Activity Scheduling for CostTime Investment Optimization in Project Management


 Gabriella Ward
 3 years ago
 Views:
Transcription
1 PROJECT MANAGEMENT 4 th Internatonal Conference on Industral Engneerng and Industral Management XIV Congreso de Ingenería de Organzacón Donosta San Sebastán, September 8 th 10 th 010 Actvty Schedulng for CostTme Investment Optmzaton n Project Management Dego Fernando Manotas Duque 1, Leonardo Rvera Cadavd 1 Escuela de Ingenería Industral y Estadístca. Facultad de Ingenería. Unversdad del Valle. Calle Cal, Colomba. Department of Industral Engneerng, Unversdad ICESI, Cal, Colomba. Keywords: CostTme Profle, Project Management, Actvty Schedulng, TmeValue of Money Abstract The CostTme Profle s a tool that presents the combned mpact of dsbursements made durng the executon of a project, and ther tmng. The CostTme Profle chart presents the accumulated cost at any gven tme, and the area under the curve s the CostTme Investment. Ths CostTme Investment has a quantfable mpact on the workng captal the company uses, and t s also useful for the determnaton of the Drect Cost of a product. Ths paper ams to develop a model to create the schedule of actvtes that mnmzes the CostTme Investment for a project. 1. Introducton It s unversally recognzed that money has value, and t also has value related to ts poston n tme. If somebody owes money, they would prefer to pay ther loan later rather than earler. If some revenue s expected, t would be much better to receve t now nstead of next week. Ths prncple s more than applcable n ths era of JustInTme, when actvtes are beng performed when needed and not before. Ths paper brefly presents the CostTme Profle (CTP), whch s a smple, graphcal tool to consder both dmensons of cost (dollar amount and tmng), and the resultng CostTme Investment (CTI  the area under the CTP curve, whch represents the combnaton of how much money and for how much tme t has been nvested on a project), to fnally propose a MxedInteger Program to schedule the actvtes of a project n such a way that the resultng CTI s mnmal. In the followng subsectons we wll present how to get there, startng from the concept and constructon of a CostTme Profle and endng wth the MIP model to create an optmal schedule that mnmzes the CTI.. Methodology.1. What s a CostTme Profle (CTP)? A CostTme Profle s a graph that depcts the Accumulated Costs that have been expended durng the executon of a project at every tme unt durng the process. Ths way of presentng the nformaton follows the use of resources through tme, from the moment the executon begns untl the company recovers those nvested resources through the sale of the product. The area under the CTP s called the CostTme Investment (CTI), because t presents how 1453
2 much money has been ted up n the manufacturng process and for how long before beng recovered through sales. The reader wll recognze the term Investment because the CTI shares the two common components of any fnancal nvestment: Money and Tme. Fgure 1 gves a smple llustraton of a CostTme Profle. 00 A ccum ulated C ost (dollars) W at 3 W at Actvty C 100 Actvty A Wat 1 Actvty B CostTme Investment T o tal C o st M atera ls Fgure 1. Example of a CostTme Profle tm e (hours).. How do you buld a CTP? There are several mportant parts on a CTP. Actvtes: These are the parts that actvely add cost. They are represented by postveslope lnes. Materals: Some actvtes requre materals to be performed. The assumpton s that the materals arrve rght at the begnnng of the actvty and all at once, therefore they are represented by a vertcal lne (nstantaneous accumulaton of cost). Wats: These are moments when nothng that adds cost s actvely happenng. Wats are of nterest manly for manufacturng actvtes, because n projects there s always some cost happenng (overhead?), even f you are not actvely operatng on the project. Snce they do not add cost, they are represented by flat lnes n the CTP curve (the accumulated cost remans constant durng the wat). Total Cost: Ths s the heght of the curve at the end of the project. It represents the total accumulated cost of the project. CostTme Investment (CTI): Ths s the area under the CTP curve, and t represents how much money and for how long has t been nvested n the project. Ths s a measure of the utlzaton of workng captal, and snce t s captal you are usng, ths captal wll undoubtedly have a cost that wll be whatever rate the company has to pay for ts workng captal. Workng Captal Cost (WCC): Ths s the cost the company has to pay for the use of captal. It can be expressed as n Equaton 1. WCC = CTI * Cost of Captal Rate (1) 1454
3 To buld a CTP, we need to know several thngs. Frst, we need to know when s each element of the CTP happenng (actvtes, wats and materals releases). We also need to know how much does each of these elements cost. Puttng the two prevous ponts together we can determne how much money s beng spent as cost at every tme unt n the process. Fnally, we tally the costs and buld the CTP wth the accumulated cost at every tme unt, and present ths nformaton n graphcal form. The area under the curve (obtaned addng the accumulated cost at each tme unt for all the tme unts) represents the CostTme Investment. In the followng subsectons, a bref dscusson on how to complete these steps for the constructon of the CTP wll be presented..3. Applcablty of CTP to Project Management CTP does not consder ndrect costs because t s truly hard to assgn these costs drectly to actvtes or ndvdual unts of a product. However, n project management t s reasonable to assume that all resources, people and equpment that take part n the project are drectly and completely assgnable to the project. Therefore, CTP s especally applcable to projects and the full spectrum of costs s ncluded n them..4. What s the contrbuton of each actvty to the CostTme Investment? [3] In order to create an optmal schedule of actvtes, t s necessary to characterze the contrbuton to the area under the CTP curve that each actvty makes. If we consder that materals are always released at the begnnng of an actvty, we can see that Fgure presents the typcal areas that we would see as a result of a gven actvty. For Fgure we have that: Y = End date of the project X = Tme when actvty fnshes T = Duraton of actvty MAT =Materals requred to perform actvty CR = Cost rate of actvty (cost per tme unt) Accumulated Cost Actvty Area Area 3 (T * CR ) Materals Area 1 MAT T tme X  T X Fgure : Areas that an actvty contrbutes to the CTI. Y Area 1 occurs when we ncorporate the expendture n materals, because they reman spent untl the end of the project (Y). Area 1 can be calculated wth Equaton. 1455
4 Area 1 = [ Y (X T) ] * MAT () Area occurs when the actvty s actvely happenng. See Equaton 3. Area CR * T * T CR * T (3) Area 3 occurs from the end of the actvty untl the end of the project. Ths s the cost added by the actvty projected untl the end date of the project. Area 3 can be found usng Equaton 4. Area 3 = () * (Y X) (4) Addng Equatons, 3 and 4 and organzng some terms we obtan the total contrbuton that each actvty makes to the CostTme Investment. See Equaton 5. Area Contrbuton Y X MAT T * MAT CR * T (5).5. Tradtonal LP model for Project Management The tradtonal LP model for project management (found n Operatons Research or Management Scence textbooks) consders precedence relatonshps between actvtes, and ts objectve functon s to mnmze the total completon tme of a project. Fgure 3 presents the text of such a model. These models have two problems for ts use wth CostTme profles: Ther objectve functon mnmzes completon tme of the project, not total CostTme Investment They consder precedence constrants, but they do not recognze resource dependences that happen when we have lmted resources that are shared by dfferent actvtes. These shared resources sometmes force that two actvtes that could be performed smultaneously wll have to be scheduled one after the other. In subsectons.6 and.7 the solutons to these two problems wll be presented. 1456
5 MODEL 1 Set: Actvtes {A, B, C, } (n actvtes). Indces:, j on Actvtes. Parameters: T Executon tme for Actvty PD,j 1 f Actvty j s an mmedate predecessor of Actvty 0 otherwse Varables: X Completon tme for Actvty. Y Completon tme for the whole project Objectve Functon: Mnmze the completon tme for the project Mn Z = Y Constrants: Completon tme for the project must be greater than or equal to the completon tme for any actvty Y X ; for all. Any actvty must only begn after ts mmedate predecessors have been completed. X X j + PD,j * T j ; for all j (Ths constrant s only enforced when the PD,j s 1, that s, when there exsts a relatonshp of precedence between and j). Fgure 3: Tradtonal Project Management LP model..6. Changng the Objectve Functon If the objectve of the model s the mnmzaton of the CostTme Investment, then the objectve functon must be to mnmze the sum of the CTI contrbutons of all the actvtes. That s, the objectve functon should be based n Equaton 5. Fgure 4 presents ths updated model. 1457
6 MODEL Set: Actvtes {A, B, C, } (n actvtes). Indces:, j on Actvtes. Parameters: T Executon tme for Actvty PD,j CR MAT T 1 f Actvty j s an mmedate predecessor of Actvty 0 otherwse Cost Rate of Actvty Materals released at the begnnng of Actvty Duraton of Actvty Varables: X Completon tme for Actvty. Y Completon tme for the whole project Objectve Functon: Mnmze the sum of contrbutons to the total area by the actvtes Mn Z Y X MAT T * MAT Constrants: Y X ; for all. X X j + PD,j * T j ; for all j Fgure 4: Project Management Model wth CTI mnmzaton as the objectve functon..7. Shared resources constrants [3] Projects have precedence constrants between actvtes. You should have the structure of a buldng before you can put up ts walls. In ths case, t s clear whch actvty needs to be completed before the dependent one starts. However, there are cases where actvtes do not have precedence relatonshps (you can landscape the front yard and the back yard n any sequence), but they cannot be performed smultaneously because they use the same resources (we only have one lawn mower, for example). When these resources are shared, t s not mmedately evdent whch actvty should be completed before the other. Therefore, a couple of new constrants and bnary varables wll be ntroduced to consder ths type of stuaton. Constructon of a logcal statement usng bnary varables: In the case of shared resources we need to tell the MIP that the actvtes that share a resource (let s call them a and b) wll happen one before the other, but NEVER at the same tme. So, t must be true that: (XOR s the exclusve OR, meanng that one proposton or the other should happen, but NEVER both). Ths XOR can be acheved usng a bnary varable called y1 j, and two other new elements appear: SR j : Ths s a parameter. Its value s 1 f actvtes and j share a resource and 0 otherwse. M: M s a BIG number that wll be used to enforce or relax a constrant accordng to the values of the y1 j (6) 1458
7 So, we wll present the two new constrants and then offer some comments about the way they would work. X T + (X j * SR,j ) (M * y1,j * SR,j ) (If j needs to happen before ) (7.1) Xj Tj + (X * SRj,) (M * y1j, * SRj,) (If needs to happen before j) (7.) y1,j + y1j, = 1 ; for all j (y1j and y1j are bnary varables) (8) Now, for the sake of argument, let s examne what happens n dfferent stuatons wth Equatons 7.1 and 7.. Actvtes and j do not share resources: When ths s the case, the parameters SR j and SR j must both be zero, therefore Equatons 7.1 and 7. transform n the followng way X T and Xj Tj These two constrants do not add any trouble to the MIP, because t s naturally obvous that an actvty s fnshng tme should be greater than or equal to ts executon tme. (7.1) (7.) Actvtes and j share a resource: When ths s the case, the parameters SR j and SR j must both be one. In ths case we also need to consder the values of y1 j and y1 j, and we know from equaton 8 that one of them must be a one and the other one zero. Assumng that y1 j = 1, and y1 j = 0, then Equatons 7.1 and 7. transform n the followng way X T + Xj (M * y1,j), that for all practcal purposes wll be X M (7.1) Xj Tj + X (7.) The real effect of usng y1 j and y1 j wll be that the constrant n Eq. 7.1 wll be relaxed (not enforced), and equaton 7. wll be held, therefore the net result wll be that actvty j wll happen after actvty. Had the y1 j and y1 j been the other way around (y1 j = 0, and y1 j = 1), actvty would happen after actvty j. Integratng all these nto the model, we obtan Model 3, presented n Fgure
8 MODEL 3 Set: Actvtes {A, B, C, } (n actvtes). Indces:, j on Actvtes. Parameters: T Executon tme for Actvty PD,j 1 f Actvty j s an mmedate predecessor of Actvty 0 otherwse SR,j 1 f Actvtes and j share a Resource or an Operator. SR,j = SR j, for all and j. Also, SR, = 0. CR Cost Rate of Actvty MAT Materals released at the begnnng of Actvty T Duraton of Actvty Varables: X Completon tme for Actvty. Y Completon tme for the whole project y1,j Bnary Varables to assst n the logcal etheror constructon for Resource and Operator sharng Objectve Functon: Mnmze the sum of contrbutons to the total area by the actvtes Mn Z Y X MAT T * MAT Constrants: Y X ; for all. X X j + PD,j * T j ; for all j y1,j + y1 j, = 1 ; for all j X T + (X j * SR,j ) (M * y1,j * SR,j ) ; for all j Fgure 5: Model wth CTI mnmzaton as the objectve functon and shared resources 3. Conclusons and Future Research The model presented n the prevous secton could be of great use for project orented organzatons, especally n those cases when the company works wth ts own resources before percevng revenue (a real estate development company that bulds governmentsubsdzed housng, for example). In these cases the mnmzaton of the completon s not as mportant an objectve as t would be the mnmzaton of the CostTme Investment (and the CostTme Profle would penalze lengthy projects anyway). It s nterestng to explore dfferent objectves and constrants that mght be ncluded n Project Management models, snce the specfc characterstcs of companes and ther projects are so vared that specfc models are always applcable to some companes. Also, models wth varable actvty tmes (a la PERT) wll be studed applyng Monte Carlo smulaton to explore the mpact of specfc actvtes on the resultng CTI and the dfferences n crtcal paths that could result. 4. References Fooks, J. H. (1993). Profles for Performance: Total Qualty Methods for Reducng Cycle Tme. AddsonWesley, Readng, MA. 1460
9 Manotas, D, Rvera, L, Chen, F.F., 007, Workng Captal Poston A New tool to Montor Economc Status n Project Management, XIII Internatonal Conference on Industral Engneerng and Operatons Management, October, Foz do Iguazu, Brasl. Rvera, L., Chen, F.F., 006, CostTme Proflng: Puttng monetary measures onto Value Stream Maps, Proc. of the Industral Engneerng Research Conference, May, Orlando, Florda. Rvera, L., 006, InterEnterprse CostTme Proflng, Ph.D. dssertaton, Vrgna Polytechnc Insttute and State Unversty. Rvera, L, Chen, F.F., 007, Measurng the mpact of Lean tools on the CostTme Investment of a product usng CostTme Profles, Journal of Robotcs and Computer Integrated Manufacturng, 3,
Abstract # 0150399 Working Capital Exposure: A Methodology to Control Economic Performance in Production Environment Projects
Abstract # 0150399 Workng Captal Exposure: A Methodology to Control Economc Performance n Producton Envronment Projects Dego F. Manotas. School of Industral Engneerng and Statstcs, Unversdad del Valle.
More informationProject Networks With MixedTime Constraints
Project Networs Wth MxedTme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa
More information1. Math 210 Finite Mathematics
1. ath 210 Fnte athematcs Chapter 5.2 and 5.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING
ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING Matthew J. Lberatore, Department of Management and Operatons, Vllanova Unversty, Vllanova, PA 19085, 6105194390,
More informationA DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATIONBASED OPTIMIZATION. Michael E. Kuhl Radhamés A. TolentinoPeña
Proceedngs of the 2008 Wnter Smulaton Conference S. J. Mason, R. R. Hll, L. Mönch, O. Rose, T. Jefferson, J. W. Fowler eds. A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATIONBASED OPTIMIZATION
More informationThursday, December 10, 2009 Noon  1:50 pm Faraday 143
1. ath 210 Fnte athematcs Chapter 5.2 and 4.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationSection 5.3 Annuities, Future Value, and Sinking Funds
Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme
More informationTime Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6  The Time Value of Money. The Time Value of Money
Ch. 6  The Tme Value of Money Tme Value of Money The Interest Rate Smple Interest Compound Interest Amortzng a Loan FIN21 Ahmed Y, Dasht TIME VALUE OF MONEY OR DISCOUNTED CASH FLOW ANALYSIS Very Important
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More informationAn MILP model for planning of batch plants operating in a campaignmode
An MILP model for plannng of batch plants operatng n a campagnmode Yanna Fumero Insttuto de Desarrollo y Dseño CONICET UTN yfumero@santafeconcet.gov.ar Gabrela Corsano Insttuto de Desarrollo y Dseño
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationA Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy Scurve Regression
Novel Methodology of Workng Captal Management for Large Publc Constructons by Usng Fuzzy Scurve Regresson ChengWu Chen, Morrs H. L. Wang and TngYa Hseh Department of Cvl Engneerng, Natonal Central Unversty,
More informationSupport Vector Machines
Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.
More informationEfficient Project Portfolio as a tool for Enterprise Risk Management
Effcent Proect Portfolo as a tool for Enterprse Rsk Management Valentn O. Nkonov Ural State Techncal Unversty Growth Traectory Consultng Company January 5, 27 Effcent Proect Portfolo as a tool for Enterprse
More informationSimple Interest Loans (Section 5.1) :
Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationSciences Shenyang, Shenyang, China.
Advanced Materals Research Vols. 314316 (2011) pp 13151320 (2011) Trans Tech Publcatons, Swtzerland do:10.4028/www.scentfc.net/amr.314316.1315 Solvng the TwoObectve Shop Schedulng Problem n MTO Manufacturng
More informationChapter 4 ECONOMIC DISPATCH AND UNIT COMMITMENT
Chapter 4 ECOOMIC DISATCH AD UIT COMMITMET ITRODUCTIO A power system has several power plants. Each power plant has several generatng unts. At any pont of tme, the total load n the system s met by the
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More informationSUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW.
SUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW. Lucía Isabel García Cebrán Departamento de Economía y Dreccón de Empresas Unversdad de Zaragoza Gran Vía, 2 50.005 Zaragoza (Span) Phone: 976761000
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationLecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.
Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More information1 Approximation Algorithms
CME 305: Dscrete Mathematcs and Algorthms 1 Approxmaton Algorthms In lght of the apparent ntractablty of the problems we beleve not to le n P, t makes sense to pursue deas other than complete solutons
More informationThe Development of Web Log Mining Based on ImproveKMeans Clustering Analysis
The Development of Web Log Mnng Based on ImproveKMeans Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More informationTime Value of Money Module
Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the
More information1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)
6.3 /  Communcaton Networks II (Görg) SS20  www.comnets.unbremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationFeature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College
Feature selecton for ntruson detecton Slobodan Petrovć NISlab, Gjøvk Unversty College Contents The feature selecton problem Intruson detecton Traffc features relevant for IDS The CFS measure The mrmr measure
More informationCommunication Networks II Contents
8 / 1  Communcaton Networs II (Görg)  www.comnets.unbremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP
More informationIntrayear Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error
Intrayear Cash Flow Patterns: A Smple Soluton for an Unnecessary Apprasal Error By C. Donald Wggns (Professor of Accountng and Fnance, the Unversty of North Florda), B. Perry Woodsde (Assocate Professor
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annutymmedate, and ts present value Study annutydue, and
More informationFINANCIAL MATHEMATICS
3 LESSON FINANCIAL MATHEMATICS Annutes What s an annuty? The term annuty s used n fnancal mathematcs to refer to any termnatng sequence of regular fxed payments over a specfed perod of tme. Loans are usually
More informationPSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 12
14 The Chsquared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationKiel Institute for World Economics Duesternbrooker Weg 120 24105 Kiel (Germany) Kiel Working Paper No. 1120
Kel Insttute for World Economcs Duesternbrooker Weg 45 Kel (Germany) Kel Workng Paper No. Path Dependences n enture Captal Markets by Andrea Schertler July The responsblty for the contents of the workng
More informationGENETIC ALGORITHM FOR PROJECT SCHEDULING AND RESOURCE ALLOCATION UNDER UNCERTAINTY
Int. J. Mech. Eng. & Rob. Res. 03 Fady Safwat et al., 03 Research Paper ISS 78 049 www.jmerr.com Vol., o. 3, July 03 03 IJMERR. All Rghts Reserved GEETIC ALGORITHM FOR PROJECT SCHEDULIG AD RESOURCE ALLOCATIO
More informationA Simple Economic Model about the Teamwork Pedagogy
Appled Mathematcal Scences, Vol. 6, 01, no. 1, 130 A Smple Economc Model about the Teamwork Pedagog Gregor L. Lght Department of Management, Provdence College Provdence, Rhode Island 0918, USA glght@provdence.edu
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes causeandeffect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationAN APPOINTMENT ORDER OUTPATIENT SCHEDULING SYSTEM THAT IMPROVES OUTPATIENT EXPERIENCE
AN APPOINTMENT ORDER OUTPATIENT SCHEDULING SYSTEM THAT IMPROVES OUTPATIENT EXPERIENCE YuL Huang Industral Engneerng Department New Mexco State Unversty Las Cruces, New Mexco 88003, U.S.A. Abstract Patent
More informationFINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals
FINANCIAL MATHEMATICS A Practcal Gude for Actuares and other Busness Professonals Second Edton CHRIS RUCKMAN, FSA, MAAA JOE FRANCIS, FSA, MAAA, CFA Study Notes Prepared by Kevn Shand, FSA, FCIA Assstant
More informationAn Overview of Financial Mathematics
An Overvew of Fnancal Mathematcs Wllam Benedct McCartney July 2012 Abstract Ths document s meant to be a quck ntroducton to nterest theory. It s wrtten specfcally for actuaral students preparng to take
More informationLinear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits
Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.
More informationPreventive Maintenance and Replacement Scheduling: Models and Algorithms
Preventve Mantenance and Replacement Schedulng: Models and Algorthms By Kamran S. Moghaddam B.S. Unversty of Tehran 200 M.S. Tehran Polytechnc 2003 A Dssertaton Proposal Submtted to the Faculty of the
More informationRisk Model of LongTerm Production Scheduling in Open Pit Gold Mining
Rsk Model of LongTerm Producton Schedulng n Open Pt Gold Mnng R Halatchev 1 and P Lever 2 ABSTRACT Open pt gold mnng s an mportant sector of the Australan mnng ndustry. It uses large amounts of nvestments,
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More informationForecasting the Demand of Emergency Supplies: Based on the CBR Theory and BP Neural Network
700 Proceedngs of the 8th Internatonal Conference on Innovaton & Management Forecastng the Demand of Emergency Supples: Based on the CBR Theory and BP Neural Network Fu Deqang, Lu Yun, L Changbng School
More informationSCHEDULING OF CONSTRUCTION PROJECTS BY MEANS OF EVOLUTIONARY ALGORITHMS
SCHEDULING OF CONSTRUCTION PROJECTS BY MEANS OF EVOLUTIONARY ALGORITHMS Magdalena Rogalska 1, Wocech Bożeko 2,Zdzsław Heduck 3, 1 Lubln Unversty of Technology, 2 Lubln, Nadbystrzycka 4., Poland. Emal:rogalska@akropols.pol.lubln.pl
More informationMethodology to Determine Relationships between Performance Factors in Hadoop Cloud Computing Applications
Methodology to Determne Relatonshps between Performance Factors n Hadoop Cloud Computng Applcatons Lus Eduardo Bautsta Vllalpando 1,2, Alan Aprl 1 and Alan Abran 1 1 Department of Software Engneerng and
More informationSoftware project management with GAs
Informaton Scences 177 (27) 238 241 www.elsever.com/locate/ns Software project management wth GAs Enrque Alba *, J. Francsco Chcano Unversty of Málaga, Grupo GISUM, Departamento de Lenguajes y Cencas de
More informationPeriod and Deadline Selection for Schedulability in RealTime Systems
Perod and Deadlne Selecton for Schedulablty n RealTme Systems Thdapat Chantem, Xaofeng Wang, M.D. Lemmon, and X. Sharon Hu Department of Computer Scence and Engneerng, Department of Electrcal Engneerng
More informationOverview of monitoring and evaluation
540 Toolkt to Combat Traffckng n Persons Tool 10.1 Overvew of montorng and evaluaton Overvew Ths tool brefly descrbes both montorng and evaluaton, and the dstncton between the two. What s montorng? Montorng
More informationThe Greedy Method. Introduction. 0/1 Knapsack Problem
The Greedy Method Introducton We have completed data structures. We now are gong to look at algorthm desgn methods. Often we are lookng at optmzaton problems whose performance s exponental. For an optmzaton
More informationMultiplePeriod Attribution: Residuals and Compounding
MultplePerod Attrbuton: Resduals and Compoundng Our revewer gave these authors full marks for dealng wth an ssue that performance measurers and vendors often regard as propretary nformaton. In 1994, Dens
More informationFinancial Mathemetics
Fnancal Mathemetcs 15 Mathematcs Grade 12 Teacher Gude Fnancal Maths Seres Overvew In ths seres we am to show how Mathematcs can be used to support personal fnancal decsons. In ths seres we jon Tebogo,
More information10.2 Future Value and Present Value of an Ordinary Simple Annuity
348 Chapter 10 Annutes 10.2 Future Value and Present Value of an Ordnary Smple Annuty In compound nterest, 'n' s the number of compoundng perods durng the term. In an ordnary smple annuty, payments are
More informationReturn decomposing of absoluteperformance multiasset class portfolios. Working Paper  Nummer: 16
Return decomposng of absoluteperformance multasset class portfolos Workng Paper  Nummer: 16 2007 by Dr. Stefan J. Illmer und Wolfgang Marty; n: Fnancal Markets and Portfolo Management; March 2007; Volume
More informationMETHODOLOGY TO DETERMINE RELATIONSHIPS BETWEEN PERFORMANCE FACTORS IN HADOOP CLOUD COMPUTING APPLICATIONS
METHODOLOGY TO DETERMINE RELATIONSHIPS BETWEEN PERFORMANCE FACTORS IN HADOOP CLOUD COMPUTING APPLICATIONS Lus Eduardo Bautsta Vllalpando 1,2, Alan Aprl 1 and Alan Abran 1 1 Department of Software Engneerng
More informationSingularity functions as new tool for integrated project management
Creatve Constructon Conference 24 Sngularty functons as new tool for ntegrated project management Gunnar LUCKO and Y SU Department of Cvl Engneerng, Catholc Unversty of Amerca, 62 Mchgan Avenue NE, Washngton,
More informationEnabling P2P Oneview Multiparty Video Conferencing
Enablng P2P Onevew Multparty Vdeo Conferencng Yongxang Zhao, Yong Lu, Changja Chen, and JanYn Zhang Abstract MultParty Vdeo Conferencng (MPVC) facltates realtme group nteracton between users. Whle P2P
More informationTexas Instruments 30X IIS Calculator
Texas Instruments 30X IIS Calculator Keystrokes for the TI30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the
More informationOn the Optimal Control of a Cascade of HydroElectric Power Stations
On the Optmal Control of a Cascade of HydroElectrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;
More informationBusiness Process Improvement using Multiobjective Optimisation K. Vergidis 1, A. Tiwari 1 and B. Majeed 2
Busness Process Improvement usng Multobjectve Optmsaton K. Vergds 1, A. Twar 1 and B. Majeed 2 1 Manufacturng Department, School of Industral and Manufacturng Scence, Cranfeld Unversty, Cranfeld, MK43
More information10. (# 45, May 2001). At time t = 0, 1 is deposited into each of Fund X and Fund Y. Fund X accumulates at a force of interest
1 Exam FM questons 1. (# 12, May 2001). Bruce and Robbe each open up new bank accounts at tme 0. Bruce deposts 100 nto hs bank account, and Robbe deposts 50 nto hs. Each account earns an annual e ectve
More informationStudy on CET4 Marks in China s Graded English Teaching
Study on CET4 Marks n Chna s Graded Englsh Teachng CHE We College of Foregn Studes, Shandong Insttute of Busness and Technology, P.R.Chna, 264005 Abstract: Ths paper deploys Logt model, and decomposes
More informationAn Enhanced SuperResolution System with Improved Image Registration, Automatic Image Selection, and Image Enhancement
An Enhanced SuperResoluton System wth Improved Image Regstraton, Automatc Image Selecton, and Image Enhancement YuChuan Kuo ( ), ChenYu Chen ( ), and ChouShann Fuh ( ) Department of Computer Scence
More informationData Broadcast on a MultiSystem Heterogeneous Overlayed Wireless Network *
JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 24, 819840 (2008) Data Broadcast on a MultSystem Heterogeneous Overlayed Wreless Network * Department of Computer Scence Natonal Chao Tung Unversty Hsnchu,
More informationThe Analysis of Outliers in Statistical Data
THALES Project No. xxxx The Analyss of Outlers n Statstcal Data Research Team Chrysses Caron, Assocate Professor (P.I.) Vaslk Karot, Doctoral canddate Polychrons Economou, Chrstna Perrakou, Postgraduate
More informationMotivation. Eingebettete Systeme. Terms. Terms. Echtzeitverhalten und Betriebssysteme. 7. Ressourcen
Motvaton Engebettete Systeme Echtzetverhalten und Betrebssysteme 7. Ressourcen 1 2 Terms A resource s any software structure that can be used by a process to advance ts executon, e.g. data structure, a
More informationEE201 Circuit Theory I 2015 Spring. Dr. Yılmaz KALKAN
EE201 Crcut Theory I 2015 Sprng Dr. Yılmaz KALKAN 1. Basc Concepts (Chapter 1 of Nlsson  3 Hrs.) Introducton, Current and Voltage, Power and Energy 2. Basc Laws (Chapter 2&3 of Nlsson  6 Hrs.) Voltage
More informationRate Monotonic (RM) Disadvantages of cyclic. TDDB47 Real Time Systems. Lecture 2: RM & EDF. Prioritybased scheduling. States of a process
Dsadvantages of cyclc TDDB47 Real Tme Systems Manual scheduler constructon Cannot deal wth any runtme changes What happens f we add a task to the set? RealTme Systems Laboratory Department of Computer
More informationConferencing protocols and Petri net analysis
Conferencng protocols and Petr net analyss E. ANTONIDAKIS Department of Electroncs, Technologcal Educatonal Insttute of Crete, GREECE ena@chana.tecrete.gr Abstract: Durng a computer conference, users desre
More informationTrade Adjustment and Productivity in Large Crises. Online Appendix May 2013. Appendix A: Derivation of Equations for Productivity
Trade Adjustment Productvty n Large Crses Gta Gopnath Department of Economcs Harvard Unversty NBER Brent Neman Booth School of Busness Unversty of Chcago NBER Onlne Appendx May 2013 Appendx A: Dervaton
More informationOptimization of network mesh topologies and link capacities for congestion relief
Optmzaton of networ mesh topologes and ln capactes for congeston relef D. de Vllers * J.M. Hattngh School of Computer, Statstcal and Mathematcal Scences Potchefstroom Unversty for CHE * Emal: rwddv@pu.ac.za
More informationBUSINESS PROCESS PERFORMANCE MANAGEMENT USING BAYESIAN BELIEF NETWORK. 0688, dskim@ssu.ac.kr
Proceedngs of the 41st Internatonal Conference on Computers & Industral Engneerng BUSINESS PROCESS PERFORMANCE MANAGEMENT USING BAYESIAN BELIEF NETWORK Yeongbn Mn 1, Yongwoo Shn 2, Km Jeehong 1, Dongsoo
More informationThe Application of Fractional Brownian Motion in Option Pricing
Vol. 0, No. (05), pp. 738 http://dx.do.org/0.457/jmue.05.0..6 The Applcaton of Fractonal Brownan Moton n Opton Prcng Qngxn Zhou School of Basc Scence,arbn Unversty of Commerce,arbn zhouqngxn98@6.com
More informationPowerofTwo Policies for Single Warehouse MultiRetailer Inventory Systems with Order Frequency Discounts
Powerofwo Polces for Sngle Warehouse MultRetaler Inventory Systems wth Order Frequency Dscounts José A. Ventura Pennsylvana State Unversty (USA) Yale. Herer echnon Israel Insttute of echnology (Israel)
More informationEXAMPLE PROBLEMS SOLVED USING THE SHARP EL733A CALCULATOR
EXAMPLE PROBLEMS SOLVED USING THE SHARP EL733A CALCULATOR 8S CHAPTER 8 EXAMPLES EXAMPLE 8.4A THE INVESTMENT NEEDED TO REACH A PARTICULAR FUTURE VALUE What amount must you nvest now at 4% compoune monthly
More informationComplex Service Provisioning in Collaborative Cloud Markets
Melane Sebenhaar, Ulrch Lampe, Tm Lehrg, Sebastan Zöller, Stefan Schulte, Ralf Stenmetz: Complex Servce Provsonng n Collaboratve Cloud Markets. In: W. Abramowcz et al. (Eds.): Proceedngs of the 4th European
More informationPOLYSA: A Polynomial Algorithm for Nonbinary Constraint Satisfaction Problems with and
POLYSA: A Polynomal Algorthm for Nonbnary Constrant Satsfacton Problems wth and Mguel A. Saldo, Federco Barber Dpto. Sstemas Informátcos y Computacón Unversdad Poltécnca de Valenca, Camno de Vera s/n
More informationA hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm
Avalable onlne www.ocpr.com Journal of Chemcal and Pharmaceutcal Research, 2014, 6(7):18841889 Research Artcle ISSN : 09757384 CODEN(USA) : JCPRC5 A hybrd global optmzaton algorthm based on parallel
More informationBrigid Mullany, Ph.D University of North Carolina, Charlotte
Evaluaton And Comparson Of The Dfferent Standards Used To Defne The Postonal Accuracy And Repeatablty Of Numercally Controlled Machnng Center Axes Brgd Mullany, Ph.D Unversty of North Carolna, Charlotte
More informationExamensarbete. Rotating Workforce Scheduling. Caroline Granfeldt
Examensarbete Rotatng Workforce Schedulng Carolne Granfeldt LTH  MAT  EX   2015 / 08   SE Rotatng Workforce Schedulng Optmerngslära, Lnköpngs Unverstet Carolne Granfeldt LTH  MAT  EX   2015
More informationJoint Scheduling of Processing and Shuffle Phases in MapReduce Systems
Jont Schedulng of Processng and Shuffle Phases n MapReduce Systems Fangfe Chen, Mural Kodalam, T. V. Lakshman Department of Computer Scence and Engneerng, The Penn State Unversty Bell Laboratores, AlcatelLucent
More informationLuby s Alg. for Maximal Independent Sets using Pairwise Independence
Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent
More informationChapter 7: Answers to Questions and Problems
19. Based on the nformaton contaned n Table 73 of the text, the food and apparel ndustres are most compettve and therefore probably represent the best match for the expertse of these managers. Chapter
More informationSolution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.
Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces
More informationConversion between the vector and raster data structures using Fuzzy Geographical Entities
Converson between the vector and raster data structures usng Fuzzy Geographcal Enttes Cdála Fonte Department of Mathematcs Faculty of Scences and Technology Unversty of Combra, Apartado 38, 3 454 Combra,
More informationBatch Scheduling for a Single Deteriorating Machine to Minimize Total Actual Flow Time
Proceedngs of the 2014 Internatonal Conference on Industral Engneerng and Operatons Management Bal, Indonesa, January 7 9, 2014 Batch Schedulng for a Sngle Deteroratng Machne to Mnmze Total Actual Flow
More informationA GENETIC ALGORITHMBASED METHOD FOR CREATING IMPARTIAL WORK SCHEDULES FOR NURSES
82 Internatonal Journal of Electronc Busness Management, Vol. 0, No. 3, pp. 8293 (202) A GENETIC ALGORITHMBASED METHOD FOR CREATING IMPARTIAL WORK SCHEDULES FOR NURSES FengCheng Yang * and WeTng Wu
More information0.02t if 0 t 3 δ t = 0.045 if 3 < t
1 Exam FM questons 1. (# 12, May 2001). Bruce and Robbe each open up new bank accounts at tme 0. Bruce deposts 100 nto hs bank account, and Robbe deposts 50 nto hs. Each account earns an annual effectve
More informationAnalysis of Premium Liabilities for Australian Lines of Business
Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton
More informationISLM Model 1 C' dy = di
 odel Solow Assumptons  demand rrelevant n long run; assumes economy s operatng at potental GDP; concerned wth growth  Assumptons  supply s rrelevant n short run; assumes economy s operatng below potental
More informationA DATA MINING APPLICATION IN A STUDENT DATABASE
JOURNAL OF AERONAUTICS AND SPACE TECHNOLOGIES JULY 005 VOLUME NUMBER (5357) A DATA MINING APPLICATION IN A STUDENT DATABASE Şenol Zafer ERDOĞAN Maltepe Ünversty Faculty of Engneerng BüyükbakkalköyIstanbul
More informationOutsourcing inventory management decisions in healthcare: Models and application
European Journal of Operatonal Research 154 (24) 271 29 O.R. Applcatons Outsourcng nventory management decsons n healthcare: Models and applcaton www.elsever.com/locate/dsw Lawrence Ncholson a, Asoo J.
More informationIMPACT ANALYSIS OF A CELLULAR PHONE
4 th ASA & μeta Internatonal Conference IMPACT AALYSIS OF A CELLULAR PHOE We Lu, 2 Hongy L Bejng FEAonlne Engneerng Co.,Ltd. Bejng, Chna ABSTRACT Drop test smulaton plays an mportant role n nvestgatng
More informationResponse Coordination of Distributed Generation and Tap Changers for Voltage Support
Response Coordnaton of Dstrbuted Generaton and Tap Changers for Voltage Support An D.T. Le, Student Member, IEEE, K.M. Muttaq, Senor Member, IEEE, M. Negnevtsky, Member, IEEE,and G. Ledwch, Senor Member,
More information