A Computer Technique for Solving LP Problems with Bounded Variables

Size: px
Start display at page:

Download "A Computer Technique for Solving LP Problems with Bounded Variables"

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, Dhaka-1000, 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 bult-n 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 bult-n MATHEMATICA code. * Correspondence author : E-mal: 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 non-basc 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 nonnegatve-that 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 non-basc) 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 b-to-b = 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 non-basc 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 co-effcent 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 co-eff. of obectve functon: 3, 5, 2, 0, and 0 Enter upper bound: 4, 3, 3, 9999, and Enter co-eff. 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 non-basc 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 1/2-1/2 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 1/2-7/4-5/4 75/4 x 0 1/2-1/2 5/2 x -1/2-3/4-1/4-3/4 Table. 5. Optmum table Basc x x x Soluton Z -1/2-7/4-5/4 83/4 x 0 1/2-1/2 5/2 x 1/2-3/4-1/4 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.) Bult-n 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 non-basc varables at ther upper bound, optmum basc feasble soluton s attaned. It not, go to step-2, 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 ). Sub-step 1: If =. (X ) leaves the basc soluton (because non-basc) at level zero and x enter by usng the regular row operaton of the smplex method. Sub-step 2: If =. (X ) leaves the basc soluton at level zero and x enters then (X ) beng non-basc at ts upper bound must be substtuted out by usng where, (X ) = (U ) (X ) 0 (X ) (U ) Sub-step 3: If = u, x s substtuted at ts upper bound by x = u x whle remanng non-basc. 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 Now-a-days 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 phase-i algorthm for the smplex method, Computatonal Optmzaton and Applcatons, 26, Maros I, 2003b, A generalzed dual phase-2 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, Prentce-Hall 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 (LD-VAM): An Approach To Find Basic Feasible Solution Of Transportation Problem

Logical Development Of Vogel s Approximation Method (LD-VAM): An Approach To Find Basic Feasible Solution Of Transportation Problem INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME, ISSUE, FEBRUARY ISSN 77-866 Logcal Development Of Vogel s Approxmaton Method (LD- An Approach To Fnd Basc Feasble Soluton Of Transportaton

More information

A hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm

A 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):1884-1889 Research Artcle ISSN : 0975-7384 CODEN(USA) : JCPRC5 A hybrd global optmzaton algorthm based on parallel

More information

1 Approximation Algorithms

1 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 information

Support Vector Machines

Support 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 information

8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by

8.5 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 information

On the Optimal Control of a Cascade of Hydro-Electric Power Stations

On the Optimal Control of a Cascade of Hydro-Electric Power Stations On the Optmal Control of a Cascade of Hydro-Electrc 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 information

J. Parallel Distrib. Comput.

J. 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 information

Yves Genin, Yurii Nesterov, Paul Van Dooren. CESAME, Universite Catholique de Louvain. B^atiment Euler, Avenue G. Lema^tre 4-6

Yves Genin, Yurii Nesterov, Paul Van Dooren. CESAME, Universite Catholique de Louvain. B^atiment Euler, Avenue G. Lema^tre 4-6 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 information

greatest common divisor

greatest 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 information

Project Networks With Mixed-Time Constraints

Project Networks With Mixed-Time Constraints Project Networs Wth Mxed-Tme 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 information

Optimal Bidding Strategies for Generation Companies in a Day-Ahead Electricity Market with Risk Management Taken into Account

Optimal Bidding Strategies for Generation Companies in a Day-Ahead Electricity Market with Risk Management Taken into Account Amercan J. of Engneerng and Appled Scences (): 8-6, 009 ISSN 94-700 009 Scence Publcatons Optmal Bddng Strateges for Generaton Companes n a Day-Ahead Electrcty Market wth Rsk Management Taken nto Account

More information

Production. 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.

Production. 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 non-empty If Y s empty, we have nothng to talk about 2. Y s closed A set

More information

Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic

Institute 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 information

The Greedy Method. Introduction. 0/1 Knapsack Problem

The 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 information

The Development of Web Log Mining Based on Improve-K-Means Clustering Analysis

The Development of Web Log Mining Based on Improve-K-Means Clustering Analysis The Development of Web Log Mnng Based on Improve-K-Means Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.

More information

Research Article Enhanced Two-Step Method via Relaxed Order of α-satisfactory Degrees for Fuzzy Multiobjective Optimization

Research Article Enhanced Two-Step Method via Relaxed Order of α-satisfactory Degrees for Fuzzy Multiobjective Optimization Hndaw Publshng Corporaton Mathematcal Problems n Engneerng Artcle ID 867836 pages http://dxdoorg/055/204/867836 Research Artcle Enhanced Two-Step Method va Relaxed Order of α-satsfactory Degrees for Fuzzy

More information

BERNSTEIN POLYNOMIALS

BERNSTEIN POLYNOMIALS On-Lne 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 information

An MILP model for planning of batch plants operating in a campaign-mode

An MILP model for planning of batch plants operating in a campaign-mode An MILP model for plannng of batch plants operatng n a campagn-mode Yanna Fumero Insttuto de Desarrollo y Dseño CONICET UTN yfumero@santafe-concet.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 *

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, 789-794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC

More information

1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)

1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP) 6.3 / -- Communcaton Networks II (Görg) SS20 -- www.comnets.un-bremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes

More information

Implementation of Deutsch's Algorithm Using Mathcad

Implementation 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 information

Fisher Markets and Convex Programs

Fisher 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 information

On fourth order simultaneously zero-finding method for multiple roots of complex polynomial equations 1

On fourth order simultaneously zero-finding method for multiple roots of complex polynomial equations 1 General Mathematcs Vol. 6, No. 3 (2008), 9 3 On fourth order smultaneously zero-fndng method for multple roots of complex polynomal euatons Nazr Ahmad Mr and Khald Ayub Abstract In ths paper, we present

More information

Forecasting the Direction and Strength of Stock Market Movement

Forecasting 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 information

How Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence

How 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 information

The circuit shown on Figure 1 is called the common emitter amplifier circuit. The important subsystems of this circuit are:

The 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 information

v a 1 b 1 i, a 2 b 2 i,..., a n b n i.

v 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 information

Power-of-Two Policies for Single- Warehouse Multi-Retailer Inventory Systems with Order Frequency Discounts

Power-of-Two Policies for Single- Warehouse Multi-Retailer Inventory Systems with Order Frequency Discounts Power-of-wo Polces for Sngle- Warehouse Mult-Retaler Inventory Systems wth Order Frequency Dscounts José A. Ventura Pennsylvana State Unversty (USA) Yale. Herer echnon Israel Insttute of echnology (Israel)

More information

2008/8. An integrated model for warehouse and inventory planning. Géraldine Strack and Yves Pochet

2008/8. 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 B-1348 Louvan-la-Neuve, Belgum. Tel (32 10) 47 43 04 Fax (32 10) 47 43 01 E-mal: corestat-lbrary@uclouvan.be

More information

Chapter 4 ECONOMIC DISPATCH AND UNIT COMMITMENT

Chapter 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 information

Communication Networks II Contents

Communication Networks II Contents 8 / 1 -- Communcaton Networs II (Görg) -- www.comnets.un-bremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP

More information

6. EIGENVALUES AND EIGENVECTORS 3 = 3 2

6. EIGENVALUES AND EIGENVECTORS 3 = 3 2 EIGENVALUES AND EIGENVECTORS The Characterstc Polynomal If A s a square matrx and v s a non-zero vector such that Av v we say that v s an egenvector of A and s the correspondng egenvalue Av v Example :

More information

Enabling P2P One-view Multi-party Video Conferencing

Enabling P2P One-view Multi-party Video Conferencing Enablng P2P One-vew Mult-party Vdeo Conferencng Yongxang Zhao, Yong Lu, Changja Chen, and JanYn Zhang Abstract Mult-Party Vdeo Conferencng (MPVC) facltates realtme group nteracton between users. Whle P2P

More information

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur

Module 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 information

Solving Factored MDPs with Continuous and Discrete Variables

Solving 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 information

Comparison of Control Strategies for Shunt Active Power Filter under Different Load Conditions

Comparison 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 information

SPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:

SPEE 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 information

An efficient constraint handling methodology for multi-objective evolutionary algorithms

An efficient constraint handling methodology for multi-objective evolutionary algorithms Rev. Fac. Ing. Unv. Antoqua N. 49. pp. 141-150. Septembre, 009 An effcent constrant handlng methodology for mult-objectve evolutonary algorthms Una metodología efcente para manejo de restrccones en algortmos

More information

A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION. Michael E. Kuhl Radhamés A. Tolentino-Peña

A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION. Michael E. Kuhl Radhamés A. Tolentino-Peña 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 SIMULATION-BASED OPTIMIZATION

More information

Period and Deadline Selection for Schedulability in Real-Time Systems

Period and Deadline Selection for Schedulability in Real-Time Systems Perod and Deadlne Selecton for Schedulablty n Real-Tme Systems Thdapat Chantem, Xaofeng Wang, M.D. Lemmon, and X. Sharon Hu Department of Computer Scence and Engneerng, Department of Electrcal Engneerng

More information

Nonlinear data mapping by neural networks

Nonlinear 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 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 96-2628-E-009-026-MY3 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 information

Traffic-light a stress test for life insurance provisions

Traffic-light a stress test for life insurance provisions MEMORANDUM Date 006-09-7 Authors Bengt von Bahr, Göran Ronge Traffc-lght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE-113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax

More information

Preventive Maintenance and Replacement Scheduling: Models and Algorithms

Preventive 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 information

Efficient Project Portfolio as a tool for Enterprise Risk Management

Efficient 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 information

Alternate Approximation of Concave Cost Functions for

Alternate 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 information

Compiling for Parallelism & Locality. Dependence Testing in General. Algorithms for Solving the Dependence Problem. Dependence Testing

Compiling 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 information

Week 6 Market Failure due to Externalities

Week 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 information

Ants Can Schedule Software Projects

Ants 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 information

SVM Tutorial: Classification, Regression, and Ranking

SVM 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 information

Loop Parallelization

Loop Parallelization - - Loop Parallelzaton C-52 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 information

IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS

IDENTIFICATION 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 information

The Retail Planning Problem Under Demand Uncertainty

The Retail Planning Problem Under Demand Uncertainty Vol., No. 5, September October 013, pp. 100 113 ISSN 1059-1478 EISSN 1937-5956 13 05 100 DOI 10.1111/j.1937-5956.01.0144.x 013 Producton and Operatons Management Socety The Retal Plannng Problem Under

More information

PERRON FROBENIUS THEOREM

PERRON 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 information

On the Solution of Indefinite Systems Arising in Nonlinear Optimization

On 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 information

A Simple Economic Model about the Teamwork Pedagogy

A Simple Economic Model about the Teamwork Pedagogy Appled Mathematcal Scences, Vol. 6, 01, no. 1, 13-0 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 information

When Network Effect Meets Congestion Effect: Leveraging Social Services for Wireless Services

When 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 information

SCHEDULING OF CONSTRUCTION PROJECTS BY MEANS OF EVOLUTIONARY ALGORITHMS

SCHEDULING 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. E-mal:rogalska@akropols.pol.lubln.pl

More information

Feature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College

Feature 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 information

APPLICATION OF COMPUTER PROGRAMMING IN OPTIMIZATION OF TECHNOLOGICAL OBJECTIVES OF COLD ROLLING

APPLICATION 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 638-643 APPLICATION OF COMPUTER PROGRAMMING IN OPTIMIZATION OF TECHNOLOGICAL OBJECTIVES OF COLD ROLLING Abdrakhman

More information

A Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy S-curve Regression

A Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy S-curve Regression Novel Methodology of Workng Captal Management for Large Publc Constructons by Usng Fuzzy S-curve Regresson Cheng-Wu Chen, Morrs H. L. Wang and Tng-Ya Hseh Department of Cvl Engneerng, Natonal Central Unversty,

More information

Mining Multiple Large Data Sources

Mining 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 information

Luby s Alg. for Maximal Independent Sets using Pairwise Independence

Luby 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 information

Time Domain simulation of PD Propagation in XLPE Cables Considering Frequency Dependent Parameters

Time 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, Hong-Je L a *

More information

Real-Time Process Scheduling

Real-Time Process Scheduling Real-Tme Process Schedulng ktw@cse.ntu.edu.tw (Real-Tme and Embedded Systems Laboratory) Independent Process Schedulng Processes share nothng but CPU Papers for dscussons: C.L. Lu and James. W. Layland,

More information

Inequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.

Inequality 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 information

Testing and Debugging Resource Allocation for Fault Detection and Removal Process

Testing and Debugging Resource Allocation for Fault Detection and Removal Process Internatonal Journal of New Computer Archtectures and ther Applcatons (IJNCAA) 4(4): 93-00 The Socety of Dgtal Informaton and Wreless Communcatons, 04 (ISSN: 0-9085) Testng and Debuggng Resource Allocaton

More information

Forecasting the Demand of Emergency Supplies: Based on the CBR Theory and BP Neural Network

Forecasting 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 information

DEFINING %COMPLETE IN MICROSOFT PROJECT

DEFINING %COMPLETE IN MICROSOFT PROJECT CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMI-SP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,

More information

7.5. Present Value of an Annuity. Investigate

7.5. 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 information

A DATA MINING APPLICATION IN A STUDENT DATABASE

A DATA MINING APPLICATION IN A STUDENT DATABASE JOURNAL OF AERONAUTICS AND SPACE TECHNOLOGIES JULY 005 VOLUME NUMBER (53-57) A DATA MINING APPLICATION IN A STUDENT DATABASE Şenol Zafer ERDOĞAN Maltepe Ünversty Faculty of Engneerng Büyükbakkalköy-Istanbul

More information

Sensor placement for leak detection and location in water distribution networks

Sensor 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 information

POLYSA: A Polynomial Algorithm for Non-binary Constraint Satisfaction Problems with and

POLYSA: A Polynomial Algorithm for Non-binary Constraint Satisfaction Problems with and POLYSA: A Polynomal Algorthm for Non-bnary 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 information

Analysis of Reactivity Induced Accident for Control Rods Ejection with Loss of Cooling

Analysis 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 information

A Simple Approach to Clustering in Excel

A 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 information

Joint Scheduling of Processing and Shuffle Phases in MapReduce Systems

Joint 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, Alcatel-Lucent

More information

Mooring Pattern Optimization using Genetic Algorithms

Mooring 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 information

A Secure Password-Authenticated Key Agreement Using Smart Cards

A Secure Password-Authenticated Key Agreement Using Smart Cards A Secure Password-Authentcated Key Agreement Usng Smart Cards Ka Chan 1, Wen-Chung Kuo 2 and Jn-Chou Cheng 3 1 Department of Computer and Informaton Scence, R.O.C. Mltary Academy, Kaohsung 83059, Tawan,

More information

Dynamic Constrained Economic/Emission Dispatch Scheduling Using Neural Network

Dynamic 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 information

A fast method for binary programming using first-order derivatives, with application to topology optimization with buckling constraints

A fast method for binary programming using first-order 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 frst-order

More information

Logistic Regression. Lecture 4: More classifiers and classes. Logistic regression. Adaboost. Optimization. Multiple class classification

Logistic 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 information

Downlink Power Allocation for Multi-class. Wireless Systems

Downlink Power Allocation for Multi-class. Wireless Systems Downlnk Power Allocaton for Mult-class 1 Wreless Systems Jang-Won Lee, Rav R. Mazumdar, and Ness B. Shroff School of Electrcal and Computer Engneerng Purdue Unversty West Lafayette, IN 47907, USA {lee46,

More information

A Study on Secure Data Storage Strategy in Cloud Computing

A 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 information

Addendum to: Importing Skill-Biased Technology

Addendum to: Importing Skill-Biased Technology Addendum to: Importng Skll-Based 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 information

Ring structure of splines on triangulations

Ring structure of splines on triangulations www.oeaw.ac.at Rng structure of splnes on trangulatons N. Vllamzar RICAM-Report 2014-48 www.rcam.oeaw.ac.at RING STRUCTURE OF SPLINES ON TRIANGULATIONS NELLY VILLAMIZAR Introducton For a trangulated regon

More information

Sciences Shenyang, Shenyang, China.

Sciences Shenyang, Shenyang, China. Advanced Materals Research Vols. 314-316 (2011) pp 1315-1320 (2011) Trans Tech Publcatons, Swtzerland do:10.4028/www.scentfc.net/amr.314-316.1315 Solvng the Two-Obectve Shop Schedulng Problem n MTO Manufacturng

More information

Time Value of Money Module

Time 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 information

Method for Production Planning and Inventory Control in Oil

Method for Production Planning and Inventory Control in Oil Memors of the Faculty of Engneerng, Okayama Unversty, Vol.41, pp.20-30, January, 2007 Method for Producton Plannng and Inventory Control n Ol Refnery TakujImamura,MasamKonshandJunIma Dvson of Electronc

More information

CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol

CHOLESTEROL 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 information

SUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW.

SUPPLIER 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: 976-76-10-00

More information

On the Interaction between Load Balancing and Speed Scaling

On 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 information

Data Broadcast on a Multi-System Heterogeneous Overlayed Wireless Network *

Data Broadcast on a Multi-System Heterogeneous Overlayed Wireless Network * JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 24, 819-840 (2008) Data Broadcast on a Mult-System Heterogeneous Overlayed Wreless Network * Department of Computer Scence Natonal Chao Tung Unversty Hsnchu,

More information

An Integrated Approach for Maintenance and Delivery Scheduling in Military Supply Chains

An 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 information

Exhaustive Regression. An Exploration of Regression-Based Data Mining Techniques Using Super Computation

Exhaustive Regression. An Exploration of Regression-Based Data Mining Techniques Using Super Computation Exhaustve Regresson An Exploraton of Regresson-Based Data Mnng Technques Usng Super Computaton Antony Daves, Ph.D. Assocate Professor of Economcs Duquesne Unversty Pttsburgh, PA 58 Research Fellow The

More information

QoS-Aware Spectrum Sharing in Cognitive Wireless Networks

QoS-Aware Spectrum Sharing in Cognitive Wireless Networks QoS-Aware Spectrum Sharng n Cogntve reless Networks Long Le and Ekram Hossan Abstract e consder QoS-aware spectrum sharng n cogntve wreless networks where secondary users are allowed to access the spectrum

More information

A Bonus-Malus System as a Markov Set-Chain

A Bonus-Malus System as a Markov Set-Chain A Bonus-alus System as a arov Set-Chan Famly and frst name: emec algorzata Organsaton: Warsaw School of Economcs Insttute of Econometrcs Al. epodleglosc 64 2-554 Warszawa Poland Telephone number: +48 6

More information

Maintenance Scheduling by using the Bi-Criterion Algorithm of Preferential Anti-Pheromone

Maintenance Scheduling by using the Bi-Criterion Algorithm of Preferential Anti-Pheromone Leonardo ournal of Scences ISSN 583-0233 Issue 2, anuary-une 2008 p. 43-64 Mantenance Schedulng by usng the B-Crteron Algorthm of Preferental Ant-Pheromone Trantafyllos MYTAKIDIS and Arstds VLACHOS Department

More information

A Genetic Programming Based Stock Price Predictor together with Mean-Variance Based Sell/Buy Actions

A Genetic Programming Based Stock Price Predictor together with Mean-Variance Based Sell/Buy Actions Proceedngs of the World Congress on Engneerng 28 Vol II WCE 28, July 2-4, 28, London, U.K. A Genetc Programmng Based Stock Prce Predctor together wth Mean-Varance Based Sell/Buy Actons Ramn Rajaboun and

More information

The Performance Analysis Of A M/M/2/2+1 Retrial Queue With Unreliable Server

The 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-, 63-74 do:.765/38-4/5.9.3 D DAV I D PUBLISHING The Performance Analyss Of A M/M//+ Retral Queue Wth Unrelable Server R. Kalyanaraman

More information

Duality for nonsmooth mathematical programming problems with equilibrium constraints

Duality for nonsmooth mathematical programming problems with equilibrium constraints uu et al. Journal of Inequaltes and Applcatons (2016) 2016:28 DOI 10.1186/s13660-016-0969-4 R E S E A R C H Open Access Dualty for nonsmooth mathematcal programmng problems wth equlbrum constrants Sy-Mng

More information