Integer Programming Di Yuan Department of Information Technology, Uppsala University January 2018 Outline Definition of integer programming Formulating some classical problems with integer
More informationTwo models of the capacitated vehicle routing problem
Croatian Operational Research Review 463 CRORR 8(2017), 463 469 Two models of the capacitated vehicle routing problem Zuzana Borčinová 1, 1 Faculty of Management Science and Informatics, University of
More informationSOLVING A NEW PRIORITY M/M/C QUEUE MODEL FOR A MULTI- MODE HUB COVERING LOCATION PROBLEM BY MULTI- OBJECTIVE PARALLEL SIMULATED ANNEALING
Samaneh SEDEHZADEH, M.Sc. Student School of Industrial Engineering, South Tehran Branch Islamic Azad University, Tehran, Iran E-mail: mehrdadmohamadi@ut.ac.ir Professor Reza TAVAKKOLI-MOGHADDAM, PhD School
More informationVariable Neighbourhood Search for Uncapacitated Warehouse Location Problems
International Journal of Engineering and Applied Sciences (IJEAS) ISSN: 2394-3661, Volume-3, Issue-1, January 2016 Variable Neighbourhood Search for Uncapacitated Warehouse Location Problems Kemal Alaykiran,
More informationBenders decomposition for the uncapacitated multiple allocation hub location problem
Computers & Operations Research 35 (2008) 1047 1064 www.elsevier.com/locate/cor Benders decomposition for the uncapacitated multiple allocation hub location problem R.S. de Camargo a,,1, G. Miranda Jr.
More information6. Tabu Search 6.1 Basic Concepts. Fall 2010 Instructor: Dr. Masoud Yaghini
6. Tabu Search 6.1 Basic Concepts Fall 2010 Instructor: Dr. Masoud Yaghini Outline Tabu Search: Part 1 Introduction Illustrative Problems Search Space Neighborhood Structure Tabus Aspiration Criteria Termination
More informationDiscrete Covering. Location. Problems. Louis. Luangkesorn. Housekeeping. Dijkstra s Shortest Path. Discrete. Covering. Models.
Network Design Network Design Network Design Network Design Office Hours Wednesday IE 079/079 Logistics and Supply Chain Office is closed Wednesday for building renovation work. I will be on campus (or
More informationA Tabu Search solution algorithm
Chapter 5 A Tabu Search solution algorithm The TS examines a trajectory sequence of solutions and moves to the best neighbor of the current solution. To avoid cycling, solutions that were recently examined
More informationHEURISTICS FOR THE NETWORK DESIGN PROBLEM
HEURISTICS FOR THE NETWORK DESIGN PROBLEM G. E. Cantarella Dept. of Civil Engineering University of Salerno E-mail: g.cantarella@unisa.it G. Pavone, A. Vitetta Dept. of Computer Science, Mathematics, Electronics
More informationBranch-and-Cut and GRASP with Hybrid Local Search for the Multi-Level Capacitated Minimum Spanning Tree Problem
Branch-and-Cut and GRASP with Hybrid Local Search for the Multi-Level Capacitated Minimum Spanning Tree Problem Eduardo Uchoa Túlio A.M. Toffolo Mauricio C. de Souza Alexandre X. Martins + Departamento
More informationA Computational Study of Conflict Graphs and Aggressive Cut Separation in Integer Programming
A Computational Study of Conflict Graphs and Aggressive Cut Separation in Integer Programming Samuel Souza Brito and Haroldo Gambini Santos 1 Dep. de Computação, Universidade Federal de Ouro Preto - UFOP
More informationA Comparison of Mixed-Integer Programming Models for Non-Convex Piecewise Linear Cost Minimization Problems
A Comparison of Mixed-Integer Programming Models for Non-Convex Piecewise Linear Cost Minimization Problems Keely L. Croxton Fisher College of Business The Ohio State University Bernard Gendron Département
More informationDETERMINISTIC OPERATIONS RESEARCH
DETERMINISTIC OPERATIONS RESEARCH Models and Methods in Optimization Linear DAVID J. RADER, JR. Rose-Hulman Institute of Technology Department of Mathematics Terre Haute, IN WILEY A JOHN WILEY & SONS,
More informationIntroduction to Mathematical Programming IE406. Lecture 20. Dr. Ted Ralphs
Introduction to Mathematical Programming IE406 Lecture 20 Dr. Ted Ralphs IE406 Lecture 20 1 Reading for This Lecture Bertsimas Sections 10.1, 11.4 IE406 Lecture 20 2 Integer Linear Programming An integer
More informationA Benders decomposition approach for the robust shortest path problem with interval data
A Benders decomposition approach for the robust shortest path problem with interval data R. Montemanni, L.M. Gambardella Istituto Dalle Molle di Studi sull Intelligenza Artificiale (IDSIA) Galleria 2,
More informationComputational Complexity CSC Professor: Tom Altman. Capacitated Problem
Computational Complexity CSC 5802 Professor: Tom Altman Capacitated Problem Agenda: Definition Example Solution Techniques Implementation Capacitated VRP (CPRV) CVRP is a Vehicle Routing Problem (VRP)
More informationAn Introduction to Dual Ascent Heuristics
An Introduction to Dual Ascent Heuristics Introduction A substantial proportion of Combinatorial Optimisation Problems (COPs) are essentially pure or mixed integer linear programming. COPs are in general
More informationGraph Coloring via Constraint Programming-based Column Generation
Graph Coloring via Constraint Programming-based Column Generation Stefano Gualandi Federico Malucelli Dipartimento di Elettronica e Informatica, Politecnico di Milano Viale Ponzio 24/A, 20133, Milan, Italy
More information56:272 Integer Programming & Network Flows Final Exam -- December 16, 1997
56:272 Integer Programming & Network Flows Final Exam -- December 16, 1997 Answer #1 and any five of the remaining six problems! possible score 1. Multiple Choice 25 2. Traveling Salesman Problem 15 3.
More informationMetaheuristic Algorithms for Hybrid Flow-Shop Scheduling Problem with Multiprocessor Tasks
MIC 2001-4th Metaheuristics International Conference 477 Metaheuristic Algorithms for Hybrid Flow-Shop Scheduling Problem with Multiprocessor Tasks Ceyda Oğuz Adam Janiak Maciej Lichtenstein Department
More informationPrinciples of Network Economics
Hagen Bobzin Principles of Network Economics SPIN Springer s internal project number, if known unknown Monograph August 12, 2005 Springer Berlin Heidelberg New York Hong Kong London Milan Paris Tokyo Contents
More informationMODELING AND HEURISTIC APPROACHES FOR THE HUB COVERING PROBLEM OVER INCOMPLETE HUB NETWORKS
MODELING AND HEURISTIC APPROACHES FOR THE HUB COVERING PROBLEM OVER INCOMPLETE HUB NETWORKS A THESIS SUBMITTED TO THE DEPARTMENT OF INDUSTRIAL ENGINEERING AND THE INSTITUTE OF ENGINEERING AND SCIENCE OF
More informationReliable capacitated single allocation hub network design under hub failure: a scenario based approach
Reliable capacitated single allocation hub network design under hub failure: a scenario based approach Zahra Booyavi Department of Industrial Engineering Science and Culture University Tehran, Iran sh.booyavi@gmail.com
More informationA NEW SIMPLEX TYPE ALGORITHM FOR THE MINIMUM COST NETWORK FLOW PROBLEM
A NEW SIMPLEX TYPE ALGORITHM FOR THE MINIMUM COST NETWORK FLOW PROBLEM KARAGIANNIS PANAGIOTIS PAPARRIZOS KONSTANTINOS SAMARAS NIKOLAOS SIFALERAS ANGELO * Department of Applied Informatics, University of
More informationA Tabu Search with Slope Scaling for the Multicommodity Capacitated Location Problem with Balancing Requirements
Annals of Operations Research 122, 193 217, 2003 2003 Kluwer Academic Publishers. Manufactured in The Netherlands. A Tabu Search with Slope Scaling for the Multicommodity Capacitated Location Problem with
More informationA Computational Study of Bi-directional Dynamic Programming for the Traveling Salesman Problem with Time Windows
A Computational Study of Bi-directional Dynamic Programming for the Traveling Salesman Problem with Time Windows Jing-Quan Li California PATH, University of California, Berkeley, Richmond, CA 94804, jingquan@path.berkeley.edu
More informationTRANSPORTATION AND ASSIGNMENT PROBLEMS
TRANSPORTATION AND ASSIGNMENT PROBLEMS Transportation problem Example P&T Company produces canned peas. Peas are prepared at three canneries (Bellingham, Eugene and Albert Lea). Shipped by truck to four
More informationReload Cost Trees and Network Design
Reload Cost Trees and Network Design Ioannis Gamvros, ILOG, Inc., 1080 Linda Vista Avenue, Mountain View, CA 94043, USA Luis Gouveia, Faculdade de Ciencias da Universidade de Lisboa, Portugal S. Raghavan,
More informationExact approach to the tariff zones design problem in public transport
Exact approach to the tariff zones design problem in public transport Michal Koháni 1 1 Introduction Abstract. An integrated transport system is the way how to provide transport service in the region by
More informationA Bi-directional Resource-bounded Dynamic Programming Approach for the Traveling Salesman Problem with Time Windows
Submitted manuscript A Bi-directional Resource-bounded Dynamic Programming Approach for the Traveling Salesman Problem with Time Windows Jing-Quan Li California PATH, University of California, Berkeley,
More informationLast topic: Summary; Heuristics and Approximation Algorithms Topics we studied so far:
Last topic: Summary; Heuristics and Approximation Algorithms Topics we studied so far: I Strength of formulations; improving formulations by adding valid inequalities I Relaxations and dual problems; obtaining
More informationSPATIAL OPTIMIZATION METHODS
DELMELLE E. (2010). SPATIAL OPTIMIZATION METHODS. IN: B. WHARF (ED). ENCYCLOPEDIA OF HUMAN GEOGRAPHY: 2657-2659. SPATIAL OPTIMIZATION METHODS Spatial optimization is concerned with maximizing or minimizing
More informationVariable Neighborhood Search for Solving the Balanced Location Problem
TECHNISCHE UNIVERSITÄT WIEN Institut für Computergraphik und Algorithmen Variable Neighborhood Search for Solving the Balanced Location Problem Jozef Kratica, Markus Leitner, Ivana Ljubić Forschungsbericht
More informationA Diversified Multi-Start Algorithm for Unconstrained Binary Quadratic Problems Leveraging the Graphics Processor Unit
A Diversified Multi-Start Algorithm for Unconstrained Binary Quadratic Problems Leveraging the Graphics Processor Unit Mark Lewis Missouri Western State University, Saint Joseph, Missouri 64507, USA mlewis14@missouriwestern.edu
More informationArc-Flow Model for the Two-Dimensional Cutting Stock Problem
Arc-Flow Model for the Two-Dimensional Cutting Stock Problem Rita Macedo Cláudio Alves J. M. Valério de Carvalho Centro de Investigação Algoritmi, Universidade do Minho Escola de Engenharia, Universidade
More informationOverview. H. R. Alvarez A., Ph. D.
Network Modeling Overview Networks arise in numerous settings: transportation, electrical, and communication networks, for example. Network representations also are widely used for problems in such diverse
More information56:272 Integer Programming & Network Flows Final Examination -- December 14, 1998
56:272 Integer Programming & Network Flows Final Examination -- December 14, 1998 Part A: Answer any four of the five problems. (15 points each) 1. Transportation problem 2. Integer LP Model Formulation
More informationOptimal network flow allocation
Optimal network flow allocation EE384Y Project intermediate report Almir Mutapcic and Primoz Skraba Stanford University, Spring 2003-04 May 10, 2004 Contents 1 Introduction 2 2 Background 2 3 Problem statement
More informationJournal of Business & Economics Research November, 2009 Volume 7, Number 11
Alternate Solutions Analysis For Transportation Problems Veena Adlakha, University of Baltimore, USA Krzysztof Kowalski, Connecticut Department of Transportation, USA ABSTRACT The constraint structure
More informationThe Job-Shop Problem: Old and New Challenges
Invited Speakers The Job-Shop Problem: Old and New Challenges Peter Brucker Universität Osnabrück, Albrechtstr. 28a, 49069 Osnabrück, Germany, pbrucker@uni-osnabrueck.de The job-shop problem is one of
More informationNew algorithm for analyzing performance of neighborhood strategies in solving job shop scheduling problems
Journal of Scientific & Industrial Research ESWARAMURTHY: NEW ALGORITHM FOR ANALYZING PERFORMANCE OF NEIGHBORHOOD STRATEGIES 579 Vol. 67, August 2008, pp. 579-588 New algorithm for analyzing performance
More informationA tabu search approach for makespan minimization in a permutation flow shop scheduling problems
A tabu search approach for makespan minimization in a permutation flow shop scheduling problems Sawat Pararach Department of Industrial Engineering, Faculty of Engineering, Thammasat University, Pathumthani
More informationLOCAL SEARCH FOR THE MINIMUM FUNDAMENTAL CYCLE BASIS PROBLEM
LOCAL SEARCH FOR THE MINIMUM FUNDAMENTAL CYCLE BASIS PROBLEM Abstract E.Amaldi, L.Liberti, N.Maculan, F.Maffioli DEI, Politecnico di Milano, I-20133 Milano amaldi,liberti,maculan,maffioli @elet.polimi.it
More informationOptimization Model for a Distribution System based on Location-Routing with Distance and forbidden route
International Refereed Journal of Engineering and Science (IRJES) ISSN (Online) 2319-183X, (Print) 2319-1821 Volume 3, Issue 3(March 2014), PP.32-40 Optimization Model for a Distribution System based on
More informationA simulated annealing algorithm for the vehicle routing problem with time windows and synchronization constraints
A simulated annealing algorithm for the vehicle routing problem with time windows and synchronization constraints Sohaib Afifi 1, Duc-Cuong Dang 1,2, and Aziz Moukrim 1 1 Université de Technologie de Compiègne
More informationLEAST COST ROUTING ALGORITHM WITH THE STATE SPACE RELAXATION IN A CENTRALIZED NETWORK
VOL., NO., JUNE 08 ISSN 896608 00608 Asian Research Publishing Network (ARPN). All rights reserved. LEAST COST ROUTING ALGORITHM WITH THE STATE SPACE RELAXATION IN A CENTRALIZED NETWORK Y. J. Lee Department
More informationOutline: Finish uncapacitated simplex method Negative cost cycle algorithm The max-flow problem Max-flow min-cut theorem
Outline: Finish uncapacitated simplex method Negative cost cycle algorithm The max-flow problem Max-flow min-cut theorem Uncapacitated Networks: Basic primal and dual solutions Flow conservation constraints
More informationMultiple Depot Vehicle Routing Problems on Clustering Algorithms
Thai Journal of Mathematics : 205 216 Special Issue: Annual Meeting in Mathematics 2017 http://thaijmath.in.cmu.ac.th ISSN 1686-0209 Multiple Depot Vehicle Routing Problems on Clustering Algorithms Kanokon
More informationA COMPUTATIONAL STUDY OF THE CONSTRAINED MAXIMUM FLOW PROBLEM
COMPUTTIONL STUDY OF THE CONSTRINED MXIMUM FLOW PROBLEM Cenk Çalışkan, Woodbury School of Business, Utah Valley University, 800 W. University Pkwy, Orem, UT 84058, (801) 863-6487, cenk.caliskan@uvu.edu
More informationEfficient Edge-Swapping Heuristics for the Reload Cost Spanning Tree Problem
Efficient Edge-Swapping Heuristics for the Reload Cost Spanning Tree Problem S. Raghavan and Mustafa Sahin Smith School of Business & Institute for Systems Research, University of Maryland, College Park,
More informationVehicle Routing Heuristic Methods
DM87 SCHEDULING, TIMETABLING AND ROUTING Outline 1. Construction Heuristics for VRPTW Lecture 19 Vehicle Routing Heuristic Methods 2. Local Search 3. Metaheuristics Marco Chiarandini 4. Other Variants
More informationA NETWORK SIMPLEX ALGORITHM FOR SOLVING THE MINIMUM DISTRIBUTION COST PROBLEM. I-Lin Wang and Shiou-Jie Lin. (Communicated by Shu-Cherng Fang)
JOURNAL OF INDUSTRIAL AND doi:10.3934/jimo.2009.5.929 MANAGEMENT OPTIMIZATION Volume 5, Number 4, November 2009 pp. 929 950 A NETWORK SIMPLEX ALGORITHM FOR SOLVING THE MINIMUM DISTRIBUTION COST PROBLEM
More informationArc Perturbation Algorithms for Optical Network Design
Applied Mathematical Sciences, Vol. 1, 2007, no. 7, 301-310 Arc Perturbation Algorithms for Optical Network Design Zbigniew R. Bogdanowicz Armament Research, Development and Engineering Center Building
More informationSimulation. Lecture O1 Optimization: Linear Programming. Saeed Bastani April 2016
Simulation Lecture O Optimization: Linear Programming Saeed Bastani April 06 Outline of the course Linear Programming ( lecture) Integer Programming ( lecture) Heuristics and Metaheursitics (3 lectures)
More informationInstituto Nacional de Pesquisas Espaciais - INPE/LAC Av. dos Astronautas, 1758 Jd. da Granja. CEP São José dos Campos S.P.
XXXIV THE MINIMIZATION OF TOOL SWITCHES PROBLEM AS A NETWORK FLOW PROBLEM WITH SIDE CONSTRAINTS Horacio Hideki Yanasse Instituto Nacional de Pesquisas Espaciais - INPE/LAC Av. dos Astronautas, 1758 Jd.
More informationGrouping Genetic Algorithm with Efficient Data Structures for the University Course Timetabling Problem
Grouping Genetic Algorithm with Efficient Data Structures for the University Course Timetabling Problem Felipe Arenales Santos Alexandre C. B. Delbem Keywords Grouping Genetic Algorithm Timetabling Problem
More informationRecursive column generation for the Tactical Berth Allocation Problem
Recursive column generation for the Tactical Berth Allocation Problem Ilaria Vacca 1 Matteo Salani 2 Michel Bierlaire 1 1 Transport and Mobility Laboratory, EPFL, Lausanne, Switzerland 2 IDSIA, Lugano,
More informationMultiple-choice Vector Bin Packing: Arc-flow Formulation with Graph Compression
Multiple-choice Vector Bin Packing: Arc-flow Formulation with Graph Compression Filipe Brandão fdabrandao@dcc.fc.up.pt arxiv:1312.3836v1 [math.oc] 13 Dec 2013 João Pedro Pedroso pp@fc.up.pt Technical Report
More informationInteger Programming and Network Modeis
H.A. Eiselt C.-L. Sandblom Integer Programming and Network Modeis With Contributions by K. Spielberg, E. Richards, B.T. Smith, G. Laporte, B.T. Boffey With 165 Figures and 43 Tables &m Springer CONTENTS
More information6 ROUTING PROBLEMS VEHICLE ROUTING PROBLEMS. Vehicle Routing Problem, VRP:
6 ROUTING PROBLEMS VEHICLE ROUTING PROBLEMS Vehicle Routing Problem, VRP: Customers i=1,...,n with demands of a product must be served using a fleet of vehicles for the deliveries. The vehicles, with given
More informationHierarchical Survivable Network Design Problems
Available online at www.sciencedirect.com Electronic Notes in Discrete Mathematics 52 (2016) 229 236 www.elsevier.com/locate/endm Hierarchical Survivable Network Design Problems Inmaculada Rodríguez-Martín
More informationIntroduction to Mathematical Programming IE406. Lecture 16. Dr. Ted Ralphs
Introduction to Mathematical Programming IE406 Lecture 16 Dr. Ted Ralphs IE406 Lecture 16 1 Reading for This Lecture Bertsimas 7.1-7.3 IE406 Lecture 16 2 Network Flow Problems Networks are used to model
More informationLinear Programming. Course review MS-E2140. v. 1.1
Linear Programming MS-E2140 Course review v. 1.1 Course structure Modeling techniques Linear programming theory and the Simplex method Duality theory Dual Simplex algorithm and sensitivity analysis Integer
More informationExploring Lin Kernighan neighborhoods for the indexing problem
INDIAN INSTITUTE OF MANAGEMENT AHMEDABAD INDIA Exploring Lin Kernighan neighborhoods for the indexing problem Diptesh Ghosh W.P. No. 2016-02-13 February 2016 The main objective of the Working Paper series
More informationConstrained Minimum Spanning Tree Algorithms
December 8, 008 Introduction Graphs and MSTs revisited Minimum Spanning Tree Algorithms Algorithm of Kruskal Algorithm of Prim Constrained Minimum Spanning Trees Bounded Diameter Minimum Spanning Trees
More informationBuilding Ride-sharing and Routing Engine for Autonomous Vehicles: A State-space-time Network Modeling Approach
Building Ride-sharing and Routing Engine for Autonomous Vehicles: A State-space-time Network Modeling Approach Xuesong Zhou (xzhou7@asu.edu) Associate professor, School of Sustainable Engineering and the
More informationAn Ant Colony Optimization Algorithm to Solve the Minimum Cost Network Flow Problem with Concave Cost Functions
An Ant Colony Optimization Algorithm to Solve the Minimum Cost Network Flow Problem with Concave Cost Functions Marta S. R. Monteiro Faculdade de Economia and LIAAD-INESC Porto L.A., Universidade do Porto
More informationOptimization of Process Plant Layout Using a Quadratic Assignment Problem Model
Optimization of Process Plant Layout Using a Quadratic Assignment Problem Model Sérgio. Franceira, Sheila S. de Almeida, Reginaldo Guirardello 1 UICAMP, School of Chemical Engineering, 1 guira@feq.unicamp.br
More informationModule 1 Lecture Notes 2. Optimization Problem and Model Formulation
Optimization Methods: Introduction and Basic concepts 1 Module 1 Lecture Notes 2 Optimization Problem and Model Formulation Introduction In the previous lecture we studied the evolution of optimization
More informationof optimization problems. In this chapter, it is explained that what network design
CHAPTER 2 Network Design Network design is one of the most important and most frequently encountered classes of optimization problems. In this chapter, it is explained that what network design is? The
More informationHYBRID GENETIC ALGORITHM WITH GREAT DELUGE TO SOLVE CONSTRAINED OPTIMIZATION PROBLEMS
HYBRID GENETIC ALGORITHM WITH GREAT DELUGE TO SOLVE CONSTRAINED OPTIMIZATION PROBLEMS NABEEL AL-MILLI Financial and Business Administration and Computer Science Department Zarqa University College Al-Balqa'
More informationConstruction Heuristics and Local Search Methods for VRP/VRPTW
DM204, 2010 SCHEDULING, TIMETABLING AND ROUTING Lecture 31 Construction Heuristics and Local Search Methods for VRP/VRPTW Marco Chiarandini Department of Mathematics & Computer Science University of Southern
More informationMethods and Models for Combinatorial Optimization Modeling by Linear Programming
Methods and Models for Combinatorial Optimization Modeling by Linear Programming Luigi De Giovanni, Marco Di Summa 1 Linear programming models Linear programming models are a special class of mathematical
More informationA Study of Neighborhood Structures for the Multiple Depot Vehicle Scheduling Problem
A Study of Neighborhood Structures for the Multiple Depot Vehicle Scheduling Problem Benoît Laurent 1,2 and Jin-Kao Hao 2 1 Perinfo SA, Strasbourg, France 2 LERIA, Université d Angers, Angers, France blaurent@perinfo.com,
More informationMixed-Integer Optimization for the Combined capacitated Facility Location-Routing Problem
Mixed-Integer Optimization for the Combined capacitated Facility Location-Routing Problem Dimitri Papadimitriou 1, Didier Colle 2, Piet Demeester 2 dimitri.papadimitriou@nokia.com, didier.colle@ugent.be,
More informationBCN Decision and Risk Analysis. Syed M. Ahmed, Ph.D.
Linear Programming Module Outline Introduction The Linear Programming Model Examples of Linear Programming Problems Developing Linear Programming Models Graphical Solution to LP Problems The Simplex Method
More informationAdjusted Clustering Clarke-Wright Saving Algorithm for Two Depots-N Vehicles
Adjusted Clustering Clarke-Wright Saving Algorithm for Two Depots-N Vehicles S. Halim, L. Yoanita Department of Industrial Engineering, Petra Christian University, Surabaya, Indonesia (halim@petra.ac.id)
More informationVariable Neighborhood Search for the Dial-a-Ride Problem
Variable Neighborhood Search for the Dial-a-Ride Problem Sophie N. Parragh, Karl F. Doerner, Richard F. Hartl Department of Business Administration, University of Vienna, Bruenner Strasse 72, 1210 Vienna,
More informationCourse Introduction. Scheduling: Terminology and Classification
Outline DM87 SCHEDULING, TIMETABLING AND ROUTING Lecture 1 Course Introduction. Scheduling: Terminology and Classification 1. Course Introduction 2. Scheduling Problem Classification Marco Chiarandini
More informationHeuristic solution methods for the Fiber To The Home cabling problem
Lecture Notes in Management Science (2014) Vol. 6: 198 206 6 th International Conference on Applied Operational Research, Proceedings Tadbir Operational Research Group Ltd. All rights reserved. www.tadbir.ca
More informationA Development of Hybrid Cross Entropy-Tabu Search Algorithm for Travelling Repairman Problem
Proceedings of the 2012 International Conference on Industrial Engineering and Operations Management Istanbul, Turkey, July 3 6, 2012 A Development of Hybrid Cross Entropy-Tabu Search Algorithm for Travelling
More informationA SWEEP BASED ALGORITHM FOR THE FLEET SIZE AND MIX VEHICLE ROUTING PROBLEM
A SWEEP BASED ALGORITHM FOR THE FLEET SIZE AND MIX VEHICLE ROUTING PROBLEM Jacques Renaud and Fayez F. Boctor Centre de recherche sur les technologies de l organisation réseau (CENTOR) & Faculté des sciences
More informationA Computational Study on the Number of. Iterations to Solve the Transportation Problem
Applied Mathematical Sciences, Vol. 8, 2014, no. 92, 4579-4583 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.46435 A Computational Study on the Number of Iterations to Solve the Transportation
More informationA Randomized Algorithm for Minimizing User Disturbance Due to Changes in Cellular Technology
A Randomized Algorithm for Minimizing User Disturbance Due to Changes in Cellular Technology Carlos A. S. OLIVEIRA CAO Lab, Dept. of ISE, University of Florida Gainesville, FL 32611, USA David PAOLINI
More informationSolutions for Operations Research Final Exam
Solutions for Operations Research Final Exam. (a) The buffer stock is B = i a i = a + a + a + a + a + a 6 + a 7 = + + + + + + =. And the transportation tableau corresponding to the transshipment problem
More informationA comparison of two new exact algorithms for the robust shortest path problem
TRISTAN V: The Fifth Triennal Symposium on Transportation Analysis 1 A comparison of two new exact algorithms for the robust shortest path problem Roberto Montemanni Luca Maria Gambardella Alberto Donati
More informationImproved K-Means Algorithm for Capacitated Clustering Problem
Improved K-Means Algorithm for Capacitated Clustering Problem S. GEETHA 1 G. POONTHALIR 2 P. T. VANATHI 3 PSG College of Technology Tamil Nadu India 1 geet_shan@yahoo.com 2 thalirkathir@rediffmail.com
More informationSOME GREEDY BASED ALGORITHMS FOR MULTI PERIODS DEGREE CONSTRAINED MINIMUM SPANNING TREE PROBLEM
SOME GREEDY BASED ALGORITHMS FOR MULTI PERIODS DEGREE CONSTRAINED MINIMUM SPANNING TREE PROBLEM Wamiliana 1, Faiz A. M. Elfaki 2, Mustofa Usman 1 and M. Azram 2 1 Department of Mathematics, Faculty of
More informationBranch and Bound Method for Scheduling Precedence Constrained Tasks on Parallel Identical Processors
, July 2-4, 2014, London, U.K. Branch and Bound Method for Scheduling Precedence Constrained Tasks on Parallel Identical Processors N.S.Grigoreva Abstract The multiprocessor scheduling problem is one of
More informationA Kruskal-Based Heuristic for the Rooted Delay-Constrained Minimum Spanning Tree Problem
A Kruskal-Based Heuristic for the Rooted Delay-Constrained Minimum Spanning Tree Problem Mario Ruthmair and Günther R. Raidl Institute of Computer Graphics and Algorithms Vienna University of Technology,
More information