A two storage inventory model with variable demand and time dependent deterioration rate and with partial backlogging
|
|
- Kathryn Rose
- 5 years ago
- Views:
Transcription
1 Malaya Journal of Matematik, Vol. S, No., 35-40, 08 A two storage inventory model with variable demand and time dependent deterioration rate and with partial baklogging Rihi Singh *, Ashok Kumar and Dharmendra Yadav3 Abstrat In this paper an inventory model is developed for single deteriorating items, partially baklogged shortages under two storehouses (first is owned and seond is rented warehouse). The deterioration rate has been onsidered here to be time dependent. The demand rate of the item depends on () time; () selling prie; and (3) the frequeny of advertisement. The stoks of first warehouse are filled from seond warehouse by using ontinuous release pattern. Here different ases and sub-ases are assumed aording to the stok level at initial and reorder points, with respet to the relative size of storing apaities of storehouses. The proposed inventory model is formulated for eah sub-ase as non linear onstrained mixed integer optimization problem. Here GRG tehnique is used to solve the problem. Also a numerial example is presented to demonstrate the proposed model. Keywords Two-storehouse inventory; Variable deterioration rate; Variable demand rate; Partial baklogging. Researh Sholar, Meerut College Meerut, Uttar Pradesh, India. College, Meerut, Uttar Pradesh, India. 3 Vardhman College, Bijnore, Uttar Pradesh, India. *Corresponding author: singhrihi5@gmail.om; drashokkumar@meerutollege.org; 3 dharmendrayadav3580@gmail.om 08 MJM. Artile History: Reeived 4 Deember 07 ; Aepted January 08 Meerut Contents Introdution Notations and assumptions Mathematial formulation Numerial illustration Conlusions Referenes Introdution Hartely (97) firstly worked on inventory models assuming two storehouses and onstant demand rate. Deaying items are the items that happen to spoil, damage, lost of its marginal value, and so on through time. The deterioration of produts in inventory is an atual harateristi that is neessary to study its effet on inventory. Yang (004) and Hsieh et al., (008) analysed inventory models for deaying items assuming two storehouses. Xu et al., (07) analysed two storehouses inventory model with different poliies of dis- pathing assuming deaying items. Today, advertisement is an effetive way to introdue a produt in the market. As the number of advertisements inreases the demand of the produt in the market also inreases. Demand is also affeted by the selling prie of the produt. Bhunia and Maiti (997) first reported that the demand rate of a produt in the inventory model depends on number of advertisements, selling prie and time. Goswami and Chaudhuri (99) disussed the models with or without shortages for linearly time-dependent demand. Abad (000), Goyal and Gunasekaran (995), Luo (998), Mondal et al. (007) studied the effets on the demand aused by variations in prie and number of the advertisement on deteriorating items. Chung et al., (00) developed an inventory model with prie (linearly dereasing) dependent demand that also analysis the disount prie, the frequeny of deliveries and yle time. Sarkar and Sarkar (03) presented an inventory model whih depends on demand and variable (linear) deterioration rate. Bhunia et al., (05) developed a two storehouse inventory model taking demand as variable with partial baklogging for deaying items. Wu (0) disussed two inventory systems assuming demand rate as trapezoidal under
2 baklogging 3/40 baklogging and time dependent (linear) deterioration rate. In Setion the notations and assumptions of the model are shown. In setion 3 mathematial formulations of different ases with sub-ases are disussed. In Setion 4, a numerial example and optimal solution is presented. Setion 5 gives onluding remark and sope for the future researh. m (> ): The mark up rate. p: Selling prie per unit of item, whih is taken as p = mc p. N: Rate of reurrene of advertisement. A: Advertisement ost per advertisement. T : The duration of yle.. Notations and assumptions 3. Mathematial formulation The mathematial model rest on the following assumptions: Aording to the storage apaities of both store houses and highest stok level, two ases arise: Case : H < S H + H (L system) Case : S H (L system) Aording to the reorder point of stok level four sub-ases may arise: Sub-ase 3.: H < S H + H and R < 0 Sub-ase 3.: H < S H + H and R > 0 Sub-ase 3.3: S H and R < 0 Sub-ase 3.4: S H and R > 0 The Sub-ase 3. is explained as follows Sub-ase 3.: H < S H + H and R < 0 () The rate of replenishment is taken infinite. () Lead time is taken onstant. (3) The rate of demand rate is taken as D(N, p,t) = N (a bp + t), a, b,, > 0. (4) Extent of inventory sheduling is taken infinite. (5) The entire lot size is supplied in one bath. () Both the warehouses are of finite storing apaities. (7) The time gap in selling from first storehouse (OW) and oupying the spae by the units of seond storehouse (RW) is not signifiant. (8) Baklogging rate is taken as [ + (T t)], where >0. The mathematial model rest on the following notations: I(t): Inventory level during time t. H : Storing apaity of first storehouse (OW). H : Storing apaity of seond storehouse (RW). S: Highest stok level (initially) L : An inventory system having a single storing faility. L : An inventory system having two storing failities. C : Holding ost of unit in unit of time at first storehouse (OW). C0 (C0 > C ): Holding ost of unit in unit of time at seond storehouse (RW). C : Shortage ost of unit in unit of time. C3 : Purhase ost of unit of item. C4 : Transportation ost unit of item. θow (t): (= a + bt): Rate of deay in OW, where a is sale parameter and 0 < b <. θrw (t): (= a + bt): Rate of deay in RW, where a is sale parameter and 0 < b <. R: Reorder point. A : Replenishment ost/ordering ost per replenishment for L system. A : Replenishment ost/ordering ost per replenishment for L system. Figure Inventory level Ir (t) at seond storehouse (RW) is presented by the following equations dir (t) + (a + bt)ir (t) = D(t), 0 t t () s. t. Ir (t ) = 0, () Ir (t) = S H at t = 0 (3) Using equation (), the solution of equation () is as follows Ir (t) = N (t t ) t + t (a bp) + {(a bp)a + } 3
3 baklogging 37/40 t e (a t+b ) log + (T t ) (T t ) (4) Using equation (3), t S = H + N t (a bp) + {(a bp)a + } The Inventory arrying units in seond storehouse (RW) = R t I (t) r 0 (5) = In first storehouse (OW) the inventory level Io (t) during [0, T ] is presented as + (a + bt)io (t) = 0, 0 t < t + (a + bt)io (t) = D(t), t t t D(t) =, t < t T + (T t) t {4(a bp)(3 at ) + t (8 3at )}. 4 Io (t) = 0 at t = t (8) The Inventory arrying units in first storehouse () (OW ) = Z t 0 (7) Io (t) t )+ (a bp)(t t ) {(a bp)a + }(t t ) {3 a (t + t )} {3at t (8 3at ) t (4 at )}. (9) = H (t a (8) s. t. Io (t) = H at t = 0, (7) (9) (0) The total shortage ost and Z T Io (t) = R at t = T. = C () t [ I0 (t)] a bp + T + = C log + (T t ) { + (T t )} (T t)} d (t t ) R(T t ) (0) Using the ontinuity of Io (t) at t and t and above onditions the solutions of the equations are as follows t () Io (t) = H e (a +b ), 0 t < t Io (t) = N (T t ) (a bp) + {(a bp)a + } t t + t (3) e (a t+b ), t t t Io (t) = a bp + T + log + (T t) (T t) R, t < t T The total transportation ost = Ct Z t 0 () D(N, pt) = Ct N (a bp)t + t Now total profit (P = total sales revenue total ost of the system (4) P(N,t, T ) = p N (a bp)t + t + R and, we have H = N (t t ) (a bp) + {(a bp)a + } t + t (5) C3 (S + R ) (R + R ) t C H (t a ) + (a bp)(t t ) {3 a (t + t )} {(a bp)a + }(t t ) {3at t (8 3at ) t (4 at )}] N C0 t {4(a bp)(3 at ) + t (8 3at )} 4 N +C a bp + T + log + (T t ) { + (T t )} (T t )} d The above equation redues to At + Bt C = 0, where A = N {(a bp)a +}, B = N (a bp), C = W +N +(a bp)t + N t {(a bp)a + } gives the solution B + B + 4AB t = () A Using equations (3) and (4) R= a bp + T + 37
4 baklogging 38/40 (t t ) R(T t ) C4 N (a bp)t + t NA, (a bp)(t t) {3 a (t + T )} {(a bp)a + }(t t) {3at t(8 3a T ) 0 N t (4 a T )} C t {4(a bp)(3 at ) 4 + t (8 3at )} C4 N (a bp)t + t NA (8) + () where N is an integer variable and t, T are ontinuous variables. Hene the problem of Sub-ase 3. is to P, T s.t. 0 < t < T, H < S < H + H, and R < 0 Maximize Z(N,t, T ) = Hene the average profit per unit time of sub-ase 3. is given by Z(N,t, T ) = TP. (3) Sub-ase 3.: H < S H + H and R > 0 Sub-ase 3.3: S H and R < 0 Figure Figure 3 In this sub-ase, the inventory level Ir (t) at seond warehouse (RW) is presented as follows dir (t) + (a + bt)ir (t) = D(t), 0 t t s.t.ir (t ) = 0 and Ir (t) = S H at t = 0 The inventory level Io (t) at OW is presented by the equations + (a + bt)io (t) = D(t), 0 t t D(t) =, t < t T + (T t) s.t. Io (t ) = 0, Io (0) = S and Io (T ) = R. (4) (5) The inventory level Io (t) at first storehouse (OW) in the interval [0, T ] is presented as follows + (a + bt)io (t) = 0, 0 t < t + (a + bt)io (t) = D(t), t t T s.t. Io (t) = H at t = 0 and Io (t) = R at t = T. (9) (30) (3) Hene the net profit is given by P = p N (a bp)t + t + R C3 (S + R ) N R C t {4(a bp)(3 at ) + t (8 3at )} 4 N +C a bp + T + log + (T t ) { + (T t )} (T t ) d (t t ) R(T t ) NA (3) () (7) The Total profit (P) for this sub-ase is as follows P = pn (a bp)t + T C3 (S R) (R + R ) t C H t a + R(T t ) 38
5 baklogging 39/40 Hene the average profit per unit time of sub-ase 3.3 is given by Z(N,t, T ) = TP. onavity of the funtion is presented numerially. Figure4 represents that the profit funtion is onave for the above mentioned example. Sub-ase 3.4: S H and R > 0 The inventory level Io (t) at first storehouse (OW) is expressed by the following equations + (a + bt)io (t) = D(t), 0 t T s.t. Io (0) = S and Io (T ) = R. 5. Conlusions This paper introdues an inventory model with two storehouses of limited spae apaity under time dependent deterioration rate. Here demand rate of the produt hanges aording to () number of advertisement, () selling prie and (3) time. In the model shortages ours of whih only some units are baklogged. To make model more realisti the rate of deay is taken linear in both storehouses. Also the optimal net profit is alulated by solving proposed model for different system parameters. Finally a numerial example is taken to maximize the total profit of the system. By taking more assumptions, suh as inflation, learning effets, greening effets et the model an be better fitted to real world senarios. It an also be analysed further by introduing different preservation tehnologies in storehouses. (33) (34) Here the total profit is given by P = pn (a bp)t + T C3 (S R) R ST C ( a T ) t (a bp)(3 a T ) N t 3 {(a bp)a + }(4 3a T ) NA 4 (35) The average profit per unit time is given by Z(N,t, T ) = TP. Referenes 4. Numerial illustration [] C = Re..0/unit/unit time, C = Rs. /unit/unit time, C0 = Rs..5/unit/unit time, R = Rs. 50/order, R = Rs.50/order, a = 0., a = 0.08, b =.0, b =.0, C3 = Rs. 5/unit, C4 = Rs. 0.5/unit, H = 00; H = 00, a = 50, b = 3.5, = 5, = 0.3, A = Rs. 50/advertisement, =.5. We used Mathematia 5. to solve this example for determining the optimal values of N, t, t T, S, and R along with the average profit Z of the system. We obtained the following results: t =.908, t = 3.95, N = 5, T = , R = 3.705, S = 47.97, Z = [] [3] [4] [5] [] [7] T 0.3 t 0.4 [8] Figure 4. Represents the Average profit vs. t and T [9] The profit funtion Z(N,t, T ) obtained from equation (3) is highly nonlinear so it is very tedious to solve, thus the 39 R.V. Hartely, Operations Researh A Managerial Emphasis, Goodyear Publishing Company, California, CA, 97. A. Goswami and K.S. Chaudhuri, An eonomi order quantity model for items with two levels of storage for a linear trend in demand, Journal of the Operational Researh Soiety, 43(99), H. Yang, Two-warehouse inventory models for deteriorating items with shortage under inflation, European Journal of Operational Researh, 57(004), T. Hsieh, C. Dye and L.Y. Ouyang, Determining optimal lot size for a two warehouse system with deterioration and shortages using net present value, European Journal of Operational Researh, 9(00), 8 9. S.K. Goyal and A. Gunasekaran, An integrated prodution-inventory-marketing model for deteriorating items, Computers & Industrial Engineering, 8(995), X. Xu, Q. Bai and M. Chen, A omparison of different dispathing poliies in two-warehouse inventory systems for deteriorating items over a finite time horizon, Applied Mathematial Modelling, 4(07), A.K. Bhunia, A.A. Shaikh, G. Sharma and S. Pareek, A two storage inventory model for deteriorating items with variable demand and partial baklogging, Journal of Industrial and Prodution Engineering, 3(4)(05), 3 7. A.K. Bhunia and M. Maiti, An inventory model for deaying items with selling prie, frequeny of advertisement and linearly time-dependent demand with shortages, IAPQR Transations, (997), P.L. Abad, Optimal lot size for a perishable good under onditions of finite prodution and partial bak order-
6 baklogging 40/40 [0] [] [] [3] [4] ing and lost sale, Computers & Industrial Engineering, 38(000), W. Luo, An integrated inventory system for perishable goods with bakordering, Computers & Industrial Engineering, 34(998), B. Mondal, A.K. Bhunia and M. Maiti, A model of two storage inventory system under stok dependent selling rate inorporating marketing deisions and transportation ost with optimum release rule, Tamsui Oxford Journal of Mathematial Sienes, 3(007), S.L. Chung and H.M. Wee, Priing disount for a supply hain oordination poliy with prie dependent demand, Journal of the Chinese Institute of Industrial Engineers, 3(3)(00), 3. B. Sarkar and S. Sarkar, Variable deterioration and demand An inventory model, Eonomi Modelling, 3(03), J. Wu, K. Skouri, J.T. Teng and Y. Hu, Two inventory systems with trapezoidal-type demand rate and timedependent deterioration and baklogging, Expert Systems with Appliations, 4(0), ????????? ISSN(P): Malaya Journal of Matematik ISSN(O):3-5????????? 40
Dr.Pravat Kumar Sukla P.S College, Koksara,Kalahandi,Odisa,INDIA
nternational Journal of Engineering Researh & ehnology (JER) SSN: 78-08 Vol. ssue 7, September - 0 An nventory Ordering Poliy Using Constant Deteriorating tems With Constant Demand. Abstrat Dr.Pravat Kumar
More informationA fuzzified Industrial warehouse inventory model for deteriorating items with decreasing demand and various fuzzy cost parameters
International Journal of Engineering Researh and General Siene Volume 5, Issue 2, Marh-April, 2017 A fuzzified Industrial warehouse inventory model for deteriorating items with dereasing demand and various
More informationOPTIMAL PRICING AND LOT-SIZING DECISIONS UNDER WEIBULL DISTRIBUTION DETERIORATION AND TRADE CREDIT POLICY
Yugoslav Journal of Operations Researh Vol 8 (8), Number, -34 DOI:.98/YUJOR8M OPIMAL PRICING AND LO-SIZING DECISIONS UNDER WEIBULL DISRIBUION DEERIORAION AND RADE CREDI POLICY S. K. MANNA Department of
More informationTaste for variety and optimum product diversity in an open economy
Taste for variety and optimum produt diversity in an open eonomy Javier Coto-Martínez City University Paul Levine University of Surrey Otober 0, 005 María D.C. Garía-Alonso University of Kent Abstrat We
More informationarxiv:gr-qc/ v2 6 Feb 2004
Hubble Red Shift and the Anomalous Aeleration of Pioneer 0 and arxiv:gr-q/0402024v2 6 Feb 2004 Kostadin Trenčevski Faulty of Natural Sienes and Mathematis, P.O.Box 62, 000 Skopje, Maedonia Abstrat It this
More informationOptimization of Statistical Decisions for Age Replacement Problems via a New Pivotal Quantity Averaging Approach
Amerian Journal of heoretial and Applied tatistis 6; 5(-): -8 Published online January 7, 6 (http://www.sienepublishinggroup.om/j/ajtas) doi:.648/j.ajtas.s.65.4 IN: 36-8999 (Print); IN: 36-96 (Online)
More informationDesign and Development of Three Stages Mixed Sampling Plans for Variable Attribute Variable Quality Characteristics
International Journal of Statistis and Systems ISSN 0973-2675 Volume 12, Number 4 (2017), pp. 763-772 Researh India Publiations http://www.ripubliation.om Design and Development of Three Stages Mixed Sampling
More informationA Queueing Model for Call Blending in Call Centers
A Queueing Model for Call Blending in Call Centers Sandjai Bhulai and Ger Koole Vrije Universiteit Amsterdam Faulty of Sienes De Boelelaan 1081a 1081 HV Amsterdam The Netherlands E-mail: {sbhulai, koole}@s.vu.nl
More informationINTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 2, No 4, 2012
INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume, No 4, 01 Copyright 010 All rights reserved Integrated Publishing servies Researh artile ISSN 0976 4399 Strutural Modelling of Stability
More information7.1 INTRODUCTION. In this era of extreme competition, each subsystem in different
7.1 INTRODUCTION In this era of extreme competition, each subsystem in different echelons of integrated model thrives to improve their operations, reduce costs and increase profitability. Currently, the
More informationWord of Mass: The Relationship between Mass Media and Word-of-Mouth
Word of Mass: The Relationship between Mass Media and Word-of-Mouth Roman Chuhay Preliminary version Marh 6, 015 Abstrat This paper studies the optimal priing and advertising strategies of a firm in the
More informationFiber Optic Cable Transmission Losses with Perturbation Effects
Fiber Opti Cable Transmission Losses with Perturbation Effets Kampanat Namngam 1*, Preeha Yupapin 2 and Pakkinee Chitsakul 1 1 Department of Mathematis and Computer Siene, Faulty of Siene, King Mongkut
More informationNormative and descriptive approaches to multiattribute decision making
De. 009, Volume 8, No. (Serial No.78) China-USA Business Review, ISSN 57-54, USA Normative and desriptive approahes to multiattribute deision making Milan Terek (Department of Statistis, University of
More informationMicroeconomic Theory I Assignment #7 - Answer key
Miroeonomi Theory I Assignment #7 - Answer key. [Menu priing in monopoly] Consider the example on seond-degree prie disrimination (see slides 9-93). To failitate your alulations, assume H = 5, L =, and
More informationOn the Licensing of Innovations under Strategic Delegation
On the Liensing of Innovations under Strategi Delegation Judy Hsu Institute of Finanial Management Nanhua University Taiwan and X. Henry Wang Department of Eonomis University of Missouri USA Abstrat This
More informationJAST 2015 M.U.C. Women s College, Burdwan ISSN a peer reviewed multidisciplinary research journal Vol.-01, Issue- 01
JAST 05 M.U.C. Women s College, Burdwan ISSN 395-353 -a peer reviewed multidisiplinary researh journal Vol.-0, Issue- 0 On Type II Fuzzy Parameterized Soft Sets Pinaki Majumdar Department of Mathematis,
More informationMillennium Relativity Acceleration Composition. The Relativistic Relationship between Acceleration and Uniform Motion
Millennium Relativity Aeleration Composition he Relativisti Relationship between Aeleration and niform Motion Copyright 003 Joseph A. Rybzyk Abstrat he relativisti priniples developed throughout the six
More informationThe Effectiveness of the Linear Hull Effect
The Effetiveness of the Linear Hull Effet S. Murphy Tehnial Report RHUL MA 009 9 6 Otober 009 Department of Mathematis Royal Holloway, University of London Egham, Surrey TW0 0EX, England http://www.rhul.a.uk/mathematis/tehreports
More informationA Spatiotemporal Approach to Passive Sound Source Localization
A Spatiotemporal Approah Passive Sound Soure Loalization Pasi Pertilä, Mikko Parviainen, Teemu Korhonen and Ari Visa Institute of Signal Proessing Tampere University of Tehnology, P.O.Box 553, FIN-330,
More informationA Mathematically Reduced Approach to Predictive Control of Perishable Inventory Systems
A Mathematially Redued Approah to Preditive Control of Perishable Inventory Systems Orzehowska, J. E. Submitted version deposited in CURVE Marh 2016 Original itation: Orzehowska, J. E. (2014) A Mathematially
More informationThe Second Postulate of Euclid and the Hyperbolic Geometry
1 The Seond Postulate of Eulid and the Hyperboli Geometry Yuriy N. Zayko Department of Applied Informatis, Faulty of Publi Administration, Russian Presidential Aademy of National Eonomy and Publi Administration,
More informationThe Hanging Chain. John McCuan. January 19, 2006
The Hanging Chain John MCuan January 19, 2006 1 Introdution We onsider a hain of length L attahed to two points (a, u a and (b, u b in the plane. It is assumed that the hain hangs in the plane under a
More informationUTC. Engineering 329. Proportional Controller Design. Speed System. John Beverly. Green Team. John Beverly Keith Skiles John Barker.
UTC Engineering 329 Proportional Controller Design for Speed System By John Beverly Green Team John Beverly Keith Skiles John Barker 24 Mar 2006 Introdution This experiment is intended test the variable
More informationDetermination of the Aerodynamic Characteristics of Flying Vehicles Using Method Large Eddy Simulation with Software ANSYS
Automation, Control and Intelligent Systems 15; 3(6): 118-13 Published online Deember, 15 (http://www.sienepublishinggroup.om//ais) doi: 1.11648/.ais.1536.14 ISSN: 38-5583 (Print); ISSN: 38-5591 (Online)
More informationThe First Integral Method for Solving a System of Nonlinear Partial Differential Equations
ISSN 179-889 (print), 179-897 (online) International Journal of Nonlinear Siene Vol.5(008) No.,pp.111-119 The First Integral Method for Solving a System of Nonlinear Partial Differential Equations Ahmed
More informationNonreversibility of Multiple Unicast Networks
Nonreversibility of Multiple Uniast Networks Randall Dougherty and Kenneth Zeger September 27, 2005 Abstrat We prove that for any finite direted ayli network, there exists a orresponding multiple uniast
More informationDiscrete Bessel functions and partial difference equations
Disrete Bessel funtions and partial differene equations Antonín Slavík Charles University, Faulty of Mathematis and Physis, Sokolovská 83, 186 75 Praha 8, Czeh Republi E-mail: slavik@karlin.mff.uni.z Abstrat
More informationResearch Article A Partial Backlogging Inventory Model for Deteriorating Items with Fluctuating Selling Price and Purchasing Cost
Advances in Operations Research Volume 2012, Article ID 385371, 15 pages doi:10.1155/2012/385371 Research Article A Partial Backlogging Inventory Model for Deteriorating Items with Fluctuating Selling
More informationNon-Markovian study of the relativistic magnetic-dipole spontaneous emission process of hydrogen-like atoms
NSTTUTE OF PHYSCS PUBLSHNG JOURNAL OF PHYSCS B: ATOMC, MOLECULAR AND OPTCAL PHYSCS J. Phys. B: At. Mol. Opt. Phys. 39 ) 7 85 doi:.88/953-75/39/8/ Non-Markovian study of the relativisti magneti-dipole spontaneous
More informationTwo Points Hybrid Block Method for Solving First Order Fuzzy Differential Equations
Journal of Soft Computing and Appliations 2016 No.1 (2016) 43-53 Available online at www.ispas.om/jsa Volume 2016, Issue 1, Year 2016 Artile ID jsa-00083, 11 Pages doi:10.5899/2016/jsa-00083 Researh Artile
More informationDevelopment of Fuzzy Extreme Value Theory. Populations
Applied Mathematial Sienes, Vol. 6, 0, no. 7, 58 5834 Development of Fuzzy Extreme Value Theory Control Charts Using α -uts for Sewed Populations Rungsarit Intaramo Department of Mathematis, Faulty of
More informationSpace Time Hotelling Model and Its Application to Retail Competition in a Duopoly
Proeedings of the International MultiConferene of Engineers and Computer Sientists 5 Vol II, IMECS 5, Marh 8 -, 5, Hong Kong Spae Time Hotelling Model and Its Appliation Retail Competition in a Duopoly
More information5.1 Composite Functions
SECTION. Composite Funtions 7. Composite Funtions PREPARING FOR THIS SECTION Before getting started, review the following: Find the Value of a Funtion (Setion., pp. 9 ) Domain of a Funtion (Setion., pp.
More informationComplexity of Regularization RBF Networks
Complexity of Regularization RBF Networks Mark A Kon Department of Mathematis and Statistis Boston University Boston, MA 02215 mkon@buedu Leszek Plaskota Institute of Applied Mathematis University of Warsaw
More informationThe simulation analysis of the bridge rectifier continuous operation in AC circuit
Computer Appliations in Eletrial Engineering Vol. 4 6 DOI 8/j.8-448.6. The simulation analysis of the bridge retifier ontinuous operation in AC iruit Mirosław Wiślik, Paweł Strząbała Kiele University of
More informationEffect of Different Types of Promoters on Bed Expansion in a Gas-Solid Fluidized Bed with Varying Distributor Open Areas
Journal of Chemial Engineering of Japan, Vol. 35, No. 7, pp. 681 686, 2002 Short Communiation Effet of Different Types of Promoters on Bed Expansion in a Gas-Solid Fluidized Bed with Varying Distributor
More informationDeveloping Excel Macros for Solving Heat Diffusion Problems
Session 50 Developing Exel Maros for Solving Heat Diffusion Problems N. N. Sarker and M. A. Ketkar Department of Engineering Tehnology Prairie View A&M University Prairie View, TX 77446 Abstrat This paper
More informationMATHEMATICAL AND NUMERICAL BASIS OF BINARY ALLOY SOLIDIFICATION MODELS WITH SUBSTITUTE THERMAL CAPACITY. PART II
Journal of Applied Mathematis and Computational Mehanis 2014, 13(2), 141-147 MATHEMATICA AND NUMERICA BAI OF BINARY AOY OIDIFICATION MODE WITH UBTITUTE THERMA CAPACITY. PART II Ewa Węgrzyn-krzypzak 1,
More informationSupplementary information for: All-optical signal processing using dynamic Brillouin gratings
Supplementary information for: All-optial signal proessing using dynami Brillouin gratings Maro Santagiustina, Sanghoon Chin 2, Niolay Primerov 2, Leonora Ursini, Lu Thévena 2 Department of Information
More informationRESEARCH ON RANDOM FOURIER WAVE-NUMBER SPECTRUM OF FLUCTUATING WIND SPEED
The Seventh Asia-Paifi Conferene on Wind Engineering, November 8-1, 9, Taipei, Taiwan RESEARCH ON RANDOM FORIER WAVE-NMBER SPECTRM OF FLCTATING WIND SPEED Qi Yan 1, Jie Li 1 Ph D. andidate, Department
More informationEXACT TRAVELLING WAVE SOLUTIONS FOR THE GENERALIZED KURAMOTO-SIVASHINSKY EQUATION
Journal of Mathematial Sienes: Advanes and Appliations Volume 3, 05, Pages -3 EXACT TRAVELLING WAVE SOLUTIONS FOR THE GENERALIZED KURAMOTO-SIVASHINSKY EQUATION JIAN YANG, XIAOJUAN LU and SHENGQIANG TANG
More informationHankel Optimal Model Order Reduction 1
Massahusetts Institute of Tehnology Department of Eletrial Engineering and Computer Siene 6.245: MULTIVARIABLE CONTROL SYSTEMS by A. Megretski Hankel Optimal Model Order Redution 1 This leture overs both
More informationCollinear Equilibrium Points in the Relativistic R3BP when the Bigger Primary is a Triaxial Rigid Body Nakone Bello 1,a and Aminu Abubakar Hussain 2,b
International Frontier Siene Letters Submitted: 6-- ISSN: 9-8, Vol., pp -6 Aepted: -- doi:.8/www.sipress.om/ifsl.. Online: --8 SiPress Ltd., Switzerland Collinear Equilibrium Points in the Relativisti
More informationA new method of measuring similarity between two neutrosophic soft sets and its application in pattern recognition problems
Neutrosophi Sets and Systems, Vol. 8, 05 63 A new method of measuring similarity between two neutrosophi soft sets and its appliation in pattern reognition problems Anjan Mukherjee, Sadhan Sarkar, Department
More informationResearch Article Approximation of Analytic Functions by Solutions of Cauchy-Euler Equation
Funtion Spaes Volume 2016, Artile ID 7874061, 5 pages http://d.doi.org/10.1155/2016/7874061 Researh Artile Approimation of Analyti Funtions by Solutions of Cauhy-Euler Equation Soon-Mo Jung Mathematis
More informationA simple expression for radial distribution functions of pure fluids and mixtures
A simple expression for radial distribution funtions of pure fluids and mixtures Enrio Matteoli a) Istituto di Chimia Quantistia ed Energetia Moleolare, CNR, Via Risorgimento, 35, 56126 Pisa, Italy G.
More information755. A survey of Hopf bifurcation analysis in nonlinear railway wheelset dynamics
755. A survey of Hopf bifuration analysis in nonlinear railway wheelset dynamis Hamid M. Sedighi, Kourosh H. Shirazi Department of Mehanial Engineering, Shahid Chamran University, Ahvaz, Iran E-mail: hmsedighi@gmail.om,
More informationHILLE-KNESER TYPE CRITERIA FOR SECOND-ORDER DYNAMIC EQUATIONS ON TIME SCALES
HILLE-KNESER TYPE CRITERIA FOR SECOND-ORDER DYNAMIC EQUATIONS ON TIME SCALES L ERBE, A PETERSON AND S H SAKER Abstrat In this paper, we onsider the pair of seond-order dynami equations rt)x ) ) + pt)x
More informationAppendix A Market-Power Model of Business Groups. Robert C. Feenstra Deng-Shing Huang Gary G. Hamilton Revised, November 2001
Appendix A Market-Power Model of Business Groups Roert C. Feenstra Deng-Shing Huang Gary G. Hamilton Revised, Novemer 200 Journal of Eonomi Behavior and Organization, 5, 2003, 459-485. To solve for the
More informationAn Integer Solution of Fractional Programming Problem
Gen. Math. Notes, Vol. 4, No., June 0, pp. -9 ISSN 9-784; Copyright ICSRS Publiation, 0 www.i-srs.org Available free online at http://www.geman.in An Integer Solution of Frational Programming Problem S.C.
More informationSimple Considerations on the Cosmological Redshift
Apeiron, Vol. 5, No. 3, July 8 35 Simple Considerations on the Cosmologial Redshift José Franiso Garía Juliá C/ Dr. Maro Mereniano, 65, 5. 465 Valenia (Spain) E-mail: jose.garia@dival.es Generally, the
More informationAN EOQ MODEL FOR TWO-WAREHOUSE WITH DETERIORATING ITEMS, PERIODIC TIME DEPENDENT DEMAND AND SHORTAGES
IJMS, Vol., No. 3-4, (July-December 0), pp. 379-39 Serials Publications ISSN: 097-754X AN EOQ MODEL FOR TWO-WAREHOUSE WITH DETERIORATING ITEMS, PERIODIC TIME DEPENDENT DEMAND AND SHORTAGES Karabi Dutta
More informationDynamic Simulation and Composition Control in A 10 L Mixing Tank
roeeding of International Conferene on Chemial and Material Engineering ISBN : 978--97-8-7 SE.4 - Dynami Simulation and Composition Control in A L Mixing Tank Yulius Deddy Hermawan Chemial Engineering
More informationRetailer s Optimal Ordering Policy for Deteriorating Items with Ramp-Type Demand under Stock-Dependent Consumption Rate
Information and Management Sciences Volume 19, Number 2, pp. 245-262, 28 Retailer s Optimal Ordering Policy for Deteriorating Items with Ramp-Type Demand under Stock-Dependent Consumption Rate Kun-Shan
More informationMetric of Universe The Causes of Red Shift.
Metri of Universe The Causes of Red Shift. ELKIN IGOR. ielkin@yande.ru Annotation Poinare and Einstein supposed that it is pratially impossible to determine one-way speed of light, that s why speed of
More informationCONDITIONAL CONFIDENCE INTERVAL FOR THE SCALE PARAMETER OF A WEIBULL DISTRIBUTION. Smail Mahdi
Serdia Math. J. 30 (2004), 55 70 CONDITIONAL CONFIDENCE INTERVAL FOR THE SCALE PARAMETER OF A WEIBULL DISTRIBUTION Smail Mahdi Communiated by N. M. Yanev Abstrat. A two-sided onditional onfidene interval
More informationAN INVENTORY MODEL WITH TIME DEPENDENT DETERIORATION RATE AND EXPONENTIAL DEMAND RATE UNDER TRADE CREDITS
International Journal of athematis an Computer Appliations Researh (IJCAR ISSN 9-6955 Vol., Issue Sep 5-6 JPRC Pvt. Lt., AN INVENORY ODEL WIH IE DEPENDEN DEERIORAION RAE AND EXPONENIAL DEAND RAE UNDER
More informationSufficient Conditions for a Flexible Manufacturing System to be Deadlocked
Paper 0, INT 0 Suffiient Conditions for a Flexile Manufaturing System to e Deadloked Paul E Deering, PhD Department of Engineering Tehnology and Management Ohio University deering@ohioedu Astrat In reent
More informationToulouse School of Economics, M2 Macroeconomics 1 Professor Franck Portier. Exam Solution
Toulouse Shool of Eonomis, 214-215 M2 Maroeonomis 1 Professor Frank Portier Exam Solution This is a 3 hours exam. Class slides and any handwritten material are allowed. You must write legibly. I True,
More informationOn Industry Structure and Firm Conduct in Long Run Equilibrium
www.siedu.a/jms Journal of Management and Strategy Vol., No. ; Deember On Industry Struture and Firm Condut in Long Run Equilibrium Prof. Jean-Paul Chavas Department of Agriultural and Applied Eonomis
More informationmax min z i i=1 x j k s.t. j=1 x j j:i T j
AM 221: Advaned Optimization Spring 2016 Prof. Yaron Singer Leture 22 April 18th 1 Overview In this leture, we will study the pipage rounding tehnique whih is a deterministi rounding proedure that an be
More informationOptimal Control of Air Pollution
Punjab University Journal of Mathematis (ISSN 1016-2526) Vol. 49(1)(2017) pp. 139-148 Optimal Control of Air Pollution Y. O. Aderinto and O. M. Bamigbola Mathematis Department, University of Ilorin, Ilorin,
More information6 Dynamic Optimization in Continuous Time
6 Dynami Optimization in Continuous Time 6.1 Dynami programming in ontinuous time Consider the problem Z T max e rt u (k,, t) dt (1) (t) T s.t. k ú = f (k,, t) (2) k () = k, (3) with k (T )= k (ase 1),
More informationController Design Based on Transient Response Criteria. Chapter 12 1
Controller Design Based on Transient Response Criteria Chapter 12 1 Desirable Controller Features 0. Stable 1. Quik responding 2. Adequate disturbane rejetion 3. Insensitive to model, measurement errors
More information3 Tidal systems modelling: ASMITA model
3 Tidal systems modelling: ASMITA model 3.1 Introdution For many pratial appliations, simulation and predition of oastal behaviour (morphologial development of shorefae, beahes and dunes) at a ertain level
More informationVolume 29, Issue 3. On the definition of nonessentiality. Udo Ebert University of Oldenburg
Volume 9, Issue 3 On the definition of nonessentiality Udo Ebert University of Oldenburg Abstrat Nonessentiality of a good is often used in welfare eonomis, ost-benefit analysis and applied work. Various
More informationA NONLILEAR CONTROLLER FOR SHIP AUTOPILOTS
Vietnam Journal of Mehanis, VAST, Vol. 4, No. (), pp. A NONLILEAR CONTROLLER FOR SHIP AUTOPILOTS Le Thanh Tung Hanoi University of Siene and Tehnology, Vietnam Abstrat. Conventional ship autopilots are
More informationArray Design for Superresolution Direction-Finding Algorithms
Array Design for Superresolution Diretion-Finding Algorithms Naushad Hussein Dowlut BEng, ACGI, AMIEE Athanassios Manikas PhD, DIC, AMIEE, MIEEE Department of Eletrial Eletroni Engineering Imperial College
More informationCOMBINED PROBE FOR MACH NUMBER, TEMPERATURE AND INCIDENCE INDICATION
4 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES COMBINED PROBE FOR MACH NUMBER, TEMPERATURE AND INCIDENCE INDICATION Jiri Nozika*, Josef Adame*, Daniel Hanus** *Department of Fluid Dynamis and
More informationSubject: Introduction to Component Matching and Off-Design Operation % % ( (1) R T % (
16.50 Leture 0 Subjet: Introdution to Component Mathing and Off-Design Operation At this point it is well to reflet on whih of the many parameters we have introdued (like M, τ, τ t, ϑ t, f, et.) are free
More informationBattery Sizing for Grid Connected PV Systems with Fixed Minimum Charging/Discharging Time
Battery Sizing for Grid Conneted PV Systems with Fixed Minimum Charging/Disharging Time Yu Ru, Jan Kleissl, and Sonia Martinez Abstrat In this paper, we study a battery sizing problem for grid-onneted
More informationOptimal control of solar energy systems
Optimal ontrol of solar energy systems Viorel Badesu Candida Oanea Institute Polytehni University of Buharest Contents. Optimal operation - systems with water storage tanks 2. Sizing solar olletors 3.
More informationThe gravitational phenomena without the curved spacetime
The gravitational phenomena without the urved spaetime Mirosław J. Kubiak Abstrat: In this paper was presented a desription of the gravitational phenomena in the new medium, different than the urved spaetime,
More informationDynamic Programming and Multi Objective Linear Programming approaches
0 NSP Vol. () (0), 9 Dynami Programming and Multi Objetive Linear Programming approahes P. K. De and Amita Bhinher Department o Mathematis, National Institute o Tehnology SILCHAR - 788 00 (Assam) India
More informationQ c, Q f denote the outputs of good C and F, respectively. The resource constraints are: T since the technology implies: Tc = Qc
Fall 2008 Eon 455 Ansers - Problem Set 3 Harvey Lapan 1. Consider a simpliied version o the Heksher-Ohlin model ith the olloing tehnology: To produe loth: three units o labor and one unit o land are required
More informationPhysical Laws, Absolutes, Relative Absolutes and Relativistic Time Phenomena
Page 1 of 10 Physial Laws, Absolutes, Relative Absolutes and Relativisti Time Phenomena Antonio Ruggeri modexp@iafria.om Sine in the field of knowledge we deal with absolutes, there are absolute laws that
More informationAverage Rate Speed Scaling
Average Rate Speed Saling Nikhil Bansal David P. Bunde Ho-Leung Chan Kirk Pruhs May 2, 2008 Abstrat Speed saling is a power management tehnique that involves dynamially hanging the speed of a proessor.
More informationFinite-time stabilization of chaotic gyros based on a homogeneous supertwisting-like algorithm
OP Conferene Series: Materials Siene Engineering PAPER OPEN ACCESS Finite-time stabilization of haoti gyros based on a homogeneous supertwisting-like algorithm To ite this artile: Pitha Khamsuwan et al
More informationFuzzy inner product space and its properties 1
International Journal of Fuzzy Mathematis and Systems IJFMS). ISSN 48-9940 Volume 5, Number 1 015), pp. 57-69 Researh India Publiations http://www.ripubliation.om Fuzzy inner produt spae and its properties
More informationA NETWORK SIMPLEX ALGORITHM FOR THE MINIMUM COST-BENEFIT NETWORK FLOW PROBLEM
NETWORK SIMPLEX LGORITHM FOR THE MINIMUM COST-BENEFIT NETWORK FLOW PROBLEM Cen Çalışan, Utah Valley University, 800 W. University Parway, Orem, UT 84058, 801-863-6487, en.alisan@uvu.edu BSTRCT The minimum
More informationThe universal model of error of active power measuring channel
7 th Symposium EKO TC 4 3 rd Symposium EKO TC 9 and 5 th WADC Workshop nstrumentation for the CT Era Sept. 8-2 Kosie Slovakia The universal model of error of ative power measuring hannel Boris Stogny Evgeny
More informationFINITE WORD LENGTH EFFECTS IN DSP
FINITE WORD LENGTH EFFECTS IN DSP PREPARED BY GUIDED BY Snehal Gor Dr. Srianth T. ABSTRACT We now that omputers store numbers not with infinite preision but rather in some approximation that an be paed
More informationQCLAS Sensor for Purity Monitoring in Medical Gas Supply Lines
DOI.56/sensoren6/P3. QLAS Sensor for Purity Monitoring in Medial Gas Supply Lines Henrik Zimmermann, Mathias Wiese, Alessandro Ragnoni neoplas ontrol GmbH, Walther-Rathenau-Str. 49a, 7489 Greifswald, Germany
More informationUPPER-TRUNCATED POWER LAW DISTRIBUTIONS
Fratals, Vol. 9, No. (00) 09 World Sientifi Publishing Company UPPER-TRUNCATED POWER LAW DISTRIBUTIONS STEPHEN M. BURROUGHS and SARAH F. TEBBENS College of Marine Siene, University of South Florida, St.
More informationThe Impact of Information on the Performance of an M/M/1 Queueing System
The Impat of Information on the Performane of an M/M/1 Queueing System by Mojgan Nasiri A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Master
More informationElectromagnetic radiation of the travelling spin wave propagating in an antiferromagnetic plate. Exact solution.
arxiv:physis/99536v1 [physis.lass-ph] 15 May 1999 Eletromagneti radiation of the travelling spin wave propagating in an antiferromagneti plate. Exat solution. A.A.Zhmudsky November 19, 16 Abstrat The exat
More informationPossibility of Refuse Derived Fuel Fire Inception by Spontaneous Ignition
Possibility of Refuse Derived Fuel Fire Ineption by Spontaneous Ignition Lijing Gao 1, Takashi Tsuruda 1, Takeshi Suzuki 1, Yoshio Ogawa 1, Chihong Liao 1 and Yuko Saso 1 1 National Researh Institute of
More informationSocially-Optimal Locations of Duopoly Firms with Non-Uniform Consumer Densities
Theoretial Eonomis Letters, 04, 4, 43-445 Published Online June 04 in ires. http://www.sirp.org/journal/tel http://d.doi.org/0.436/tel.04.46055 oially-optimal Loations of Duopoly Firms with Non-Uniform
More informationControl Theory association of mathematics and engineering
Control Theory assoiation of mathematis and engineering Wojieh Mitkowski Krzysztof Oprzedkiewiz Department of Automatis AGH Univ. of Siene & Tehnology, Craow, Poland, Abstrat In this paper a methodology
More informationON A COURNOT DUOPOLY GAME WITH DIFFERENTIATED GOODS, HETEROGENEOUS EXPECTATIONS AND A COST FUNCTION INCLUDING EMISSION COSTS
Sientifi Bulletin Eonomi Sienes, Volume 6/ Issue ON A COURNOT DUOPOLY GAME WITH DIFFERENTIATED GOODS, HETEROGENEOUS EXPECTATIONS AND A COST FUNCTION INCLUDING EMISSION COSTS Georges SARAFOPOULOS, Kosmas
More informationA Recursive Approach to the Kauffman Bracket
Applied Mathematis, 204, 5, 2746-2755 Published Online Otober 204 in SiRes http://wwwsirporg/journal/am http://ddoiorg/04236/am20457262 A Reursive Approah to the Kauffman Braet Abdul Rauf Nizami, Mobeen
More informationA model for measurement of the states in a coupled-dot qubit
A model for measurement of the states in a oupled-dot qubit H B Sun and H M Wiseman Centre for Quantum Computer Tehnology Centre for Quantum Dynamis Griffith University Brisbane 4 QLD Australia E-mail:
More informationEffect of Rotation, Magnetic Field and Initial Stresses on Propagation of Plane Waves in Transversely Isotropic Dissipative Half Space
Applied Mathematis 4 7- http://dx.doi.org/.436/am..48a5 Published Online August (http://www.sirp.org/journal/am) Effet of otation Magneti Field and Initial Stresses on Propagation of Plane Waves in Transversely
More informationInternet Appendix for Proxy Advisory Firms: The Economics of Selling Information to Voters
Internet Appendix for Proxy Advisory Firms: The Eonomis of Selling Information to Voters Andrey Malenko and Nadya Malenko The first part of the Internet Appendix presents the supplementary analysis for
More informationAn Inventory Model for Weibull Time-Dependence. Demand Rate with Completely Backlogged. Shortages
Inernaional Mahemaial Forum, 5, 00, no. 5, 675-687 An Invenory Model for Weibull Time-Dependene Demand Rae wih Compleely Baklogged Shorages C. K. Tripahy and U. Mishra Deparmen of Saisis, Sambalpur Universiy
More informationCORC Report TR : Short Version Optimal Procurement Mechanisms for Divisible Goods with Capacitated Suppliers
CORC Report TR-2006-01: Short Version Optimal Prourement Mehanisms for Divisible Goods with Capaitated Suppliers Garud Iyengar Anuj Kumar First version: June 30, 2006 This version: August 31, 2007 Abstrat
More informationLOGISTIC REGRESSION IN DEPRESSION CLASSIFICATION
LOGISIC REGRESSIO I DEPRESSIO CLASSIFICAIO J. Kual,. V. ran, M. Bareš KSE, FJFI, CVU v Praze PCP, CS, 3LF UK v Praze Abstrat Well nown logisti regression and the other binary response models an be used
More informationA Functional Representation of Fuzzy Preferences
Theoretial Eonomis Letters, 017, 7, 13- http://wwwsirporg/journal/tel ISSN Online: 16-086 ISSN Print: 16-078 A Funtional Representation of Fuzzy Preferenes Susheng Wang Department of Eonomis, Hong Kong
More informationAn Inventory Model for Gompertz Distribution Deterioration Rate with Ramp Type Demand Rate and Shortages
International Journal of Statistics and Systems ISSN 0973-675 Volume, Number (07), pp. 363-373 Research India Publications http://www.ripublication.com An Inventory Model for Gompertz Distribution Deterioration
More informationStudy On Watter Pollution Control Based On Fuzzy Cognitive Maps (FCM)
Global Journal of Pure and Applied Mathematis. ISSN 0973-1768 Volume 13, Number 9 (2017), pp. 5299-5305 Researh India Publiations http://www.ripubliation.om Study On Watter Pollution Control Based On Fuzzy
More information