A Computer Technique for Solving LP Problems with Bounded Variables


 Shon Goodman
 1 years ago
 Views:
Transcription
1 Dhaka Unv. J. Sc. 60(2): , 2012 (July) A Computer Technque for Solvng LP Problems wth Bounded Varables S. M. Atqur Rahman Chowdhury * and Sanwar Uddn Ahmad Department of Mathematcs; Unversty of Dhaka, Dhaka1000, Bangladesh Receved on Accepted for Publcaton on Abstract Lnear Programmng problem (LPP)s wth upper bounded varables can be solved usng the Bounded Smplex method (BSM), wthout the explct consderaton of the upper bounded constrants. The upper bounded constrants are consdered mplctly n ths method whch reduced the sze of the bass matrx sgnfcantly. In ths paper, we have developed MATHEMATICA codes for solvng such problems. A complete algorthm of the program wth the help of a numercal example has been provded. Fnally a comparson wth the bultn code has been made for showng the effcency of the developed code. Keywords: LPP, bounded smplex method, bounded varable, computer program, restrctons. I. Introducton Lnear Programmng problem (LPP) wth bounded varables has the form Maxmze, Z = {CX: (A, I) X = b; L X U} (1) One can solve such problems by regular smplex method by consderng the lower and upper bound constrants explctly whch s not computatonally effcent as the number of constrants as well as the number of varables become very large. Dantzg 1 developed the method for solvng lnear programmng wth upper bound restrctons on the varables. Wagner 2 developed the dual smplex method for LPP wth bounded varables, whch s further studed by Maros 3, 4. In 1972, Duguay 5 et al. studed lnear programmng wth relatve bounded varables. Y. Xa and J. Wang 6 used neural network for fndng an approxmate soluton of LPP wth bounded varables whch converges globally to the solutons to the LPPs. However, most of the real lfe problems deal wth large quanttes of data and parameters, whch can only reasonably be tackled by the calculatng power of a computer and researchers, are actvely engaged n developng programmng codes for solvng varous problems n Operatons Research e.g. Saha and Hasan 7, Hasan. 8, Morshed and Hasan 9. In ths paper, we wll dscuss the algorthm for solvng LPP wth Bounded Varables and develop a MATHEMATICA program for solvng such problems, whch s capable of dealng wth any number of varables. Fnally a numercal example obtaned by usng the program s provded and a comparson has been made wth the bultn MATHEMATICA code. * Correspondence author : Emal: II. Bounded Smplex Method 10 In LP models varables may have explct postve upper and lower bounds. An LPP may have n addton to the regular constrants, lower or upper bounds on some or all varables.e. constrants of the type L X U For the lower bounds.e. X L n (1), the followng substtuton X X = L, X 0 (2) can be used throughout and solve the problem n terms of X (whose lower bound now equals zero). The orgnal X s determned by back substtuton whch s legtmate because ts guarantees that X X = L wll reman nonnegatve for all X 0. However, for the upper boundng constrant, X U, the dea of drect substtuton.e. X + X = U, X 0 s not correct because back substtuton X + X = U, does not ensure that X wll reman nonnegatve. For smplcty we defne the upper bounded LP model as Maxmze, Z = {CX: (A, I) X = b, 0 X U} (3) The bounded algorthm uses only the constrants (A, I) X = b, X 0 explctly, whle accountng for X U mplctly through modfcaton of the smplex feasblty condton. Let X = B b be a current basc feasble soluton of (A, I) X = b, X 0 and suppose that accordng to the (regular) optmalty condton, P s the enterng vector. Then, gven that all the nonbasc varables are zero, the constrant equaton of the th basc varable can be wrtten as (X ) = (B b) B P x
2 164 When the enterng varable x ncreases above zero level, (X ) wll ncrease or decrease dependng on whether B P s negatve or postve, respectvely. Thus, n determnng the value of the enterng varable x three condtons must be satsfed: Condton1: The basc varable (X ) remans nonnegatvethat s, (X ) 0. Ths s not volated f ( B 1 b) x θ mn : 1 B P ( B 1 P ) 0 (4) Condton2: The basc varable (X ) does not exceed ts upper bound.e., (X ) (U ), where U comprse the ordered elements of U correspondng to X. Ths s not volated f ( B 1 b) ( ) 1 x θ mn U B : B P 0 (5) ( B 1 P ) Condton3: The enterng varable x cannot assume a value larger than ts upper bound that s x u, where u s the th element of U. Combnng the three restrctons together, x enters the soluton at the level that satsfes all three condtons and the level s defned as x = mn {,, u } (6) The change of bass for the next teraton depends on whether x enters the soluton at level 1, 2 or u. Assumng that (X ) s the leavng varable, then we have the followng rules: Rule1: x = u. The basc vector X remans unchanged because x = u stops short of forcng any of the current basc varables to reach ts lower (=0) or upper bound. Ths means that x wll reman nonbasc but at upper bound. Followng the argument ust presented, the new teraton s generated by usng the substtuton x = u x. Rule2: x = ; (X ) leaves the basc soluton (becomes nonbasc) at level zero. The new teraton s generated n the normal smplex manner by usng x and (X ) as the enterng and the leavng varables, respectvely. S. M. Atqur Rahman Chowdhury and Sanwar Uddn Ahmad of, x =, wth one modfcaton that accounts for the fact that (X ) wll be nonbasc at upper bound. Because the values of and are developed under the assumpton that all nonbasc varables are at zero level. Ths s acheved by usng the substtuton (X ) = (U ) (X ), where (X ) 0. It s mmateral whether the substtuton s made before or after the new bass s computed. A te among,, and u may be taken arbtrarly. However, t s preferable to mplement the rule for x = u because t entals less computaton. The substtuton x = u x wll change the orgnal c, P and b to c = c, P = P and btob = u P. Ths means that f the revsed smplex method s used, all the computaton (e.g, B, X, and z c ) should be based on the updated values of C, A, and b at each teraton. III. MATHEMATICA codes For convenence we have presented the developed MATHEMATICA codes for solvng LPP wth bounded varables whle solvng a numercal example. LPP1 Maxmze, Z = 3x 1 + 5x 2 + 2x 3 Subect to, x 1 + 2x 2 + 2x x 1 + 4x 2 + 3x x 1 4, 0 x 2 3, 0 x 3 3 Introducng slack varables x 4 0, x 5 0 one to each constrant, we have Maxmze, Z = 3x 1 + 5x 2 + 2x 3 + 0x 4 + 0x 5 Subect to, x 1 + 2x 2 + 2x 3 + x 4 + 0x 5 = 10 2x 1 + 4x 2 + 3x 3 + 0x 4 + x 5 = 15 0 x 1 4, 0 x 2 3, 0 x 3 3, x 4 0, x 5 0 The followng codes are used to take the necessary nputs. Rule3: x = ; (X ), becomes nonbasc at ts upper bound. The new teratons s generated as n the case
3 A Computer Technque for Solvng LP Problems wth Bounded Varables 165 The nputs are made nto the followng nput box: Here, a, b are the 1 st and 2 nd row of the ntal table, K s the coeffcent matrx, U[[ ]] represents the upper bounds of x, CNT s the ntal basc feasble solutons (b ), B s the bass matrx and CJ[[ ]] represents the coeffcent of the proft vector (C ). Enter the desre functon Z: 3x 1 + 5x 2 + 2x 3 ; Then, n = 5; Enter Row 1: 1, 2, 2, 1, and 0 Enter Row 2: 2, 4, 3, 0, and 1 Enter coeff. of obectve functon: 3, 5, 2, 0, and 0 Enter upper bound: 4, 3, 3, 9999, and Enter coeff. of bass element: 0, 0 Enter constant: 10, 15 X = 0; X = 0; X = 0; X = 0; X = 0 The ntal smplex table s generated by the followng codes. Table. 1. Intal smplex table C Bass 0 0 x 4 x x 1 x 2 x 3 x 4 x Soluton(b ) C Z = 0
4 166 The followng codes are used for dentfyng the enterng nonbasc varable. S. M. Atqur Rahman Chowdhury and Sanwar Uddn Ahmad Table 3 s obtaned by rule 2 n secton 2 as, Table. 3. Basc x x x Soluton Z 1 5/2 3/2 39/2 x 0 1/21/2 5/2 x 2 3/2 1/2 3/2 The developed codes for Rule2 are, Here, l4 = C = C z = relatve proft vector, MP = Max{C : C > 0}, θ s the value of θ n (5), θ s the value of θ n (4) and θ represents the value of x n (6). By Rule1 n secton 2, we obtaned Table 2 as, Table. 2. Basc x x x Soluton Z x x For Rule3, developed codes are: The developed codes for Rule1 are,
5 A Computer Technque for Solvng LP Problems wth Bounded Varables 167 These codes are teratvely mplemented untl the optmum table s obtaned. Table. 4. Basc x x x Soluton Z 1/27/45/4 75/4 x 0 1/21/2 5/2 x 1/23/41/43/4 Table. 5. Optmum table Basc x x x Soluton Z 1/27/45/4 83/4 x 0 1/21/2 5/2 x 1/23/41/4 5/4 By back substtuton the optmal values of x, x, and x are x = u x = 4, x = u x = 4 7 and 83 x = 0. Fnally, the optmal value of Z s. 4 Output Table. 6. Comparson of used tmed for solvng LPP1 Machne Confguratons Intel[R] 4 CPU 2.00GHz,512M B of RAM Tme Used(Sec.) Bultn Code 10, 11 IV. Algorthm of BSM Developed Code In ths secton we present the algorthm of our developed code. Step 1. Calculate the net evaluaton C Z. For a maxmzaton problem f C Z 0 for the nonbasc varables at ther upper bound, optmum basc feasble soluton s attaned. It not, go to step2, revenue s true for a mnmzaton problem. Step 2. Select the most postve C Z. Step 3. Let x be a non basc varable at zero level whch s selected to enter the soluton. Compute the quanttes defned n (4) & (5) Step 4. x = mn (,, u ). Substep 1: If =. (X ) leaves the basc soluton (because nonbasc) at level zero and x enter by usng the regular row operaton of the smplex method. Substep 2: If =. (X ) leaves the basc soluton at level zero and x enters then (X ) beng nonbasc at ts upper bound must be substtuted out by usng where, (X ) = (U ) (X ) 0 (X ) (U ) Substep 3: If = u, x s substtuted at ts upper bound by x = u x whle remanng nonbasc. Flowchart: The flowchart of the developed code s presented n ths secton.
6 168 S. M. Atqur Rahman Chowdhury and Sanwar Uddn Ahmad Start Input Construct ntal Table Prnt C Z 0 No Stop Identfyng pvot column From (2)&(3), calculate θ & θ respectvely U = upperbound of x x = mn {,, u } x = x = x = u x enters the bass (X ) (X ) = (U ) (X ) x = u x V. Concluson Nowadays computer programmng plays an mportant role for solvng varous problems n Operatons Research and s a much needed tool for solvng large scale problems. In ths paper we have dscussed the algorthm for solvng LPP wth Bounded Varables, have developed a MATHEMATICA program for solvng such problems. It s evdent from table 6 that the developed program can reduce sgnfcantly the tme taken to provde optmum soluton. Despte the restrctons, ths program may be used more effcently for solvng LPP wth bounded varables Dantzg, G. B., 1955, Upper Bounds, Secondary Constrants and Trangularty n Lnear Programmng, Econometrca, 23, No Wagner, H. M., 1958, The Dual Smplex Algorthm for Bounded Varables, Nav. Res. Log. Quart. 5, Maros I, 2003a, A pecewse lnear dual phasei algorthm for the smplex method, Computatonal Optmzaton and Applcatons, 26, Maros I, 2003b, A generalzed dual phase2 smplex algorthm, European Journal of Operatonal Research, 149, C. Duguay, M. Todd and H.M. Wagner, 1972/73, Lnear programmng wth relatve bounded varables, Management Sc., 19, Youshen Xa and Jasong Wang, 1995, Neural Network for Solvng Lnear Programmng Problems transacton on neural networks, 6(2). wth Bounded Varables, IEEE 7. Ron Saha and M. Babul Hasan, 2010, A Computer Technque for Senstvty Analyss n Lnear Programs, Dhaka Unv.J.Sc. 58(2), Hasan, M.B. Hasan, 2008, Soluton Lnear Fractonal Programmng Problems through Computer Algebra, The Dhaka Unversty Journal of Scence, 57(1), Morshed, M.B. Hasan, 2005, Graphcal representaton of feasble regon of Lnear programmng problems usng Mathematca, The Dhaka Unversty Journal of Scence, 53(1), Taha H. A., 1999, Operaton Research An Introducton, PrentceHall of Inda Pvt. Ltd, New Delh. 11. Gupta, P.K. & Hra, D.S., 1998, Problems n Operatons Research, S. Chand & Company, New Delh.
Logical Development Of Vogel s Approximation Method (LDVAM): An Approach To Find Basic Feasible Solution Of Transportation Problem
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME, ISSUE, FEBRUARY ISSN 77866 Logcal Development Of Vogel s Approxmaton Method (LD An Approach To Fnd Basc Feasble Soluton Of Transportaton
More informationA hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm
Avalable onlne www.ocpr.com Journal of Chemcal and Pharmaceutcal Research, 2014, 6(7):18841889 Research Artcle ISSN : 09757384 CODEN(USA) : JCPRC5 A hybrd global optmzaton algorthm based on parallel
More information1 Approximation Algorithms
CME 305: Dscrete Mathematcs and Algorthms 1 Approxmaton Algorthms In lght of the apparent ntractablty of the problems we beleve not to le n P, t makes sense to pursue deas other than complete solutons
More informationSupport Vector Machines
Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More informationOn the Optimal Control of a Cascade of HydroElectric Power Stations
On the Optmal Control of a Cascade of HydroElectrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;
More informationJ. Parallel Distrib. Comput.
J. Parallel Dstrb. Comput. 71 (2011) 62 76 Contents lsts avalable at ScenceDrect J. Parallel Dstrb. Comput. journal homepage: www.elsever.com/locate/jpdc Optmzng server placement n dstrbuted systems n
More informationYves Genin, Yurii Nesterov, Paul Van Dooren. CESAME, Universite Catholique de Louvain. B^atiment Euler, Avenue G. Lema^tre 46
Submtted to ECC 99 as a regular paper n Lnear Systems Postve transfer functons and convex optmzaton 1 Yves Genn, Yur Nesterov, Paul Van Dooren CESAME, Unverste Catholque de Louvan B^atment Euler, Avenue
More informationgreatest common divisor
4. GCD 1 The greatest common dvsor of two ntegers a and b (not both zero) s the largest nteger whch s a common factor of both a and b. We denote ths number by gcd(a, b), or smply (a, b) when there s no
More informationProject Networks With MixedTime Constraints
Project Networs Wth MxedTme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa
More informationOptimal Bidding Strategies for Generation Companies in a DayAhead Electricity Market with Risk Management Taken into Account
Amercan J. of Engneerng and Appled Scences (): 86, 009 ISSN 94700 009 Scence Publcatons Optmal Bddng Strateges for Generaton Companes n a DayAhead Electrcty Market wth Rsk Management Taken nto Account
More informationProduction. 2. Y is closed A set is closed if it contains its boundary. We need this for the solution existence in the profit maximization problem.
Producer Theory Producton ASSUMPTION 2.1 Propertes of the Producton Set The producton set Y satsfes the followng propertes 1. Y s nonempty If Y s empty, we have nothng to talk about 2. Y s closed A set
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationThe Greedy Method. Introduction. 0/1 Knapsack Problem
The Greedy Method Introducton We have completed data structures. We now are gong to look at algorthm desgn methods. Often we are lookng at optmzaton problems whose performance s exponental. For an optmzaton
More informationThe Development of Web Log Mining Based on ImproveKMeans Clustering Analysis
The Development of Web Log Mnng Based on ImproveKMeans Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More informationResearch Article Enhanced TwoStep Method via Relaxed Order of αsatisfactory Degrees for Fuzzy Multiobjective Optimization
Hndaw Publshng Corporaton Mathematcal Problems n Engneerng Artcle ID 867836 pages http://dxdoorg/055/204/867836 Research Artcle Enhanced TwoStep Method va Relaxed Order of αsatsfactory Degrees for Fuzzy
More informationBERNSTEIN POLYNOMIALS
OnLne Geometrc Modelng Notes BERNSTEIN POLYNOMIALS Kenneth I. Joy Vsualzaton and Graphcs Research Group Department of Computer Scence Unversty of Calforna, Davs Overvew Polynomals are ncredbly useful
More informationAn MILP model for planning of batch plants operating in a campaignmode
An MILP model for plannng of batch plants operatng n a campagnmode Yanna Fumero Insttuto de Desarrollo y Dseño CONICET UTN yfumero@santafeconcet.gov.ar Gabrela Corsano Insttuto de Desarrollo y Dseño
More information"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *
Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC
More information1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)
6.3 /  Communcaton Networks II (Görg) SS20  www.comnets.unbremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes
More informationImplementation of Deutsch's Algorithm Using Mathcad
Implementaton of Deutsch's Algorthm Usng Mathcad Frank Roux The followng s a Mathcad mplementaton of Davd Deutsch's quantum computer prototype as presented on pages  n "Machnes, Logc and Quantum Physcs"
More informationFisher Markets and Convex Programs
Fsher Markets and Convex Programs Nkhl R. Devanur 1 Introducton Convex programmng dualty s usually stated n ts most general form, wth convex objectve functons and convex constrants. (The book by Boyd and
More informationOn fourth order simultaneously zerofinding method for multiple roots of complex polynomial equations 1
General Mathematcs Vol. 6, No. 3 (2008), 9 3 On fourth order smultaneously zerofndng method for multple roots of complex polynomal euatons Nazr Ahmad Mr and Khald Ayub Abstract In ths paper, we present
More informationForecasting the Direction and Strength of Stock Market Movement
Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract  Stock market s one of the most complcated systems
More informationHow Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence
1 st Internatonal Symposum on Imprecse Probabltes and Ther Applcatons, Ghent, Belgum, 29 June 2 July 1999 How Sets of Coherent Probabltes May Serve as Models for Degrees of Incoherence Mar J. Schervsh
More informationThe circuit shown on Figure 1 is called the common emitter amplifier circuit. The important subsystems of this circuit are:
polar Juncton Transstor rcuts Voltage and Power Amplfer rcuts ommon mtter Amplfer The crcut shown on Fgure 1 s called the common emtter amplfer crcut. The mportant subsystems of ths crcut are: 1. The basng
More informationv a 1 b 1 i, a 2 b 2 i,..., a n b n i.
SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 455 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces we have studed thus far n the text are real vector spaces snce the scalars are
More informationPowerofTwo Policies for Single Warehouse MultiRetailer Inventory Systems with Order Frequency Discounts
Powerofwo Polces for Sngle Warehouse MultRetaler Inventory Systems wth Order Frequency Dscounts José A. Ventura Pennsylvana State Unversty (USA) Yale. Herer echnon Israel Insttute of echnology (Israel)
More information2008/8. An integrated model for warehouse and inventory planning. Géraldine Strack and Yves Pochet
2008/8 An ntegrated model for warehouse and nventory plannng Géraldne Strack and Yves Pochet CORE Voe du Roman Pays 34 B1348 LouvanlaNeuve, Belgum. Tel (32 10) 47 43 04 Fax (32 10) 47 43 01 Emal: corestatlbrary@uclouvan.be
More informationChapter 4 ECONOMIC DISPATCH AND UNIT COMMITMENT
Chapter 4 ECOOMIC DISATCH AD UIT COMMITMET ITRODUCTIO A power system has several power plants. Each power plant has several generatng unts. At any pont of tme, the total load n the system s met by the
More informationCommunication Networks II Contents
8 / 1  Communcaton Networs II (Görg)  www.comnets.unbremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP
More information6. EIGENVALUES AND EIGENVECTORS 3 = 3 2
EIGENVALUES AND EIGENVECTORS The Characterstc Polynomal If A s a square matrx and v s a nonzero vector such that Av v we say that v s an egenvector of A and s the correspondng egenvalue Av v Example :
More informationEnabling P2P Oneview Multiparty Video Conferencing
Enablng P2P Onevew Multparty Vdeo Conferencng Yongxang Zhao, Yong Lu, Changja Chen, and JanYn Zhang Abstract MultParty Vdeo Conferencng (MPVC) facltates realtme group nteracton between users. Whle P2P
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationSolving Factored MDPs with Continuous and Discrete Variables
Solvng Factored MPs wth Contnuous and screte Varables Carlos Guestrn Berkeley Research Center Intel Corporaton Mlos Hauskrecht epartment of Computer Scence Unversty of Pttsburgh Branslav Kveton Intellgent
More informationComparison of Control Strategies for Shunt Active Power Filter under Different Load Conditions
Comparson of Control Strateges for Shunt Actve Power Flter under Dfferent Load Condtons Sanjay C. Patel 1, Tushar A. Patel 2 Lecturer, Electrcal Department, Government Polytechnc, alsad, Gujarat, Inda
More informationSPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:
SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and
More informationAn efficient constraint handling methodology for multiobjective evolutionary algorithms
Rev. Fac. Ing. Unv. Antoqua N. 49. pp. 141150. Septembre, 009 An effcent constrant handlng methodology for multobjectve evolutonary algorthms Una metodología efcente para manejo de restrccones en algortmos
More informationA DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATIONBASED OPTIMIZATION. Michael E. Kuhl Radhamés A. TolentinoPeña
Proceedngs of the 2008 Wnter Smulaton Conference S. J. Mason, R. R. Hll, L. Mönch, O. Rose, T. Jefferson, J. W. Fowler eds. A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATIONBASED OPTIMIZATION
More informationPeriod and Deadline Selection for Schedulability in RealTime Systems
Perod and Deadlne Selecton for Schedulablty n RealTme Systems Thdapat Chantem, Xaofeng Wang, M.D. Lemmon, and X. Sharon Hu Department of Computer Scence and Engneerng, Department of Electrcal Engneerng
More informationNonlinear data mapping by neural networks
Nonlnear data mappng by neural networks R.P.W. Dun Delft Unversty of Technology, Netherlands Abstract A revew s gven of the use of neural networks for nonlnear mappng of hgh dmensonal data on lower dmensonal
More information行 政 院 國 家 科 學 委 員 會 補 助 專 題 研 究 計 畫 成 果 報 告 期 中 進 度 報 告
行 政 院 國 家 科 學 委 員 會 補 助 專 題 研 究 計 畫 成 果 報 告 期 中 進 度 報 告 畫 類 別 : 個 別 型 計 畫 半 導 體 產 業 大 型 廠 房 之 設 施 規 劃 計 畫 編 號 :NSC 962628E009026MY3 執 行 期 間 : 2007 年 8 月 1 日 至 2010 年 7 月 31 日 計 畫 主 持 人 : 巫 木 誠 共 同
More informationTrafficlight a stress test for life insurance provisions
MEMORANDUM Date 006097 Authors Bengt von Bahr, Göran Ronge Traffclght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax
More informationPreventive Maintenance and Replacement Scheduling: Models and Algorithms
Preventve Mantenance and Replacement Schedulng: Models and Algorthms By Kamran S. Moghaddam B.S. Unversty of Tehran 200 M.S. Tehran Polytechnc 2003 A Dssertaton Proposal Submtted to the Faculty of the
More informationEfficient Project Portfolio as a tool for Enterprise Risk Management
Effcent Proect Portfolo as a tool for Enterprse Rsk Management Valentn O. Nkonov Ural State Techncal Unversty Growth Traectory Consultng Company January 5, 27 Effcent Proect Portfolo as a tool for Enterprse
More informationAlternate Approximation of Concave Cost Functions for
Alternate Approxmaton of Concave Cost Functons for Process Desgn and Supply Chan Optmzaton Problems Dego C. Cafaro * and Ignaco E. Grossmann INTEC (UNL CONICET), Güemes 3450, 3000 Santa Fe, ARGENTINA Department
More informationCompiling for Parallelism & Locality. Dependence Testing in General. Algorithms for Solving the Dependence Problem. Dependence Testing
Complng for Parallelsm & Localty Dependence Testng n General Assgnments Deadlne for proect 4 extended to Dec 1 Last tme Data dependences and loops Today Fnsh data dependence analyss for loops General code
More informationWeek 6 Market Failure due to Externalities
Week 6 Market Falure due to Externaltes 1. Externaltes n externalty exsts when the acton of one agent unavodably affects the welfare of another agent. The affected agent may be a consumer, gvng rse to
More informationAnts Can Schedule Software Projects
Ants Can Schedule Software Proects Broderck Crawford 1,2, Rcardo Soto 1,3, Frankln Johnson 4, and Erc Monfroy 5 1 Pontfca Unversdad Católca de Valparaíso, Chle FrstName.Name@ucv.cl 2 Unversdad Fns Terrae,
More informationSVM Tutorial: Classification, Regression, and Ranking
SVM Tutoral: Classfcaton, Regresson, and Rankng Hwanjo Yu and Sungchul Km 1 Introducton Support Vector Machnes(SVMs) have been extensvely researched n the data mnng and machne learnng communtes for the
More informationLoop Parallelization
  Loop Parallelzaton C52 Complaton steps: nested loops operatng on arrays, sequentell executon of teraton space DECLARE B[..,..+] FOR I :=.. FOR J :=.. I B[I,J] := B[I,J]+B[I,J] ED FOR ED FOR analyze
More informationIDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS
IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,
More informationThe Retail Planning Problem Under Demand Uncertainty
Vol., No. 5, September October 013, pp. 100 113 ISSN 10591478 EISSN 19375956 13 05 100 DOI 10.1111/j.19375956.01.0144.x 013 Producton and Operatons Management Socety The Retal Plannng Problem Under
More informationPERRON FROBENIUS THEOREM
PERRON FROBENIUS THEOREM R. CLARK ROBINSON Defnton. A n n matrx M wth real entres m, s called a stochastc matrx provded () all the entres m satsfy 0 m, () each of the columns sum to one, m = for all, ()
More informationOn the Solution of Indefinite Systems Arising in Nonlinear Optimization
On the Soluton of Indefnte Systems Arsng n Nonlnear Optmzaton Slva Bonettn, Valera Ruggero and Federca Tnt Dpartmento d Matematca, Unverstà d Ferrara Abstract We consder the applcaton of the precondtoned
More informationA Simple Economic Model about the Teamwork Pedagogy
Appled Mathematcal Scences, Vol. 6, 01, no. 1, 130 A Smple Economc Model about the Teamwork Pedagog Gregor L. Lght Department of Management, Provdence College Provdence, Rhode Island 0918, USA glght@provdence.edu
More informationWhen Network Effect Meets Congestion Effect: Leveraging Social Services for Wireless Services
When Network Effect Meets Congeston Effect: Leveragng Socal Servces for Wreless Servces aowen Gong School of Electrcal, Computer and Energy Engeerng Arzona State Unversty Tempe, AZ 8587, USA xgong9@asuedu
More informationSCHEDULING OF CONSTRUCTION PROJECTS BY MEANS OF EVOLUTIONARY ALGORITHMS
SCHEDULING OF CONSTRUCTION PROJECTS BY MEANS OF EVOLUTIONARY ALGORITHMS Magdalena Rogalska 1, Wocech Bożeko 2,Zdzsław Heduck 3, 1 Lubln Unversty of Technology, 2 Lubln, Nadbystrzycka 4., Poland. Emal:rogalska@akropols.pol.lubln.pl
More informationFeature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College
Feature selecton for ntruson detecton Slobodan Petrovć NISlab, Gjøvk Unversty College Contents The feature selecton problem Intruson detecton Traffc features relevant for IDS The CFS measure The mrmr measure
More informationAPPLICATION OF COMPUTER PROGRAMMING IN OPTIMIZATION OF TECHNOLOGICAL OBJECTIVES OF COLD ROLLING
Journal Journal of Chemcal of Chemcal Technology and and Metallurgy, 50, 6, 50, 2015, 6, 2015 638643 APPLICATION OF COMPUTER PROGRAMMING IN OPTIMIZATION OF TECHNOLOGICAL OBJECTIVES OF COLD ROLLING Abdrakhman
More informationA Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy Scurve Regression
Novel Methodology of Workng Captal Management for Large Publc Constructons by Usng Fuzzy Scurve Regresson ChengWu Chen, Morrs H. L. Wang and TngYa Hseh Department of Cvl Engneerng, Natonal Central Unversty,
More informationMining Multiple Large Data Sources
The Internatonal Arab Journal of Informaton Technology, Vol. 7, No. 3, July 2 24 Mnng Multple Large Data Sources Anmesh Adhkar, Pralhad Ramachandrarao 2, Bhanu Prasad 3, and Jhml Adhkar 4 Department of
More informationLuby s Alg. for Maximal Independent Sets using Pairwise Independence
Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent
More informationTime Domain simulation of PD Propagation in XLPE Cables Considering Frequency Dependent Parameters
Internatonal Journal of Smart Grd and Clean Energy Tme Doman smulaton of PD Propagaton n XLPE Cables Consderng Frequency Dependent Parameters We Zhang a, Jan He b, Ln Tan b, Xuejun Lv b, HongJe L a *
More informationRealTime Process Scheduling
RealTme Process Schedulng ktw@cse.ntu.edu.tw (RealTme and Embedded Systems Laboratory) Independent Process Schedulng Processes share nothng but CPU Papers for dscussons: C.L. Lu and James. W. Layland,
More informationInequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More informationTesting and Debugging Resource Allocation for Fault Detection and Removal Process
Internatonal Journal of New Computer Archtectures and ther Applcatons (IJNCAA) 4(4): 9300 The Socety of Dgtal Informaton and Wreless Communcatons, 04 (ISSN: 09085) Testng and Debuggng Resource Allocaton
More informationForecasting the Demand of Emergency Supplies: Based on the CBR Theory and BP Neural Network
700 Proceedngs of the 8th Internatonal Conference on Innovaton & Management Forecastng the Demand of Emergency Supples: Based on the CBR Theory and BP Neural Network Fu Deqang, Lu Yun, L Changbng School
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More informationA DATA MINING APPLICATION IN A STUDENT DATABASE
JOURNAL OF AERONAUTICS AND SPACE TECHNOLOGIES JULY 005 VOLUME NUMBER (5357) A DATA MINING APPLICATION IN A STUDENT DATABASE Şenol Zafer ERDOĞAN Maltepe Ünversty Faculty of Engneerng BüyükbakkalköyIstanbul
More informationSensor placement for leak detection and location in water distribution networks
Sensor placement for leak detecton and locaton n water dstrbuton networks ABSTRACT R. Sarrate*, J. Blesa, F. Near, J. Quevedo Automatc Control Department, Unverstat Poltècnca de Catalunya, Rambla de Sant
More informationPOLYSA: A Polynomial Algorithm for Nonbinary Constraint Satisfaction Problems with and
POLYSA: A Polynomal Algorthm for Nonbnary Constrant Satsfacton Problems wth and Mguel A. Saldo, Federco Barber Dpto. Sstemas Informátcos y Computacón Unversdad Poltécnca de Valenca, Camno de Vera s/n
More informationAnalysis of Reactivity Induced Accident for Control Rods Ejection with Loss of Cooling
Analyss of Reactvty Induced Accdent for Control Rods Ejecton wth Loss of Coolng Hend Mohammed El Sayed Saad 1, Hesham Mohammed Mohammed Mansour 2 Wahab 1 1. Nuclear and Radologcal Regulatory Authorty,
More informationA Simple Approach to Clustering in Excel
A Smple Approach to Clusterng n Excel Aravnd H Center for Computatonal Engneerng and Networng Amrta Vshwa Vdyapeetham, Combatore, Inda C Rajgopal Center for Computatonal Engneerng and Networng Amrta Vshwa
More informationJoint Scheduling of Processing and Shuffle Phases in MapReduce Systems
Jont Schedulng of Processng and Shuffle Phases n MapReduce Systems Fangfe Chen, Mural Kodalam, T. V. Lakshman Department of Computer Scence and Engneerng, The Penn State Unversty Bell Laboratores, AlcatelLucent
More informationMooring Pattern Optimization using Genetic Algorithms
6th World Congresses of Structural and Multdscplnary Optmzaton Ro de Janero, 30 May  03 June 005, Brazl Moorng Pattern Optmzaton usng Genetc Algorthms Alonso J. Juvnao Carbono, Ivan F. M. Menezes Luz
More informationA Secure PasswordAuthenticated Key Agreement Using Smart Cards
A Secure PasswordAuthentcated Key Agreement Usng Smart Cards Ka Chan 1, WenChung Kuo 2 and JnChou Cheng 3 1 Department of Computer and Informaton Scence, R.O.C. Mltary Academy, Kaohsung 83059, Tawan,
More informationDynamic Constrained Economic/Emission Dispatch Scheduling Using Neural Network
Dynamc Constraned Economc/Emsson Dspatch Schedulng Usng Neural Network Fard BENHAMIDA 1, Rachd BELHACHEM 1 1 Department of Electrcal Engneerng, IRECOM Laboratory, Unversty of Djllal Labes, 220 00, Sd Bel
More informationA fast method for binary programming using firstorder derivatives, with application to topology optimization with buckling constraints
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng (2012) Publshed onlne n Wley Onlne Lbrary (wleyonlnelbrary.com)..4367 A fast method for bnary programmng usng frstorder
More informationLogistic Regression. Lecture 4: More classifiers and classes. Logistic regression. Adaboost. Optimization. Multiple class classification
Lecture 4: More classfers and classes C4B Machne Learnng Hlary 20 A. Zsserman Logstc regresson Loss functons revsted Adaboost Loss functons revsted Optmzaton Multple class classfcaton Logstc Regresson
More informationDownlink Power Allocation for Multiclass. Wireless Systems
Downlnk Power Allocaton for Multclass 1 Wreless Systems JangWon Lee, Rav R. Mazumdar, and Ness B. Shroff School of Electrcal and Computer Engneerng Purdue Unversty West Lafayette, IN 47907, USA {lee46,
More informationA Study on Secure Data Storage Strategy in Cloud Computing
Journal of Convergence Informaton Technology Volume 5, Number 7, Setember 00 A Study on Secure Data Storage Strategy n Cloud Comutng Danwe Chen, Yanjun He, Frst Author College of Comuter Technology, Nanjng
More informationAddendum to: Importing SkillBiased Technology
Addendum to: Importng SkllBased Technology Arel Bursten UCLA and NBER Javer Cravno UCLA August 202 Jonathan Vogel Columba and NBER Abstract Ths Addendum derves the results dscussed n secton 3.3 of our
More informationRing structure of splines on triangulations
www.oeaw.ac.at Rng structure of splnes on trangulatons N. Vllamzar RICAMReport 201448 www.rcam.oeaw.ac.at RING STRUCTURE OF SPLINES ON TRIANGULATIONS NELLY VILLAMIZAR Introducton For a trangulated regon
More informationSciences Shenyang, Shenyang, China.
Advanced Materals Research Vols. 314316 (2011) pp 13151320 (2011) Trans Tech Publcatons, Swtzerland do:10.4028/www.scentfc.net/amr.314316.1315 Solvng the TwoObectve Shop Schedulng Problem n MTO Manufacturng
More informationTime Value of Money Module
Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the
More informationMethod for Production Planning and Inventory Control in Oil
Memors of the Faculty of Engneerng, Okayama Unversty, Vol.41, pp.2030, January, 2007 Method for Producton Plannng and Inventory Control n Ol Refnery TakujImamura,MasamKonshandJunIma Dvson of Electronc
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationSUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW.
SUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW. Lucía Isabel García Cebrán Departamento de Economía y Dreccón de Empresas Unversdad de Zaragoza Gran Vía, 2 50.005 Zaragoza (Span) Phone: 976761000
More informationOn the Interaction between Load Balancing and Speed Scaling
On the Interacton between Load Balancng and Speed Scalng Ljun Chen, Na L and Steven H. Low Engneerng & Appled Scence Dvson, Calforna Insttute of Technology, USA Abstract Speed scalng has been wdely adopted
More informationData Broadcast on a MultiSystem Heterogeneous Overlayed Wireless Network *
JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 24, 819840 (2008) Data Broadcast on a MultSystem Heterogeneous Overlayed Wreless Network * Department of Computer Scence Natonal Chao Tung Unversty Hsnchu,
More informationAn Integrated Approach for Maintenance and Delivery Scheduling in Military Supply Chains
An Integrated Approach for Mantenance and Delvery Schedulng n Mltary Supply Chans Dmtry Tsadkovch 1*, Eugene Levner 2, Hanan Tell 2 and Frank Werner 3 2 1 Bar Ilan Unversty, Department of Management, Ramat
More informationExhaustive Regression. An Exploration of RegressionBased Data Mining Techniques Using Super Computation
Exhaustve Regresson An Exploraton of RegressonBased Data Mnng Technques Usng Super Computaton Antony Daves, Ph.D. Assocate Professor of Economcs Duquesne Unversty Pttsburgh, PA 58 Research Fellow The
More informationQoSAware Spectrum Sharing in Cognitive Wireless Networks
QoSAware Spectrum Sharng n Cogntve reless Networks Long Le and Ekram Hossan Abstract e consder QoSaware spectrum sharng n cogntve wreless networks where secondary users are allowed to access the spectrum
More informationA BonusMalus System as a Markov SetChain
A Bonusalus System as a arov SetChan Famly and frst name: emec algorzata Organsaton: Warsaw School of Economcs Insttute of Econometrcs Al. epodleglosc 64 2554 Warszawa Poland Telephone number: +48 6
More informationMaintenance Scheduling by using the BiCriterion Algorithm of Preferential AntiPheromone
Leonardo ournal of Scences ISSN 5830233 Issue 2, anuaryune 2008 p. 4364 Mantenance Schedulng by usng the BCrteron Algorthm of Preferental AntPheromone Trantafyllos MYTAKIDIS and Arstds VLACHOS Department
More informationA Genetic Programming Based Stock Price Predictor together with MeanVariance Based Sell/Buy Actions
Proceedngs of the World Congress on Engneerng 28 Vol II WCE 28, July 24, 28, London, U.K. A Genetc Programmng Based Stock Prce Predctor together wth MeanVarance Based Sell/Buy Actons Ramn Rajaboun and
More informationThe Performance Analysis Of A M/M/2/2+1 Retrial Queue With Unreliable Server
Journal of Statstcal Scence and Applcaton, October 5, Vol. 3, No. 9, 6374 do:.765/384/5.9.3 D DAV I D PUBLISHING The Performance Analyss Of A M/M//+ Retral Queue Wth Unrelable Server R. Kalyanaraman
More informationDuality for nonsmooth mathematical programming problems with equilibrium constraints
uu et al. Journal of Inequaltes and Applcatons (2016) 2016:28 DOI 10.1186/s1366001609694 R E S E A R C H Open Access Dualty for nonsmooth mathematcal programmng problems wth equlbrum constrants SyMng
More information