Amiri s Supply Chain Model. System Engineering b Department of Mathematics and Statistics c Odette School of Business
|
|
- Leslie Moore
- 5 years ago
- Views:
Transcription
1 Amr s Supply Chan Model by S. Ashtab a,, R.J. Caron b E. Selvarajah c a Department of Industral Manufacturng System Engneerng b Department of Mathematcs Statstcs c Odette School of Busness Unversty of Wndsor Wndsor, ON N9B P4 WMSR # 14-01
2 Amr s Supply Chan Model Sah Ashtab a,, Rchard J. Caron b, Esagnan Selvarajah c a Department of Industral Manufacturng Systems Engneerng, Unversty of Wndsor, Wndsor, ON, Canada, N9B P4 b Department of Mathematcs Statstcs, Unversty of Wndsor, Wndsor, ON, Canada, N9B P4 c Odette School of Busness, Unversty of Wndsor, Wndsor, ON, Canada, N9B P4 Abstract We show that Amr s model admts alternate optmal solutons that are nconsstent wth the model s phlosophy we provde a set of constrants that ensure consstency of all optmal solutons. Keywords: Supply chan network desgn, Faclty locaton, Mult-echelon, Mult-capactated. 1. Introducton Amr [1] presented a model Lagrangan-based soluton technque for mult-echelon, mult-capactated supply chan network desgn. We show that Amr s model admts alternate optmal solutons some of whch are nconsstent wth the model phlosophy. We provde a new set of constrants to ensure that the optmal soluton provded by the model properly lnks the decson to buld a warehouse to the decsons to allocate dem to that warehouse; that the fractonal varables are ndeed, fractons, as requred. 2. The Amr Model [1] The set of customer zones s ndexed by, the potental warehouse locatons by j, the potental plant locatons by k, the warehouse capacty levels by r the plant capacty levels by h. Let a be the dem from customer zone durng the plannng horzon, b r j be the capacty of a warehouse at locaton j bult at level r e h k be the capacty of a plant at locaton k bult at level h. Let Yjk r be the fracton of the total dem of a warehouse at locaton j wth capacty level r that s delvered from a plant at locaton k let X j be the fracton of the total dem of customer zone that s delvered from a warehouse at locaton j. A warehouse wth capacty level r s bult at locaton Correspondng Author. Tel: Emal address: ashtab@uwndsor.ca (Sah Ashtab) Preprnt submtted to European Journal of Operatonal Research August 18, 2014
3 j f only f Uj r = 1 Vk h = 1 f only f a plant wth capacty level h s bult at locaton k. The bnary varables U V determne number, locaton capacty of the facltes whle the real-valued varables X Y determne the flow of goods. The objectve functon s to mnmze the sum of the transportaton costs the fxed costs of establshng plants warehouses. Let C jk be the cost of shppng one unt of dem to a warehouse at locaton j from a plant at locaton k let C j be the cost of shppng one unt of dem to customer zone from a warehouse at locaton j. The n-bound out-bound transportaton costs are gven by T 1 (Y ) = r,j,k C jk b r j Y r jk T 2 (X) =,j C j a X j, respectvely. The fxed costs of establshng operatng the warehouses plants over the plannng horzon are F 1 (U) = j,r F r j U r j F 2 (V ) = k,h G h k V h k, respectvely, where Fj r s the fxed cost of openng operatng warehouse at locaton j wth capacty level r G h k s the fxed cost of openng operatng plant at locaton k wth capacty level h. The objectve functon s a summaton of the four cost elements s gven by The constrants Z 0 (Y, X, U, V ) = T 1 (Y ) + T 2 (X) + F 1 (U) + F 2 (V ). X j = 1,, (1) j ensure that the dem at each customer zone s covered by bult warehouses whle constrants a X j b r j Uj r, j, (2) r ensure that the capacty level at each warehouse s suffcent to meet out-bound shpments. That each warehouse each plant s assgned a sngle capacty level s ensured by 1, j, () r h U r j respectvely. The set of constrants a X j k,r V h k 1, k, (4) b r j Y jk r, j, (5) 2
4 ensure that the total out-bound shpment from a warehouse s not greater than the total n-bound shpment from plants to that warehouse. The nequaltes j,r b r j Y r jk h e h k V h k, k, (6) ensure that the total n-bound shpment from a bult plant to the warehouses s not greater than the chosen capacty level of that plant. The fnal sets of constrants are X j 0,, j, (7) Y r jk 0, k, j, r, (8) whch, together wth the unstated constrants that Uj r V k h are bnary, gve Amr s model whch s to AM0: mn U,Vbnary { Z 0(Y, X, U, V ) (1) (8) }. The fact that there are alternate solutons, becomes clear wth the change of varables W jk = r b r jy r jk. (9) We now replace T 1 (Y ) wth T 1 (W) = j,k C jk W jk gvng the new expresson for the objectve Z 1 (W, X, U, V ) = T 1 (W) + T 2 (X) + F 1 (U) + F 1 (V ). We next replace replace constrants (5) (6) wth a X j W jk, j, (10) k W jk j h respectvely. Model AM0 s equvalent to e h k V h k, k, (11) AM1: mn U,Vbnary { Z 1(W, X, U, V ) (1) (4), (7), (8), (10), (11) } Gven the W jk from a soluton to AM1, any set of non-negatve solutons Y r jk to (9) s a soluton to AM0.
5 Example. Consder a supply chan wth one plant havng a sngle avalable capacty level of e 1 1 = one warehouse wth avalable capacty levels of b 1 1 = 1 000, b 2 1 = 000 b 1 = The three customer zones have dems a 1 = 1 500, a 2 = a = To be feasble we must have V1 1 = 1, U1 1 = 0, U1 2 = 0, U1 = 1, X 11 = 1, X 21 = 1, X 1 = W An optmal soluton wll have W 11 = Consequently, any non-negatve soluton to = Y Y Y11 wll be feasble optmal for AM0. So, whle Y11 1 = 4, Y11 2 = 0, Y11 = 0 s optmal for AM0, t has Y varables greater than one whch s nconsstent wth the model phlosophy that they are fractons. The soluton Y11 1 = 1, Y11 2 = 1, Y11 = 0 s optmal for AM0 but t s nconsstent wth U1 1 = 0 U1 2 = 0. The example shows that the model allows alternate optmal solutons that could lead to two dfferent undesrable stuatons; Y varables greater than one Y varables nconsstent wth the U varables. Both of these stuatons are corrected wth the addton to the model of the constrants Yjk r Uj r, j, r. (12) The modfed model, wthout the change of varables, s k AM2: mn{ Z 0 (Y, X, U, V ) (1) (8), (12) }. For our example, these new constrant force the unque, acceptable, optmal soluton wth Y11 1 = 0, Y11 2 = 0, Y11 = 1. To test the mpact of ths addtonal set of constrants we created, usng the method descrbed by Amr, sx nstances of an example wth 500 customer zones, 0 warehouses 20 plants (the largest nstance solved by Amr) solved the AM0 the AM2 models usng LINGO 14.0 x64 on a DELL server wth two 2500 MHz CPUs. The tmes taken to reach optmalty for the AM0 ranged from 56 to 185 seconds wth an average of 122. The tmes taken to reach optmalty for the AM2 ranged from 5 to 277 seconds wth an average of about 121. Ths lmted numercal evdence suggests that the ablty to solve the model, n reasonable tme, s not compromsed by the addtonal constrants. References [1] A. Amr, Desgnng a dstrbuton network n a supply chan system: Formulaton effcent soluton procedure, European Journal of Operatonal Research 171 (2006)
The Minimum Universal Cost Flow in an Infeasible Flow Network
Journal of Scences, Islamc Republc of Iran 17(2): 175-180 (2006) Unversty of Tehran, ISSN 1016-1104 http://jscencesutacr The Mnmum Unversal Cost Flow n an Infeasble Flow Network H Saleh Fathabad * M Bagheran
More informationIntegrated approach in solving parallel machine scheduling and location (ScheLoc) problem
Internatonal Journal of Industral Engneerng Computatons 7 (2016) 573 584 Contents lsts avalable at GrowngScence Internatonal Journal of Industral Engneerng Computatons homepage: www.growngscence.com/ec
More informationWinter 2008 CS567 Stochastic Linear/Integer Programming Guest Lecturer: Xu, Huan
Wnter 2008 CS567 Stochastc Lnear/Integer Programmng Guest Lecturer: Xu, Huan Class 2: More Modelng Examples 1 Capacty Expanson Capacty expanson models optmal choces of the tmng and levels of nvestments
More informationSingle-Facility Scheduling over Long Time Horizons by Logic-based Benders Decomposition
Sngle-Faclty Schedulng over Long Tme Horzons by Logc-based Benders Decomposton Elvn Coban and J. N. Hooker Tepper School of Busness, Carnege Mellon Unversty ecoban@andrew.cmu.edu, john@hooker.tepper.cmu.edu
More informationSolution (1) Formulate the problem as a LP model.
Benha Unversty Department: Mechancal Engneerng Benha Hgh Insttute of Technology Tme: 3 hr. January 0 -Fall semester 4 th year Eam(Regular) Soluton Subject: Industral Engneerng M4 ------------------------------------------------------------------------------------------------------.
More informationSimultaneous Optimization of Berth Allocation, Quay Crane Assignment and Quay Crane Scheduling Problems in Container Terminals
Smultaneous Optmzaton of Berth Allocaton, Quay Crane Assgnment and Quay Crane Schedulng Problems n Contaner Termnals Necat Aras, Yavuz Türkoğulları, Z. Caner Taşkın, Kuban Altınel Abstract In ths work,
More informationA Modified Vogel s Approximation Method for Obtaining a Good Primal Solution of Transportation Problems
Annals of Pure and Appled Mathematcs Vol., No., 06, 6-7 ISSN: 79-087X (P), 79-0888(onlne) Publshed on 5 January 06 www.researchmathsc.org Annals of A Modfed Vogel s Appromaton Method for Obtanng a Good
More informationAn Admission Control Algorithm in Cloud Computing Systems
An Admsson Control Algorthm n Cloud Computng Systems Authors: Frank Yeong-Sung Ln Department of Informaton Management Natonal Tawan Unversty Tape, Tawan, R.O.C. ysln@m.ntu.edu.tw Yngje Lan Management Scence
More informationSOLVING CAPACITATED VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS BY GOAL PROGRAMMING APPROACH
Proceedngs of IICMA 2013 Research Topc, pp. xx-xx. SOLVIG CAPACITATED VEHICLE ROUTIG PROBLEMS WITH TIME WIDOWS BY GOAL PROGRAMMIG APPROACH ATMII DHORURI 1, EMIUGROHO RATA SARI 2, AD DWI LESTARI 3 1Department
More informationEn Route Traffic Optimization to Reduce Environmental Impact
En Route Traffc Optmzaton to Reduce Envronmental Impact John-Paul Clarke Assocate Professor of Aerospace Engneerng Drector of the Ar Transportaton Laboratory Georga Insttute of Technology Outlne 1. Introducton
More informationA PROBABILITY-DRIVEN SEARCH ALGORITHM FOR SOLVING MULTI-OBJECTIVE OPTIMIZATION PROBLEMS
HCMC Unversty of Pedagogy Thong Nguyen Huu et al. A PROBABILITY-DRIVEN SEARCH ALGORITHM FOR SOLVING MULTI-OBJECTIVE OPTIMIZATION PROBLEMS Thong Nguyen Huu and Hao Tran Van Department of mathematcs-nformaton,
More informationA Simple Inventory System
A Smple Inventory System Lawrence M. Leems and Stephen K. Park, Dscrete-Event Smulaton: A Frst Course, Prentce Hall, 2006 Hu Chen Computer Scence Vrgna State Unversty Petersburg, Vrgna February 8, 2017
More informationAn Interactive Optimisation Tool for Allocation Problems
An Interactve Optmsaton ool for Allocaton Problems Fredr Bonäs, Joam Westerlund and apo Westerlund Process Desgn Laboratory, Faculty of echnology, Åbo Aadem Unversty, uru 20500, Fnland hs paper presents
More informationInteractive Bi-Level Multi-Objective Integer. Non-linear Programming Problem
Appled Mathematcal Scences Vol 5 0 no 65 3 33 Interactve B-Level Mult-Objectve Integer Non-lnear Programmng Problem O E Emam Department of Informaton Systems aculty of Computer Scence and nformaton Helwan
More informationTHE DETERMINATION OF PARADOXICAL PAIRS IN A LINEAR TRANSPORTATION PROBLEM
Publshed by European Centre for Research Tranng and Development UK (www.ea-ournals.org) THE DETERMINATION OF PARADOXICAL PAIRS IN A LINEAR TRANSPORTATION PROBLEM Ekeze Dan Dan Department of Statstcs, Imo
More informationSolutions to exam in SF1811 Optimization, Jan 14, 2015
Solutons to exam n SF8 Optmzaton, Jan 4, 25 3 3 O------O -4 \ / \ / The network: \/ where all lnks go from left to rght. /\ / \ / \ 6 O------O -5 2 4.(a) Let x = ( x 3, x 4, x 23, x 24 ) T, where the varable
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
More informationEEL 6266 Power System Operation and Control. Chapter 3 Economic Dispatch Using Dynamic Programming
EEL 6266 Power System Operaton and Control Chapter 3 Economc Dspatch Usng Dynamc Programmng Pecewse Lnear Cost Functons Common practce many utltes prefer to represent ther generator cost functons as sngle-
More informationECE559VV Project Report
ECE559VV Project Report (Supplementary Notes Loc Xuan Bu I. MAX SUM-RATE SCHEDULING: THE UPLINK CASE We have seen (n the presentaton that, for downlnk (broadcast channels, the strategy maxmzng the sum-rate
More informationOutline and Reading. Dynamic Programming. Dynamic Programming revealed. Computing Fibonacci. The General Dynamic Programming Technique
Outlne and Readng Dynamc Programmng The General Technque ( 5.3.2) -1 Knapsac Problem ( 5.3.3) Matrx Chan-Product ( 5.3.1) Dynamc Programmng verson 1.4 1 Dynamc Programmng verson 1.4 2 Dynamc Programmng
More informationAn Effective Modification to Solve Transportation Problems: A Cost Minimization Approach
Annals of Pure and Appled Mathematcs Vol. 6, No. 2, 204, 99-206 ISSN: 2279-087X (P), 2279-0888(onlne) Publshed on 4 August 204 www.researchmathsc.org Annals of An Effectve Modfcaton to Solve Transportaton
More informationThe Value of Demand Postponement under Demand Uncertainty
Recent Researches n Appled Mathematcs, Smulaton and Modellng The Value of emand Postponement under emand Uncertanty Rawee Suwandechocha Abstract Resource or capacty nvestment has a hgh mpact on the frm
More informationOn the Multicriteria Integer Network Flow Problem
BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 5, No 2 Sofa 2005 On the Multcrtera Integer Network Flow Problem Vassl Vasslev, Marana Nkolova, Maryana Vassleva Insttute of
More informationChapter - 2. Distribution System Power Flow Analysis
Chapter - 2 Dstrbuton System Power Flow Analyss CHAPTER - 2 Radal Dstrbuton System Load Flow 2.1 Introducton Load flow s an mportant tool [66] for analyzng electrcal power system network performance. Load
More informationSOLVING MULTI-OBJECTIVE INTERVAL TRANSPORTATION PROBLEM USING GREY SITUATION DECISION-MAKING THEORY BASED ON GREY NUMBERS
Internatonal Journal of Pure and Appled Mathematcs Volume 113 No. 2 2017, 219-233 ISSN: 1311-8080 (prnted verson; ISSN: 1314-3395 (on-lne verson url: http://www.pam.eu do: 10.12732/pam.v1132.3 PApam.eu
More informationCOS 521: Advanced Algorithms Game Theory and Linear Programming
COS 521: Advanced Algorthms Game Theory and Lnear Programmng Moses Charkar February 27, 2013 In these notes, we ntroduce some basc concepts n game theory and lnear programmng (LP). We show a connecton
More informationHeuristic Algorithm for Finding Sensitivity Analysis in Interval Solid Transportation Problems
Internatonal Journal of Innovatve Research n Advanced Engneerng (IJIRAE) ISSN: 349-63 Volume Issue 6 (July 04) http://rae.com Heurstc Algorm for Fndng Senstvty Analyss n Interval Sold Transportaton Problems
More informationCIE4801 Transportation and spatial modelling Trip distribution
CIE4801 ransportaton and spatal modellng rp dstrbuton Rob van Nes, ransport & Plannng 17/4/13 Delft Unversty of echnology Challenge the future Content What s t about hree methods Wth specal attenton for
More informationNatural Language Processing and Information Retrieval
Natural Language Processng and Informaton Retreval Support Vector Machnes Alessandro Moschtt Department of nformaton and communcaton technology Unversty of Trento Emal: moschtt@ds.untn.t Summary Support
More informationAssortment Optimization under MNL
Assortment Optmzaton under MNL Haotan Song Aprl 30, 2017 1 Introducton The assortment optmzaton problem ams to fnd the revenue-maxmzng assortment of products to offer when the prces of products are fxed.
More informationDynamic Facility Location with Stochastic Demands
Dynamc Faclty Locaton wth Stochastc Demands Martn Romauch and Rchard F. Hartl Unversty of Venna, Department of Management Scence, Brünner Straße 72 1210 Venna, Austra {martn.romauch,rchard.hartl}@unve.ac.at
More informationFUZZY GOAL PROGRAMMING VS ORDINARY FUZZY PROGRAMMING APPROACH FOR MULTI OBJECTIVE PROGRAMMING PROBLEM
Internatonal Conference on Ceramcs, Bkaner, Inda Internatonal Journal of Modern Physcs: Conference Seres Vol. 22 (2013) 757 761 World Scentfc Publshng Company DOI: 10.1142/S2010194513010982 FUZZY GOAL
More informationJournal of Physics: Conference Series. Related content PAPER OPEN ACCESS
Journal of Physcs: Conference Seres PAPER OPEN ACCESS An ntegrated producton-nventory model for the snglevendor two-buyer problem wth partal backorder, stochastc demand, and servce level constrants To
More informationTRAPEZOIDAL FUZZY NUMBERS FOR THE TRANSPORTATION PROBLEM. Abstract
TRAPEZOIDAL FUZZY NUMBERS FOR THE TRANSPORTATION PROBLEM ARINDAM CHAUDHURI* Lecturer (Mathematcs & Computer Scence) Meghnad Saha Insttute of Technology, Kolkata, Inda arndam_chau@yahoo.co.n *correspondng
More informationResource Allocation with a Budget Constraint for Computing Independent Tasks in the Cloud
Resource Allocaton wth a Budget Constrant for Computng Independent Tasks n the Cloud Wemng Sh and Bo Hong School of Electrcal and Computer Engneerng Georga Insttute of Technology, USA 2nd IEEE Internatonal
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Exerments-I MODULE III LECTURE - 2 EXPERIMENTAL DESIGN MODELS Dr. Shalabh Deartment of Mathematcs and Statstcs Indan Insttute of Technology Kanur 2 We consder the models
More informationModule 9. Lecture 6. Duality in Assignment Problems
Module 9 1 Lecture 6 Dualty n Assgnment Problems In ths lecture we attempt to answer few other mportant questons posed n earler lecture for (AP) and see how some of them can be explaned through the concept
More informationDynamic Programming. Lecture 13 (5/31/2017)
Dynamc Programmng Lecture 13 (5/31/2017) - A Forest Thnnng Example - Projected yeld (m3/ha) at age 20 as functon of acton taken at age 10 Age 10 Begnnng Volume Resdual Ten-year Volume volume thnned volume
More informationSee Book Chapter 11 2 nd Edition (Chapter 10 1 st Edition)
Count Data Models See Book Chapter 11 2 nd Edton (Chapter 10 1 st Edton) Count data consst of non-negatve nteger values Examples: number of drver route changes per week, the number of trp departure changes
More informationAn Integrated OR/CP Method for Planning and Scheduling
An Integrated OR/CP Method for Plannng and Schedulng John Hooer Carnege Mellon Unversty IT Unversty of Copenhagen June 2005 The Problem Allocate tass to facltes. Schedule tass assgned to each faclty. Subect
More informationLP-based Approximation Algorithms for Capacitated Facility Location
LP-based Approxmaton Algorthms for Capactated Faclty Locaton Retsef Lev 1, Davd B. Shmoys 2,andChatanyaSwamy 3 1 School of ORIE, Cornell Unversty, Ithaca, NY 14853. rl227@cornell.edu 2 School of ORIE and
More informationMMA and GCMMA two methods for nonlinear optimization
MMA and GCMMA two methods for nonlnear optmzaton Krster Svanberg Optmzaton and Systems Theory, KTH, Stockholm, Sweden. krlle@math.kth.se Ths note descrbes the algorthms used n the author s 2007 mplementatons
More informationLINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity
LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 31 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 6. Rdge regresson The OLSE s the best lnear unbased
More informationA Lower Bound on SINR Threshold for Call Admission Control in Multiple-Class CDMA Systems with Imperfect Power-Control
A ower Bound on SIR Threshold for Call Admsson Control n Multple-Class CDMA Systems w Imperfect ower-control Mohamed H. Ahmed Faculty of Engneerng and Appled Scence Memoral Unversty of ewfoundland St.
More informationA LINEAR PROGRAM TO COMPARE MULTIPLE GROSS CREDIT LOSS FORECASTS. Dr. Derald E. Wentzien, Wesley College, (302) ,
A LINEAR PROGRAM TO COMPARE MULTIPLE GROSS CREDIT LOSS FORECASTS Dr. Derald E. Wentzen, Wesley College, (302) 736-2574, wentzde@wesley.edu ABSTRACT A lnear programmng model s developed and used to compare
More information10.34 Numerical Methods Applied to Chemical Engineering Fall Homework #3: Systems of Nonlinear Equations and Optimization
10.34 Numercal Methods Appled to Chemcal Engneerng Fall 2015 Homework #3: Systems of Nonlnear Equatons and Optmzaton Problem 1 (30 ponts). A (homogeneous) azeotrope s a composton of a multcomponent mxture
More informationTechnical Note: Capacity Constraints Across Nests in Assortment Optimization Under the Nested Logit Model
Techncal Note: Capacty Constrants Across Nests n Assortment Optmzaton Under the Nested Logt Model Jacob B. Feldman, Huseyn Topaloglu School of Operatons Research and Informaton Engneerng, Cornell Unversty,
More informationCollege of Computer & Information Science Fall 2009 Northeastern University 20 October 2009
College of Computer & Informaton Scence Fall 2009 Northeastern Unversty 20 October 2009 CS7880: Algorthmc Power Tools Scrbe: Jan Wen and Laura Poplawsk Lecture Outlne: Prmal-dual schema Network Desgn:
More informationIJRSS Volume 2, Issue 2 ISSN:
IJRSS Volume, Issue ISSN: 49-496 An Algorthm To Fnd Optmum Cost Tme Trade Off Pars In A Fractonal Capactated Transportaton Problem Wth Restrcted Flow KAVITA GUPTA* S.R. ARORA** _ Abstract: Ths paper presents
More informationComputing Correlated Equilibria in Multi-Player Games
Computng Correlated Equlbra n Mult-Player Games Chrstos H. Papadmtrou Presented by Zhanxang Huang December 7th, 2005 1 The Author Dr. Chrstos H. Papadmtrou CS professor at UC Berkley (taught at Harvard,
More informationFuzzy approach to solve multi-objective capacitated transportation problem
Internatonal Journal of Bonformatcs Research, ISSN: 0975 087, Volume, Issue, 00, -0-4 Fuzzy aroach to solve mult-objectve caactated transortaton roblem Lohgaonkar M. H. and Bajaj V. H.* * Deartment of
More informationDepartment of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution
Department of Statstcs Unversty of Toronto STA35HS / HS Desgn and Analyss of Experments Term Test - Wnter - Soluton February, Last Name: Frst Name: Student Number: Instructons: Tme: hours. Ads: a non-programmable
More informationLecture 10 Support Vector Machines II
Lecture 10 Support Vector Machnes II 22 February 2016 Taylor B. Arnold Yale Statstcs STAT 365/665 1/28 Notes: Problem 3 s posted and due ths upcomng Frday There was an early bug n the fake-test data; fxed
More informationSTAT 511 FINAL EXAM NAME Spring 2001
STAT 5 FINAL EXAM NAME Sprng Instructons: Ths s a closed book exam. No notes or books are allowed. ou may use a calculator but you are not allowed to store notes or formulas n the calculator. Please wrte
More informationFormulations, Branch-and-Cut and a Hybrid Heuristic Algorithm for an Inventory Routing Problem with Perishable Products
Formulatons, Branch-and-Cut and a Hybrd Heurstc Algorthm for an Inventory Routng Problem wth Pershable Products Aldar Alvarez Jean-Franços Cordeau Raf Jans Pedro Munar Renaldo Morabto October 2018 CIRRELT-2018-42
More informationDual-Channel Warehouse and Inventory Management with Stochastic Demand
Unversty of Wndsor Scholarshp at UWndsor Mechancal, Automotve & Materals Engneerng Publcatons Department of Mechancal, Automotve & Materals Engneerng Wnter 2-19-2018 Dual-Channel Warehouse and Inventory
More informationU.C. Berkeley CS294: Beyond Worst-Case Analysis Luca Trevisan September 5, 2017
U.C. Berkeley CS94: Beyond Worst-Case Analyss Handout 4s Luca Trevsan September 5, 07 Summary of Lecture 4 In whch we ntroduce semdefnte programmng and apply t to Max Cut. Semdefnte Programmng Recall that
More informationPredictive Analytics : QM901.1x Prof U Dinesh Kumar, IIMB. All Rights Reserved, Indian Institute of Management Bangalore
Sesson Outlne Introducton to classfcaton problems and dscrete choce models. Introducton to Logstcs Regresson. Logstc functon and Logt functon. Maxmum Lkelhood Estmator (MLE) for estmaton of LR parameters.
More informationSolution Thermodynamics
Soluton hermodynamcs usng Wagner Notaton by Stanley. Howard Department of aterals and etallurgcal Engneerng South Dakota School of nes and echnology Rapd Cty, SD 57701 January 7, 001 Soluton hermodynamcs
More informationStructure and Drive Paul A. Jensen Copyright July 20, 2003
Structure and Drve Paul A. Jensen Copyrght July 20, 2003 A system s made up of several operatons wth flow passng between them. The structure of the system descrbes the flow paths from nputs to outputs.
More informationSupply Network Protection under Capacity Constraint
Supply Network Protecton under Capacty Constrant Naj Brcha Mustapha Nourelfath January 2014 CIRRELT-2014-06 Naj Brcha *, Mustapha Nourelfath Interunversty Research Centre on Enterprse Networks, Logstcs
More informationCOMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
More informationAssignment 4. Adsorption Isotherms
Insttute of Process Engneerng Assgnment 4. Adsorpton Isotherms Part A: Compettve adsorpton of methane and ethane In large scale adsorpton processes, more than one compound from a mxture of gases get adsorbed,
More informationChapter Newton s Method
Chapter 9. Newton s Method After readng ths chapter, you should be able to:. Understand how Newton s method s dfferent from the Golden Secton Search method. Understand how Newton s method works 3. Solve
More informationMaximizing the number of nonnegative subsets
Maxmzng the number of nonnegatve subsets Noga Alon Hao Huang December 1, 213 Abstract Gven a set of n real numbers, f the sum of elements of every subset of sze larger than k s negatve, what s the maxmum
More informationHierarchical State Estimation Using Phasor Measurement Units
Herarchcal State Estmaton Usng Phasor Measurement Unts Al Abur Northeastern Unversty Benny Zhao (CA-ISO) and Yeo-Jun Yoon (KPX) IEEE PES GM, Calgary, Canada State Estmaton Workng Group Meetng July 28,
More informationAn Upper Bound on SINR Threshold for Call Admission Control in Multiple-Class CDMA Systems with Imperfect Power-Control
An Upper Bound on SINR Threshold for Call Admsson Control n Multple-Class CDMA Systems wth Imperfect ower-control Mahmoud El-Sayes MacDonald, Dettwler and Assocates td. (MDA) Toronto, Canada melsayes@hotmal.com
More informationCalculation of time complexity (3%)
Problem 1. (30%) Calculaton of tme complexty (3%) Gven n ctes, usng exhaust search to see every result takes O(n!). Calculaton of tme needed to solve the problem (2%) 40 ctes:40! dfferent tours 40 add
More informationJournal of Applied Science and Agriculture
AENSI Journals Journal of Appled Scence and Agrculture Journal home page: www.aensweb.com/asa/nde.html Developng a New Mult-Obectve Model for Locaton-Routng Problem along wth Travelng Tmes and Fuzzy Due
More informationDynamic Slope Scaling Procedure to solve. Stochastic Integer Programming Problem
Journal of Computatons & Modellng, vol.2, no.4, 2012, 133-148 ISSN: 1792-7625 (prnt), 1792-8850 (onlne) Scenpress Ltd, 2012 Dynamc Slope Scalng Procedure to solve Stochastc Integer Programmng Problem Takayuk
More informationCHAPTER 7 STOCHASTIC ECONOMIC EMISSION DISPATCH-MODELED USING WEIGHTING METHOD
90 CHAPTER 7 STOCHASTIC ECOOMIC EMISSIO DISPATCH-MODELED USIG WEIGHTIG METHOD 7.1 ITRODUCTIO early 70% of electrc power produced n the world s by means of thermal plants. Thermal power statons are the
More informationThe written Master s Examination
he wrtten Master s Eamnaton Opton Statstcs and Probablty SPRING 9 Full ponts may be obtaned for correct answers to 8 questons. Each numbered queston (whch may have several parts) s worth the same number
More informationFinding Optimal System Time for Message Processing in Free-Sequence Multi-Stage News Agency
Recent Advances n Mathematcal Methods and Computatonal Technques n Modern Scence Fndng Optmal System Tme for Message Processng n Free-Sequence Mult-Stage News Agency ABDULLAH ABDUL ABBAR *, NASHAT FORS,
More informationWhich Separator? Spring 1
Whch Separator? 6.034 - Sprng 1 Whch Separator? Mamze the margn to closest ponts 6.034 - Sprng Whch Separator? Mamze the margn to closest ponts 6.034 - Sprng 3 Margn of a pont " # y (w $ + b) proportonal
More informationUsing T.O.M to Estimate Parameter of distributions that have not Single Exponential Family
IOSR Journal of Mathematcs IOSR-JM) ISSN: 2278-5728. Volume 3, Issue 3 Sep-Oct. 202), PP 44-48 www.osrjournals.org Usng T.O.M to Estmate Parameter of dstrbutons that have not Sngle Exponental Famly Jubran
More informationAbsorbing Markov Chain Models to Determine Optimum Process Target Levels in Production Systems with Rework and Scrapping
Archve o SID Journal o Industral Engneerng 6(00) -6 Absorbng Markov Chan Models to Determne Optmum Process Target evels n Producton Systems wth Rework and Scrappng Mohammad Saber Fallah Nezhad a, Seyed
More informationPolynomial Regression Models
LINEAR REGRESSION ANALYSIS MODULE XII Lecture - 6 Polynomal Regresson Models Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Test of sgnfcance To test the sgnfcance
More informationLATERAL TRANSSHIPMENTS IN INVENTORY MODELS
LATERAL TRANSSHIPMENTS IN INVENTORY MODELS MIN CHEN 11.2008 BMI THESIS Lateral Transshpments n Inventory Models MIN CHEN 11.2008 II PREFACE The BMI Thess s the fnal report to acqure the Master's degree
More informationfind (x): given element x, return the canonical element of the set containing x;
COS 43 Sprng, 009 Dsjont Set Unon Problem: Mantan a collecton of dsjont sets. Two operatons: fnd the set contanng a gven element; unte two sets nto one (destructvely). Approach: Canoncal element method:
More informationOpen Systems: Chemical Potential and Partial Molar Quantities Chemical Potential
Open Systems: Chemcal Potental and Partal Molar Quanttes Chemcal Potental For closed systems, we have derved the followng relatonshps: du = TdS pdv dh = TdS + Vdp da = SdT pdv dg = VdP SdT For open systems,
More informationMEM Chapter 4b. LMI Lab commands
1 MEM8-7 Chapter 4b LMI Lab commands setlms lmvar lmterm getlms lmedt lmnbr matnbr lmnfo feasp dec2mat evallm showlm setmvar mat2dec mncx dellm delmvar gevp 2 Intalzng the LMI System he descrpton of an
More informationChapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems
Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons
More informationprinceton univ. F 17 cos 521: Advanced Algorithm Design Lecture 7: LP Duality Lecturer: Matt Weinberg
prnceton unv. F 17 cos 521: Advanced Algorthm Desgn Lecture 7: LP Dualty Lecturer: Matt Wenberg Scrbe: LP Dualty s an extremely useful tool for analyzng structural propertes of lnear programs. Whle there
More informationBasic Statistical Analysis and Yield Calculations
October 17, 007 Basc Statstcal Analyss and Yeld Calculatons Dr. José Ernesto Rayas Sánchez 1 Outlne Sources of desgn-performance uncertanty Desgn and development processes Desgn for manufacturablty A general
More informationPresenters. Muscle Modeling. John Rasmussen (Presenter) Arne Kiis (Host) The web cast will begin in a few minutes.
Muscle Modelng If a part of my screen n mssng from your Vew, please press Sharng -> Vew -> Autoft The web cast wll begn n a few mnutes. Introducton (~5 mn) Overvew (~5 mn) Muscle knematcs (~10 mn) Muscle
More informationOPTIMISATION. Introduction Single Variable Unconstrained Optimisation Multivariable Unconstrained Optimisation Linear Programming
OPTIMIATION Introducton ngle Varable Unconstraned Optmsaton Multvarable Unconstraned Optmsaton Lnear Programmng Chapter Optmsaton /. Introducton In an engneerng analss, sometmes etremtes, ether mnmum or
More informationHow Strong Are Weak Patents? Joseph Farrell and Carl Shapiro. Supplementary Material Licensing Probabilistic Patents to Cournot Oligopolists *
How Strong Are Weak Patents? Joseph Farrell and Carl Shapro Supplementary Materal Lcensng Probablstc Patents to Cournot Olgopolsts * September 007 We study here the specal case n whch downstream competton
More informationINTEGER NETWORK SYNTHESIS PROBLEM FOR HOP CONSTRAINED FLOWS
INTEGER NETWORK SYNTHESIS PROBLEM FOR HOP CONSTRAINED FLOWS SANTOSH N. KABADI AND K.P.K. NAIR Abstract. Hop constrant s assocated wth modern communcaton network flows. We consder the problem of desgnng
More informationExtensions of the Psuedo-Boolean Representation of the p-median Problem
Extensons of the Psuedo-Boolean Representaton of the p-medan Problem Gabrel Sloggy Advsed by Professor Rchard Church, Department of Geography Abstract The p-medan problem (PMP) s nherently a graph theoretc
More informationMulti-product budget-constrained acquistion and pricing with uncertain demand and supplier quantity discounts
Unversty of Wndsor Scholarshp at UWndsor Mechancal, Automotve & Materals Engneerng Publcatons Department of Mechancal, Automotve & Materals Engneerng 11-2010 Mult-product budget-constraned acquston and
More informationSiqian Shen. Department of Industrial and Operations Engineering University of Michigan, Ann Arbor, MI 48109,
Page 1 of 38 Naval Research Logstcs Sngle-commodty Stochastc Network Desgn under Demand and Topologcal Uncertantes wth Insuffcent Data Accepted Artcle Sqan Shen Department of Industral and Operatons Engneerng
More informationService-Level Differentiation in Many-Server Service Systems via Queue-Ratio Routing
Publshed onlne ahead of prnt October 28, 2009 OPERATIONS RESEARCH Artcles n Advance, pp. 1 13 ssn 0030-364X essn 1526-5463 nforms do 10.1287/opre.1090.0736 2009 INFORMS Copyrght: INFORMS holds copyrght
More informationAn Integrated Strategy for a Production Planning and Warehouse Layout Problem: Modeling and Solution Approaches
Unversty of Wndsor Scholarshp at UWndsor Mechancal, Automotve & Materals Engneerng Publcatons Department of Mechancal, Automotve & Materals Engneerng Summer 6-18-2016 An Integrated Strategy for a Producton
More informationSupplementary Notes for Chapter 9 Mixture Thermodynamics
Supplementary Notes for Chapter 9 Mxture Thermodynamcs Key ponts Nne major topcs of Chapter 9 are revewed below: 1. Notaton and operatonal equatons for mxtures 2. PVTN EOSs for mxtures 3. General effects
More informationChapter 3 Describing Data Using Numerical Measures
Chapter 3 Student Lecture Notes 3-1 Chapter 3 Descrbng Data Usng Numercal Measures Fall 2006 Fundamentals of Busness Statstcs 1 Chapter Goals To establsh the usefulness of summary measures of data. The
More informationFor now, let us focus on a specific model of neurons. These are simplified from reality but can achieve remarkable results.
Neural Networks : Dervaton compled by Alvn Wan from Professor Jtendra Malk s lecture Ths type of computaton s called deep learnng and s the most popular method for many problems, such as computer vson
More informationTHE SUMMATION NOTATION Ʃ
Sngle Subscrpt otaton THE SUMMATIO OTATIO Ʃ Most of the calculatons we perform n statstcs are repettve operatons on lsts of numbers. For example, we compute the sum of a set of numbers, or the sum of the
More informationNP-Completeness : Proofs
NP-Completeness : Proofs Proof Methods A method to show a decson problem Π NP-complete s as follows. (1) Show Π NP. (2) Choose an NP-complete problem Π. (3) Show Π Π. A method to show an optmzaton problem
More information8. Modelling Uncertainty
8. Modellng Uncertanty. Introducton. Generatng Values From Known Probablty Dstrbutons. Monte Carlo Smulaton 4. Chance Constraned Models 5 5. Markov Processes and Transton Probabltes 6 6. Stochastc Optmzaton
More informationSome modelling aspects for the Matlab implementation of MMA
Some modellng aspects for the Matlab mplementaton of MMA Krster Svanberg krlle@math.kth.se Optmzaton and Systems Theory Department of Mathematcs KTH, SE 10044 Stockholm September 2004 1. Consdered optmzaton
More information