Determine the Optimal Order Quantity in Multi-items&s EOQ Model with Backorder
|
|
- Quentin Morton
- 6 years ago
- Views:
Transcription
1 Australan Journal of Basc and Appled Scences, 5(7): , 0 ISSN Determne the Optmal Order Quantty n Mult-tems&s EOQ Model wth Backorder Babak Khabr, Had Nasser, 3 Ehsan Ehsan and Nma Kazem Department of Mathement, Islamc Azad Unversty, Jouybar Branch, Jouybar, Iran. Department of Mathematcal Scences, Mazandaran Unversty, Babolsar, Iran. 3, Department of Industral Engneerng, Alghadr Unversty, Tabrz, Iran. Abstract: In ths paper we survey the nventory problem for tem s whch delay occurred for supply them. In ths stuaton the shortage of nventory happen and order whch encounter shortage, wll ncrease and make backorders and mpose new costs on nventory system and mpact on optmal quantty of order n EOQ model. Snce n practce and n real stuatons we don't have accurate value for much data of model, we determne the optmal order quantty n fuzzy sense. For ths objectve frst we consder an EOQ model wth fuzzy costs and then we consder EOQ model wth fuzzy backorder and for deffuzfy of these two fuzzy models we employ sgned dstance, a defuzzfcaton method for fuzzy number. At the end of ths paper for mply the applcaton of proposed model we menton a numercal example and furthermore we compare the result of fuzzy case wth those of crsp case for one tem. Key words: Inventory; Backlog Demands; Fuzzy theory; Sgned dstance; Mult tem's EOQ INTRODUCTION In the classcal Economc Order Quantty (EOQ) models, t's assumed that the systems don t encounter the shortage of nventory and ever order delver to customer on tme and wthout delay. Whle ths capablty don't always exsts n the nventory systems. In producton process problems such as; mpossblty of on tme supply of raw materal for entrance n producton flow, unforcastable defect rate of machnes and mpossblty of precse forecast of market demand wth due to the term of socety that lead to the shortage of nventory. In the nventory control, orders that can't satsfy n order to mentoned reasons called backorders. These orders mpose many costs on nventory system that called shortage costs. Shortage cost s consstng of two costs: a fxed cost of nventory shortage and shortage whch happen n the cycle of tme. Ordnary n systems whch are face to the shortage of nventory due to backlog orders, cost coeffcent, annual demand, take crsp nto account n mult tems EOQ model. In the classcal nventory models, demands, costs and etc descrbe wth crsp statstcal dstrbutons. Whle n real stuatons and n real world most of these parameters are vague and mprecse. For these knds of uncertantes t s possble to use fuzzy numbers nstead of probablstc approaches. In recent years, several researchers have appled the fuzzy sets theory and technque to develop and solve nventory problems. For example Change, (00) worked out fuzzy modfcatons of the model of Salameh and Jabber, (000) whch took the defectve rate of goods nto account Björk, (009). Yao and Lee, (996) fuzzfed the order quantty to the trangular fuzzy number, whle the backorder quantty s an ordnary varable Ln, (008). Yao and Lee, (999) and Yao and Lee, (996) fuzzfed the order quantty q as a trangular fuzzy number and trapezod fuzzy number and kept shortage quantty as a crsp real varable n the total cost of nventory wth backorder Chang, et al., (005). Other relevant contrbutons n ths feld are Roy and Mat, (997) and Vjayan and Kumaran, (008), for nstance. Fnally Björk and Carlsson, (005) solved the case, where the lead tmes are fuzzy, but the demand kept crsp. Ths paper addresses an EOQ-model wth backorders, where the demand and the lead tmes are kept fuzzy (general trangular fuzzy numbers) Björk, (009). In the past research the authors had less attenton on mult tems model whle n real world most of cases have more than one tem. The purpose of the research s to determne the optmal quantty of order n mult tem case wth backorder. The paper s organzed as follows; n secton the classcal Economc order quantty (EOQ) model n mult tem case wth backorders s ntroduced. In secton 3 some defntons and propertes about fuzzy number and sgn dstance method are ntroduced. In secton, model wth fuzzy costs s presented and solved. In the next secton a numercal example s provded to llustrate the results of proposed model accompaned by compare between fuzzy and crsp case for one tem and senstvty analyss. Correspondng Author: Had Nasser, Department of Mathematcal Scences, Mazandaran Unversty, Babolsar, Iran E-mal: nasser@umz.ac.r 863
2 Aust. J. Basc & Appl. Sc., 5(7): , 0. Mult Item EOQ Model wth Backorders: In stuaton that we face to shortage of nventory, arrved orders add to each other and make backlog orders. Whenever order come to depostory, before satsfy any other order, frst backlog orders must satsfy. It s trval that f backlog order doesn t have any cost then the optmal way s that the nventory n hand shouldn't be bgger than Zero. On the other hand t may ths cost be so expensve, meanwhle f backlogged orders be between these two borders the optmal way s that some backlog order must exst at the end of T cycle. The cost of each backlog request contan a fxed cost ( ˆ ) plus proportonate cost wth tme that order can't satsfy. The behavor of ths model s shown n fg.. Also parameters of ths model are: ˆ : Fxed cost of each unt shortage π : Tme Dependent cost for each unt shortage T : Tme perod that we don't have shortage T : Tme perod that we encounter shortage S ; Quantty of shortage. Q : Quantty of each order. W : Cost of rent depostory that depend on the quantty of order. O : Annual demand. T : Tme perod of cycle C o : Cost order n each order C h : Holdng cost n tme cycle per each unt. Fg. : The behavor of nventory model n length cycle Form trangular () we have: Qs Qs Tan D T T D From trangular () we have: S S Tan D T T D The mean nventory n a cycle s equvalent to the bottom surface of nventory bent dvde to T. It's mean that: QS QS ( QS). ( ) Mean nventory = D D Q S () T Q Q D The mean backlog demand n a cycle s trangular's backlog demand's surface dvde to T gven by : 86
3 Aust. J. Basc & Appl. Sc., 5(7): , 0. S S. S S T Mean backlog demand= S D D () T T Q Q D S. ˆ s Q ˆ. SD. S Shortage cost = constant cost + varable wth tme cost = (3) T T Q Q The total cost of a system n a cycle s: K = total cost = set up cost + Holdng nventory cost + shortage cost + rent cost + purchase cost ( ).. (, ) D Q KQS C ( ˆ O S C S D S h ) QW. CD.. Q Q Q Q Snce the goal s determne the quantty of economc order shortage s optmal quantty ore as follows: () (5) (6) (7) If system be contanng of mult tem nstead of one tem (6), (7) change as follows: (8) (9) whch shows the -th tem n a nventory system. Defntons and property about fuzzy number: Some bascs from fuzzy set theory need to be ntroduced n order to make the followng model development self Contaned. Much of these can be found n Chang, (00). Defnton.: Consder the fuzzy set A=(a,b,c) where a<b<c and defned on R, whch s called a trangular fuzzy number f the membershp A s gvent by: ( x a) a xb ( b a ) ( x) ( c x) b x c A ( c b) 0 other wse (0) 865
4 Aust. J. Basc & Appl. Sc., 5(7): , 0 Defnton.: Let B be a fuzzy set on R and 0 # α #. The α - cut B(a) of B s all the pont x such that ( x ),.e. B B( ) { x ( x) } B Defnton 3.: For 0 # α #, the fuzzy set functon of [ a, b ] ( ) [ a, b ] x 0 s gven by a xb other wse [ a, b ] () defned on R s called an a - level fuzzy nterval f the membershp () Decomposton Prncple: Let B be a fuzzy set on R and 0 # α #. Suppose the a-cut of B to be a closed nterval [B L (α)b U (α)], that s, B(α)=[B L (α)b U (α)]. Then we have: B B( ) 0 or ( x ) C B( )( x ) B 0 Where () α B (α) s a fuzzy set wth membershp functon B( ), x B( ) ( x) 0, other wse (3) () () C ( ) B( ) x s a characterstc functon of B(α), that s C B( ), x B( ) ( x) 0, x B( ) Remark.: From the decomposton Prncple and (), we obtan B B( ) [ B ( ), B ( )] 0 0 or ( B C ( x) ( x) L B( ) [ B ( ), ( ) ] 0 0 L BU U (5) (6) For any a,b,c,k 0R, a < b and c<d, the nterval operaton are as follows: ( ) [ a, b]( )[ c, d] [ ac, bd] ( )[ a, b]( )[ c, d] [ a d, b c] [ ka, kb], k 0, ( ) k(.)[ a, b] [ kb, ka], k 0, 866
5 Aust. J. Basc & Appl. Sc., 5(7): , 0 Further, for a>0 and c>0. In order to fnd non fuzzy values for model n the next secton we need to use some dstance measures as n Cheng [], we wll use sgned dstance method. Defntons 3: For any a and 0MBOL06\f"Symbol"\sR,defne the sgn dstance from a to 0 as d 0 (a,0). If a>0, the dstance from a to 0 s d 0 (a,0)=a; f a<0, the dstance from a to 0 s -a=-d 0 (a,0). Hence d 0 (a,0)=a s called the sgned dstance from a to 0. Let Ω be the famly of all fuzzy sets B defned on R for whch the a - cut are contnuous functons on α0[0,]. Then, for any 0 B B [ B ( ), B ( ) ] L, we have: From Chang [ ] t can be fnally stated how to calculate the sgned dstance. (7) Defnton.: For B, defne the sgned dstance of B to (.e, y axs) as db (,0 ) d([ B( ), ( ) ],0 0 L B ) d ( B 0 ( ) B( )) d Accordng to defnton, we obtan the followng property: (8) Property : For the trangular fuzzy number A = ( a, b, c), the a - cut A s A U (a) = c (c-b)a. The sgned dstance of A to s: d( A,0 ) ( a bc) (9) Fuzzy Mult Item EOQ Model wth Backorders: In ths secton we fuzzfy mult tem case of (). In ths model fuzzy cost s consst of : holdng cost of each unt tem (C h ), set up cost n each order for tem (C o ), fxed shortage cost for each unt tem ( ˆ ), tme dependent shortage cost for each unt tem (π), rent cost for each unt tem (w ) and purchase cost of each unt tem (C ). The mult tem of () s: D ( Q S ) S D S X ( Q, S ) ( C C wq CD) m ˆ o h Q Q Q Q The Cost coeffcent take consder as trangular fuzzy number and nter n (0). The result gven by () m D ( Q S) SD S X XQS (, ) ( ˆ C o C h QW DC ) () Q Q Q Q Where (0) () 867
6 Aust. J. Basc & Appl. Sc., 5(7): , 0 ˆ ˆ, ˆ, ˆ 5 6,, 7 8 W W, W, W 9 0 C C, C, C (3) () (5) (6) (7) Also and Δ j, j=,,, are determned by decson makers. Now we deffuzfy () and for ths objectve we used sgned dstance method based on property, the sgned dstance of X to 0 s gven by: D ( Q S ) S D S dx (,0 ) [ dc (,0 ) dc (,0 ) d(,0 ) d(,0 ) QdW (,0 ) DdC (,0 )] m ˆ ˆ o h Q Q Q Q (8) Where dc (,0 ), dc (,0 ), d( ˆ,0 ), d(,0 ), dw (,0 ), dc (,0 ) o h Obtan accordng to property calculated as follows: dc (,0 o ) [( Co ) Co ( Co )] Co ( ) (9) dc (,0 h ) [( Ch 3 ) Ch ( Ch )] Ch ( 3 ) (30) d( ˆ,0 ˆ ˆ ˆ ˆ ) [( 5) ( 6)] ( 6 5) (3) d(,0 ˆ ) [( 7) ( 8)] ( 8 7) dw (,0 ) ( W 9) W ( W 0) W ( 0 9) dc (,0 ) [( C ) C ( C )] C ( ) Based on (9), (30), (3), (3), (33), (3) and substtoton n (8) we Wll have the followng : D ( Q S ) (, ) (, ) [ ( ( )) ( ( )) m * X Q S d X O Co Ch 3 Q Q SD S ( ( )) ( ( )) ( ( )) ˆ Q W 0 9 Q Q D( C ( )] (3) (33) (3) (35) 868
7 Aust. J. Basc & Appl. Sc., 5(7): , 0 In order to obtan we must mprove that X * ( Q, S ) s convex n pont. It mean that we must mprove the second dervatve of X * ( Q, S ) s greater than zero. Snce the cost functon has tow varable we must examne ts convexty through the hessan matrx. Therefore frst we have to compute the frst and second dervatve. (36) X ( Q, S ) D S S D [ ( ) ( )( ) ( ) * C ˆ o Ch Q Q Q Q S ( ) ( )] Q W X ( Q, S ) D S S D ( ) ( ) ( ) * C ˆ 3 o C 3 h 3 Q Q Q Q S Q ( ) (37) (38) (39) (0) () + + () A=
8 Aust. J. Basc & Appl. Sc., 5(7): , 0 A= () If we let A>0 have: + + ] (5) It s mean that equaton (6) must be true to X * ( Q, S ) be convex n pont. Whle decson maker want to ntend about, frst they should examne obtaned relaton. Therefore for determne. we must solve ths equaton gven by: =0 (6) (7) =0 + + = (8) 870
9 Aust. J. Basc & Appl. Sc., 5(7): , 0 we let (8) n (9) then we have: After smplfy, we can wrte: (9) If we have closer look on (9), the optmal order quantty n fuzzy case s close to crsp case. If dentcal to the crsp case. Hence the fuzzy case s expandng of the crsp case. then the fuzzy case s 5. Comparson and Senstvty Analyss of Model s Parameters n Fuzzy and Crsp Case: In the followng some examples provde for comparson between the result of proposed model and those of crsp model n addton to senstvty analyss. Snce the proposed model s mult tem, ths comparson can apply for all tems n an nventory system, but we perform operaton for one tem for example. Assume the tem A s a product n a company and nventory control department want to order ths product for company and obtan data are gven by: D A =056 unt/year, C OA = 500 $/cycle, C ha = $/unt/year,, π A = 3$unt/year, W A = 500$/year C A = 0.33$/unt/year. Furthermore assume that expert's vewpont about these values are respectvely set as: * * In Table the optmal order quantty ( ) and optmal total cost n each year ( TC ) are calculate n both fuzzy and crsp case and varaton between them are measured by Q A 87. The results n Table * * ndcate that there s an ncrease wth 0.% n ( Q A ) and 0.58% n ( TC ) n fuzzy case rather than crsp case. Now n order to perform senstvty analyss we take consder two parameters of model n each table. In table 5 tow parameters, annual demand D A whch s consder as crsp, and order cost C oa whch s one the fuzzy parameters of proposed model, are consder. If we decrease wth 5% n D A and C oa result show that there s a decrease respectvely 3.3% and 3.38% wth D A and C oa. Keepng ths If we ncrease wth 5% n D A and C oa result show that there s an ncrease respectvely.79% and.79% wth D A and C oa. Hence
10 Aust. J. Basc & Appl. Sc., 5(7): , 0 varaton n these two parameters s almost dentcal. It s mean that f we ncrease the mentoned values, the optmal order quantty wll ncrease and nversely f we decrease these values the optmal quantty wll decrease. The same result could be deducted for optmal total cost (see Table 5). Accordng to analyss of Table 5, the other tables can be analyzed. Table : Comparson between fuzzy and crsp case Q * A TC * A Crsp Fuzzy Increase Table : Senstvty analyss of two parameters * A Q A TC * A W A Q * A TC * A Table 3: Senstvty analyss of two parameters * A Q A TC * A W A Q * A TC * A Table : Senstvty analyss of two parameters * A Q A TC * A W A Q * A TC * A Conclusons: In many problems n nventory context, exstence vague n many classcal model causes to unrelablty to result of models, therefore use of fuzzy models sound more desrable. In ths paper we fuzzfy classcal EOQ model wth backorders n case whch costs are fuzzy and other value are crsp. In ths case we obtan optmal quantty of order for each tem. Meanwhle for deffuzfy proposed model we apply sgned dstance method. One cases of the model wth sx cost component fuzzy and all others crsp are consdered for composton between fuzzy and crsp case and senstvty study. The concluson from the comparsons was that there s an ncrease to 0.% n optmal order quantty whle ths value s 0.58% for total annual cost. Future research ncludes the task to cover the combnaton of more fuzzy and crsp parameters and also composton between dfferent methods of dffuzfcaton. ACKNOWLEDGMENT The frst authors thanks to the Research Center of Algebrac Hyperstructures and Fuzzy Mathematcs, Babolsar, Iran for ts support. REFERENCES Björk, K.M., 009. An analytcal soluton to a fuzzy economc order quantty problem, Internatonal Journal of Approxmate Reasonng, 50: Björk, K-M., C. Carlsson, 005. The outcome of mprecse lead tmes on the dstrbutors, n: Proceedngs of the 38th Annual Hawa Internatonal Conference on System Scences (HICSS 05), Track 3, HICSS, pp: Chang, H-C., 00. An applcaton of fuzzy sets theory to the EOQ model wth mperfect qualty tems, Computers and Operatons Research, 3:
11 Aust. J. Basc & Appl. Sc., 5(7): , 0 Chang, J., J-S. Yao, H-M. Lee, 005. Fuzzy nventory wth backorder defuzzfcaton by sgned dstance method, Journal of Informaton Scence and Engneerng, : Ln, Y.J., 008. A perodc revew nventory model nvolvng fuzzy expected demand short and fuzzy backorder rate, Computers & Industral Engneerng, 5: Roy, T.K., M.A. Mat, 997. Fuzzy EOQ model wth demand dependent unt cost under lmted storage faclty, European Journal of Operatonal Research, 99: 5-3. Salameh, M.K., M.Y. Jaber, 000. Economc producton quantty model for tems wth mperfect qualty, Internatonal Journal of Producton Economcs, 6: Vjayan, T., M. Kumaran, 008. Inventory models wth a mxture of backorders and lost sales under fuzzy cost, European Journal of Operatonal Research, 89: Yao, J.S., & H.M. Lee, 996. Fuzzy nventory wth or wthout backorder for fuzzy order quantty, Informaton Scences, 93: Yao, J.S. and H.M. Lee, 996. Fuzzy nventory wth backorder for fuzzy order quantty Informaton Scences, 93: Yao, J.S. and H.M. Lee, 999. Fuzzy nventory wth or wthout backorder for fuzzy order quantty wth trapezod fuzzy number, Fuzzy Sets and Systems, 05:
The Order Relation and Trace Inequalities for. Hermitian Operators
Internatonal Mathematcal Forum, Vol 3, 08, no, 507-57 HIKARI Ltd, wwwm-hkarcom https://doorg/0988/mf088055 The Order Relaton and Trace Inequaltes for Hermtan Operators Y Huang School of Informaton Scence
More informationThe 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 informationFormulas for the Determinant
page 224 224 CHAPTER 3 Determnants e t te t e 2t 38 A = e t 2te t e 2t e t te t 2e 2t 39 If 123 A = 345, 456 compute the matrx product A adj(a) What can you conclude about det(a)? For Problems 40 43, use
More informationFuzzy Boundaries of Sample Selection Model
Proceedngs of the 9th WSES Internatonal Conference on ppled Mathematcs, Istanbul, Turkey, May 7-9, 006 (pp309-34) Fuzzy Boundares of Sample Selecton Model L. MUHMD SFIIH, NTON BDULBSH KMIL, M. T. BU OSMN
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 informationConvexity preserving interpolation by splines of arbitrary degree
Computer Scence Journal of Moldova, vol.18, no.1(52), 2010 Convexty preservng nterpolaton by splnes of arbtrary degree Igor Verlan Abstract In the present paper an algorthm of C 2 nterpolaton of dscrete
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 informationComplement of Type-2 Fuzzy Shortest Path Using Possibility Measure
Intern. J. Fuzzy Mathematcal rchve Vol. 5, No., 04, 9-7 ISSN: 30 34 (P, 30 350 (onlne Publshed on 5 November 04 www.researchmathsc.org Internatonal Journal of Complement of Type- Fuzzy Shortest Path Usng
More information3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X
Statstcs 1: Probablty Theory II 37 3 EPECTATION OF SEVERAL RANDOM VARIABLES As n Probablty Theory I, the nterest n most stuatons les not on the actual dstrbuton of a random vector, but rather on a number
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 informationAmiri s Supply Chain Model. System Engineering b Department of Mathematics and Statistics c Odette School of Business
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
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 informationSTOCHASTIC INVENTORY MODELS INVOLVING VARIABLE LEAD TIME WITH A SERVICE LEVEL CONSTRAINT * Liang-Yuh OUYANG, Bor-Ren CHUANG 1.
Yugoslav Journal of Operatons Research 10 (000), Number 1, 81-98 STOCHASTIC INVENTORY MODELS INVOLVING VARIABLE LEAD TIME WITH A SERVICE LEVEL CONSTRAINT Lang-Yuh OUYANG, Bor-Ren CHUANG Department of Management
More informationInventory Model with Backorder Price Discount
Vol. No. 7-7 ead Tme and Orderng Cost Reductons are Interdependent n Inventory Model wth Bacorder Prce scount Yu-Jen n Receved: Mar. 7 Frst Revson: May. 7 7 ccepted: May. 7 bstract The stochastc nventory
More informationA Hybrid Variational Iteration Method for Blasius Equation
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015), pp. 223-229 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) A Hybrd Varatonal Iteraton Method
More informationNeryškioji dichotominių testo klausimų ir socialinių rodiklių diferencijavimo savybių klasifikacija
Neryškoj dchotomnų testo klausmų r socalnų rodklų dferencjavmo savybų klasfkacja Aleksandras KRYLOVAS, Natalja KOSAREVA, Julja KARALIŪNAITĖ Technologcal and Economc Development of Economy Receved 9 May
More informationTransfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system
Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng
More informationColor Rendering Uncertainty
Australan Journal of Basc and Appled Scences 4(10): 4601-4608 010 ISSN 1991-8178 Color Renderng Uncertanty 1 A.el Bally M.M. El-Ganany 3 A. Al-amel 1 Physcs Department Photometry department- NIS Abstract:
More informationCHAPTER 14 GENERAL PERTURBATION THEORY
CHAPTER 4 GENERAL PERTURBATION THEORY 4 Introducton A partcle n orbt around a pont mass or a sphercally symmetrc mass dstrbuton s movng n a gravtatonal potental of the form GM / r In ths potental t moves
More informationGlobal Sensitivity. Tuesday 20 th February, 2018
Global Senstvty Tuesday 2 th February, 28 ) Local Senstvty Most senstvty analyses [] are based on local estmates of senstvty, typcally by expandng the response n a Taylor seres about some specfc values
More informationComputers and Mathematics with Applications. Computing a fuzzy shortest path in a network with mixed fuzzy arc lengths using α-cuts
Computers and Mathematcs wth Applcatons 60 (00) 989 00 Contents lsts avalable at ScenceDrect Computers and Mathematcs wth Applcatons journal homepage: www.elsever.com/locate/camwa Computng a fuzzy shortest
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 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 informationLectures - Week 4 Matrix norms, Conditioning, Vector Spaces, Linear Independence, Spanning sets and Basis, Null space and Range of a Matrix
Lectures - Week 4 Matrx norms, Condtonng, Vector Spaces, Lnear Independence, Spannng sets and Bass, Null space and Range of a Matrx Matrx Norms Now we turn to assocatng a number to each matrx. We could
More informationCOMPLEX NUMBERS AND QUADRATIC EQUATIONS
COMPLEX NUMBERS AND QUADRATIC EQUATIONS INTRODUCTION We know that x 0 for all x R e the square of a real number (whether postve, negatve or ero) s non-negatve Hence the equatons x, x, x + 7 0 etc are not
More information8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS
SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 493 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces you have studed thus far n the text are real vector spaces because the scalars
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 informationMULTI-ITEM FUZZY INVENTORY MODEL FOR DETERIORATING ITEMS WITH FINITE TIME-HORIZON AND TIME-DEPENDENT DEMAND
Yugoslav Journal of Operatons Research 16 (2006), Number 2, 161-176 MULI-IEM FUZZY INVENORY MODEL FOR DEERIORAING IEMS WI FINIE IME-ORIZON AND IME-DEPENDEN DEMAND S. KAR 1,. K. ROY 2, M. MAII 3 1 Department
More informationx i1 =1 for all i (the constant ).
Chapter 5 The Multple Regresson Model Consder an economc model where the dependent varable s a functon of K explanatory varables. The economc model has the form: y = f ( x,x,..., ) xk Approxmate ths by
More informationPower law and dimension of the maximum value for belief distribution with the max Deng entropy
Power law and dmenson of the maxmum value for belef dstrbuton wth the max Deng entropy Bngy Kang a, a College of Informaton Engneerng, Northwest A&F Unversty, Yanglng, Shaanx, 712100, Chna. Abstract Deng
More informationCOEFFICIENT DIAGRAM: A NOVEL TOOL IN POLYNOMIAL CONTROLLER DESIGN
Int. J. Chem. Sc.: (4), 04, 645654 ISSN 097768X www.sadgurupublcatons.com COEFFICIENT DIAGRAM: A NOVEL TOOL IN POLYNOMIAL CONTROLLER DESIGN R. GOVINDARASU a, R. PARTHIBAN a and P. K. BHABA b* a Department
More informationThe Multiple Classical Linear Regression Model (CLRM): Specification and Assumptions. 1. Introduction
ECONOMICS 5* -- NOTE (Summary) ECON 5* -- NOTE The Multple Classcal Lnear Regresson Model (CLRM): Specfcaton and Assumptons. Introducton CLRM stands for the Classcal Lnear Regresson Model. The CLRM s also
More informationEFFECTS OF JOINT REPLENISHMENT POLICY ON COMPANY COST UNDER PERMISSIBLE DELAY IN PAYMENTS
Mathematcal and Computatonal Applcatons, Vol. 5, No., pp. 8-58,. Assocaton for Scentfc Research EFFECS OF JOIN REPLENISHMEN POLICY ON COMPANY COS UNDER PERMISSIBLE DELAY IN PAYMENS Yu-Chung sao, Mng-Yu
More informationFinite Element Modelling of truss/cable structures
Pet Schreurs Endhoven Unversty of echnology Department of Mechancal Engneerng Materals echnology November 3, 214 Fnte Element Modellng of truss/cable structures 1 Fnte Element Analyss of prestressed structures
More informationModule 2. Random Processes. Version 2 ECE IIT, Kharagpur
Module Random Processes Lesson 6 Functons of Random Varables After readng ths lesson, ou wll learn about cdf of functon of a random varable. Formula for determnng the pdf of a random varable. Let, X be
More informationLinear Approximation with Regularization and Moving Least Squares
Lnear Approxmaton wth Regularzaton and Movng Least Squares Igor Grešovn May 007 Revson 4.6 (Revson : March 004). 5 4 3 0.5 3 3.5 4 Contents: Lnear Fttng...4. Weghted Least Squares n Functon Approxmaton...
More informationComparison of the COG Defuzzification Technique and Its Variations to the GPA Index
Amercan Journal of Computatonal and Appled Mathematcs 06, 6(): 87-93 DOI: 0.93/.acam.06060.03 Comparson of the COG Defuzzfcaton Technque and Its Varatons to the GPA Index Mchael Gr. Voskoglou Department
More informationELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM
ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM An elastc wave s a deformaton of the body that travels throughout the body n all drectons. We can examne the deformaton over a perod of tme by fxng our look
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 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 informationApplication of B-Spline to Numerical Solution of a System of Singularly Perturbed Problems
Mathematca Aeterna, Vol. 1, 011, no. 06, 405 415 Applcaton of B-Splne to Numercal Soluton of a System of Sngularly Perturbed Problems Yogesh Gupta Department of Mathematcs Unted College of Engneerng &
More informationChapter 2 A Class of Robust Solution for Linear Bilevel Programming
Chapter 2 A Class of Robust Soluton for Lnear Blevel Programmng Bo Lu, Bo L and Yan L Abstract Under the way of the centralzed decson-makng, the lnear b-level programmng (BLP) whose coeffcents are supposed
More informationAffine transformations and convexity
Affne transformatons and convexty The purpose of ths document s to prove some basc propertes of affne transformatons nvolvng convex sets. Here are a few onlne references for background nformaton: http://math.ucr.edu/
More information829. An adaptive method for inertia force identification in cantilever under moving mass
89. An adaptve method for nerta force dentfcaton n cantlever under movng mass Qang Chen 1, Mnzhuo Wang, Hao Yan 3, Haonan Ye 4, Guola Yang 5 1,, 3, 4 Department of Control and System Engneerng, Nanng Unversty,
More informationAn Application of Fuzzy Hypotheses Testing in Radar Detection
Proceedngs of the th WSES Internatonal Conference on FUZZY SYSEMS n pplcaton of Fuy Hypotheses estng n Radar Detecton.K.ELSHERIF, F.M.BBDY, G.M.BDELHMID Department of Mathematcs Mltary echncal Collage
More informationDUE: WEDS FEB 21ST 2018
HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant
More informationMEM 255 Introduction to Control Systems Review: Basics of Linear Algebra
MEM 255 Introducton to Control Systems Revew: Bascs of Lnear Algebra Harry G. Kwatny Department of Mechancal Engneerng & Mechancs Drexel Unversty Outlne Vectors Matrces MATLAB Advanced Topcs Vectors A
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 informationAppendix for Causal Interaction in Factorial Experiments: Application to Conjoint Analysis
A Appendx for Causal Interacton n Factoral Experments: Applcaton to Conjont Analyss Mathematcal Appendx: Proofs of Theorems A. Lemmas Below, we descrbe all the lemmas, whch are used to prove the man theorems
More informationCOMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD
COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,
More informationA New Algorithm for Finding a Fuzzy Optimal. Solution for Fuzzy Transportation Problems
Appled Mathematcal Scences, Vol. 4, 200, no. 2, 79-90 A New Algorthm for Fndng a Fuzzy Optmal Soluton for Fuzzy Transportaton Problems P. Pandan and G. Nataraan Department of Mathematcs, School of Scence
More informationAPPENDIX A Some Linear Algebra
APPENDIX A Some Lnear Algebra The collecton of m, n matrces A.1 Matrces a 1,1,..., a 1,n A = a m,1,..., a m,n wth real elements a,j s denoted by R m,n. If n = 1 then A s called a column vector. Smlarly,
More informationA new Approach for Solving Linear Ordinary Differential Equations
, ISSN 974-57X (Onlne), ISSN 974-5718 (Prnt), Vol. ; Issue No. 1; Year 14, Copyrght 13-14 by CESER PUBLICATIONS A new Approach for Solvng Lnear Ordnary Dfferental Equatons Fawz Abdelwahd Department of
More informationSystem in Weibull Distribution
Internatonal Matheatcal Foru 4 9 no. 9 94-95 Relablty Equvalence Factors of a Seres-Parallel Syste n Webull Dstrbuton M. A. El-Dacese Matheatcs Departent Faculty of Scence Tanta Unversty Tanta Egypt eldacese@yahoo.co
More informationEcon107 Applied Econometrics Topic 3: Classical Model (Studenmund, Chapter 4)
I. Classcal Assumptons Econ7 Appled Econometrcs Topc 3: Classcal Model (Studenmund, Chapter 4) We have defned OLS and studed some algebrac propertes of OLS. In ths topc we wll study statstcal propertes
More informationUncertainty in measurements of power and energy on power networks
Uncertanty n measurements of power and energy on power networks E. Manov, N. Kolev Department of Measurement and Instrumentaton, Techncal Unversty Sofa, bul. Klment Ohrdsk No8, bl., 000 Sofa, Bulgara Tel./fax:
More informationThe Geometry of Logit and Probit
The Geometry of Logt and Probt Ths short note s meant as a supplement to Chapters and 3 of Spatal Models of Parlamentary Votng and the notaton and reference to fgures n the text below s to those two chapters.
More informationThe Second Anti-Mathima on Game Theory
The Second Ant-Mathma on Game Theory Ath. Kehagas December 1 2006 1 Introducton In ths note we wll examne the noton of game equlbrum for three types of games 1. 2-player 2-acton zero-sum games 2. 2-player
More informationLecture 3. Ax x i a i. i i
18.409 The Behavor of Algorthms n Practce 2/14/2 Lecturer: Dan Spelman Lecture 3 Scrbe: Arvnd Sankar 1 Largest sngular value In order to bound the condton number, we need an upper bound on the largest
More informationNUMERICAL DIFFERENTIATION
NUMERICAL DIFFERENTIATION 1 Introducton Dfferentaton s a method to compute the rate at whch a dependent output y changes wth respect to the change n the ndependent nput x. Ths rate of change s called the
More informationYong Joon Ryang. 1. Introduction Consider the multicommodity transportation problem with convex quadratic cost function. 1 2 (x x0 ) T Q(x x 0 )
Kangweon-Kyungk Math. Jour. 4 1996), No. 1, pp. 7 16 AN ITERATIVE ROW-ACTION METHOD FOR MULTICOMMODITY TRANSPORTATION PROBLEMS Yong Joon Ryang Abstract. The optmzaton problems wth quadratc constrants often
More informationNumerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationFuzzy Optimization of Multi Item Inventory Model with Imprecise Production and Demand
Internatonal Journal of Computatonal and ppled Mathematcs. ISSN 89-4966 Volume, Number 3 (7), pp. 699-75 esearch Inda Publcatons http://www.rpublcaton.com Fuzzy Optmzaton of Mult Item Inventory Model wth
More informationn α j x j = 0 j=1 has a nontrivial solution. Here A is the n k matrix whose jth column is the vector for all t j=0
MODULE 2 Topcs: Lnear ndependence, bass and dmenson We have seen that f n a set of vectors one vector s a lnear combnaton of the remanng vectors n the set then the span of the set s unchanged f that vector
More informationAssignment 5. Simulation for Logistics. Monti, N.E. Yunita, T.
Assgnment 5 Smulaton for Logstcs Mont, N.E. Yunta, T. November 26, 2007 1. Smulaton Desgn The frst objectve of ths assgnment s to derve a 90% two-sded Confdence Interval (CI) for the average watng tme
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 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 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 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 informationSpeeding up Computation of Scalar Multiplication in Elliptic Curve Cryptosystem
H.K. Pathak et. al. / (IJCSE) Internatonal Journal on Computer Scence and Engneerng Speedng up Computaton of Scalar Multplcaton n Ellptc Curve Cryptosystem H. K. Pathak Manju Sangh S.o.S n Computer scence
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 informationLinear Regression Analysis: Terminology and Notation
ECON 35* -- Secton : Basc Concepts of Regresson Analyss (Page ) Lnear Regresson Analyss: Termnology and Notaton Consder the generc verson of the smple (two-varable) lnear regresson model. It s represented
More information(1, T) policy for a Two-echelon Inventory System with Perishableon-the-Shelf
Journal of Optmzaton n Industral Engneerng 6 (24) 3-4 (, ) polcy for a wo-echelon Inventory ystem wth Pershableon-the-helf Items Anwar Mahmood a,, Alreza Ha b a PhD Canddate, Industral Engneerng, Department
More informationPHYS 705: Classical Mechanics. Calculus of Variations II
1 PHYS 705: Classcal Mechancs Calculus of Varatons II 2 Calculus of Varatons: Generalzaton (no constrant yet) Suppose now that F depends on several dependent varables : We need to fnd such that has a statonary
More informationFoundations of Arithmetic
Foundatons of Arthmetc Notaton We shall denote the sum and product of numbers n the usual notaton as a 2 + a 2 + a 3 + + a = a, a 1 a 2 a 3 a = a The notaton a b means a dvdes b,.e. ac = b where c s an
More informationVariations of the Rectangular Fuzzy Assessment Model and Applications to Human Activities
Varatons of the Rectangular Fuzzy Assessment Model and Applcatons to Human Actvtes MICHAEl GR. VOSKOGLOU Department of Mathematcal Scence3s Graduate Technologcal Educatonal Insttute of Western Greece Meg.
More informationInternational Journal of Mathematical Archive-3(3), 2012, Page: Available online through ISSN
Internatonal Journal of Mathematcal Archve-3(3), 2012, Page: 1136-1140 Avalable onlne through www.ma.nfo ISSN 2229 5046 ARITHMETIC OPERATIONS OF FOCAL ELEMENTS AND THEIR CORRESPONDING BASIC PROBABILITY
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 informationThe Two-scale Finite Element Errors Analysis for One Class of Thermoelastic Problem in Periodic Composites
7 Asa-Pacfc Engneerng Technology Conference (APETC 7) ISBN: 978--6595-443- The Two-scale Fnte Element Errors Analyss for One Class of Thermoelastc Problem n Perodc Compostes Xaoun Deng Mngxang Deng ABSTRACT
More informationA NOTE ON A PERIODIC REVIEW INVENTORY MODEL WITH UNCERTAIN DEMAND IN A RANDOM ENVIRONMENT. Hirotaka Matsumoto and Yoshio Tabata
Scentae Mathematcae Japoncae Onlne, Vol. 9, (23), 419 429 419 A NOTE ON A PERIODIC REVIEW INVENTORY MODEL WITH UNCERTAIN DEMAND IN A RANDOM ENVIRONMENT Hrotaka Matsumoto and Yosho Tabata Receved September
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 informationLecture 5 Decoding Binary BCH Codes
Lecture 5 Decodng Bnary BCH Codes In ths class, we wll ntroduce dfferent methods for decodng BCH codes 51 Decodng the [15, 7, 5] 2 -BCH Code Consder the [15, 7, 5] 2 -code C we ntroduced n the last lecture
More informationPerron Vectors of an Irreducible Nonnegative Interval Matrix
Perron Vectors of an Irreducble Nonnegatve Interval Matrx Jr Rohn August 4 2005 Abstract As s well known an rreducble nonnegatve matrx possesses a unquely determned Perron vector. As the man result of
More information2E Pattern Recognition Solutions to Introduction to Pattern Recognition, Chapter 2: Bayesian pattern classification
E395 - Pattern Recognton Solutons to Introducton to Pattern Recognton, Chapter : Bayesan pattern classfcaton Preface Ths document s a soluton manual for selected exercses from Introducton to Pattern Recognton
More informationVQ widely used in coding speech, image, and video
at Scalar quantzers are specal cases of vector quantzers (VQ): they are constraned to look at one sample at a tme (memoryless) VQ does not have such constrant better RD perfomance expected Source codng
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 informationOrientation Model of Elite Education and Mass Education
Proceedngs of the 8th Internatonal Conference on Innovaton & Management 723 Orentaton Model of Elte Educaton and Mass Educaton Ye Peng Huanggang Normal Unversty, Huanggang, P.R.Chna, 438 (E-mal: yepeng@hgnc.edu.cn)
More informationFUZZY FINITE ELEMENT METHOD
FUZZY FINITE ELEMENT METHOD RELIABILITY TRUCTURE ANALYI UING PROBABILITY 3.. Maxmum Normal tress Internal force s the shear force, V has a magntude equal to the load P and bendng moment, M. Bendng moments
More informationHongyi Miao, College of Science, Nanjing Forestry University, Nanjing ,China. (Received 20 June 2013, accepted 11 March 2014) I)ϕ (k)
ISSN 1749-3889 (prnt), 1749-3897 (onlne) Internatonal Journal of Nonlnear Scence Vol.17(2014) No.2,pp.188-192 Modfed Block Jacob-Davdson Method for Solvng Large Sparse Egenproblems Hongy Mao, College of
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 informationTensor Smooth Length for SPH Modelling of High Speed Impact
Tensor Smooth Length for SPH Modellng of Hgh Speed Impact Roman Cherepanov and Alexander Gerasmov Insttute of Appled mathematcs and mechancs, Tomsk State Unversty 634050, Lenna av. 36, Tomsk, Russa RCherepanov82@gmal.com,Ger@npmm.tsu.ru
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 informationAn identification algorithm of model kinetic parameters of the interfacial layer growth in fiber composites
IOP Conference Seres: Materals Scence and Engneerng PAPER OPE ACCESS An dentfcaton algorthm of model knetc parameters of the nterfacal layer growth n fber compostes o cte ths artcle: V Zubov et al 216
More informationSection 8.3 Polar Form of Complex Numbers
80 Chapter 8 Secton 8 Polar Form of Complex Numbers From prevous classes, you may have encountered magnary numbers the square roots of negatve numbers and, more generally, complex numbers whch are the
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 informationNegative Binomial Regression
STATGRAPHICS Rev. 9/16/2013 Negatve Bnomal Regresson Summary... 1 Data Input... 3 Statstcal Model... 3 Analyss Summary... 4 Analyss Optons... 7 Plot of Ftted Model... 8 Observed Versus Predcted... 10 Predctons...
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 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 informationHomogenization of reaction-diffusion processes in a two-component porous medium with a non-linear flux-condition on the interface
Homogenzaton of reacton-dffuson processes n a two-component porous medum wth a non-lnear flux-condton on the nterface Internatonal Conference on Numercal and Mathematcal Modelng of Flow and Transport n
More informationA New Refinement of Jacobi Method for Solution of Linear System Equations AX=b
Int J Contemp Math Scences, Vol 3, 28, no 17, 819-827 A New Refnement of Jacob Method for Soluton of Lnear System Equatons AX=b F Naem Dafchah Department of Mathematcs, Faculty of Scences Unversty of Gulan,
More information