Project Networks With MixedTime Constraints


 Edwin Haynes
 2 years ago
 Views:
Transcription
1 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 Abstract : A Project can be vewed as a welldefned collecton of tass jobs or actvtes that must be performed n some order and when all tass are completed the desred project objectve s acheved. For example n the constructon of a buldng there are many tass such as: ste preparaton; pourng of footng and slab; the constructon of walls; and roofng; whch must be completed n some order. A fundamental problem n project management s that of determnng the mnmum project duraton tme and the schedule whch acheves ths. The Crtcal Path Method (CPM) and Project Evaluaton and Revew Technque (PERT) are fundamental tools for determnng ths schedule. In ths paper we concentrate on tme constrants that specfy when each actvty can be n progress. More precsely the Tme Constrant Crtcal Path Problem can be stated as: Gven a project networ G n whch each actvty has a specfed duraton tme and a tme constrant specfyng when the actvty can be carred out fnd the mnmum total project duraton tme and the schedule whch acheves ths. The tme constrants can be specfed as: tmewndows; tmeschedule; or normal tme. Chen et al. (1997) consdered these and presented a twophase algorthm for determnng the crtcal path. We develop a new mxed nteger lnear program (MILP) formulaton for ths problem. We also consder the tmecost tradeoff problem for networs wth mxedtme constrants. The method for tradtonal networs extends to ths problem. In addton we develop a MILP model for determnng the mnmum cost schedule. Keywords : Project networ; schedulng; crtcal paths. 1. INTRODUCTION Project Management s concerned wth projects such as the constructon of a buldng the plannng and launchng of a new product the nstallaton of a new manufacturer s faclty the mplementaton of perodc mantenance n a plant faclty etc. The basc characterstc of a project conssts of a welldefned collecton of tass (or actvtes) that must be performed n some technologcal sequence. Wthn the specfed sequence the tass may be started and stopped ndependently of each other. When all the tass are completed the project s completed. A project can be represented as a networ n whch the arcs represent actvtes and the nodes represent events (ponts where a group of actvtes are accomplshed and where a new set of actvtes can be ntated). Ths yelds the actvty onarc model. An alternatve networ model s the actvtyonnode model n whch the arcs represent the predecessor restrctons and the nodes represent the actvty. In ths paper we consder only the actvtyonarc model. In the early days the schedulng of a project was done only wth lmted plannng. The tool used for solvng ths problem was the Gantt chart whch specfes the start and fnsh tme for each actvty on a horzontal scale. In 1950 s the crtcal path method (CPM) and the project evaluaton and revew technque (PERT) were developed. CPM was frst developed by E.I. du Pont de Neumours & Company as an applcaton to constructon projects and was later extended to a more advanced status by Mauchy Assocates; PERT was developed for the U.S. Navy for schedulng the research and development actvtes for the Polars mssle program. PERT and CPM are twophase labellng methods that are computatonally very effcent. In project management there s usually a due date for the project completon. Therefore n some stuatons a project could be completed n a shorter tme than the normal program. The method of reducng the project duraton by shortenng the actvty tme at a cost s called crashng. Another cost assocated wth projects s the ndrect cost. When both the cost components are consdered we have the mportant tmecost tradeoff problem. Ths can be modelled as a mathematcal program. By assumng that the drect cost of an actvty vares lnearly wth tme the problem can be expressed as a lnear program. The soluton of ths lnear program smultaneously determnes the
2 optmal duraton of a project and the approprate tme of each actvty n the networ so that project cost s mnmzed. The early wor on the tme constrant project management problem was carred out by Fulerson (1961) and Kelley (1961). The tmecost tradeoff problem has more recently been studed by many authors ncludng : Phllps and Dessouy (1977) De et al. (1995) Sunde and Lchtenberg (1995) Demeulemeester et al. (1996) Baer (1997) and Demeulemeester et al. (1988). Soluton methods for ths problem nclude : a mnmal cut approach; Dynamc Programmng; a heurstc costtme tradeoff Lnear Programmng (LP); and the Branch and Bound procedure. EF : earlest fnsh tme on actvty (j). Phase I : Forwardpass Procedure (Calculates the early start and fnsh tmes) Step1 Set E = 0. Step2 For each arc (j) drected nto node j: () If (j) s a normaltme arc then ES = E and EF = ES + t. () If (j) s a tmeschedule arc wth tmes ts 1 ts 2... ts... ts v then Wth regard to the Crtcal path problem recently Chen and Tang (1997) presented a mxedtme constrant model. These tme constrants consst of two types namely tmewndow (nterval) constrant and tmeschedule (lst of start tmes). They presented an effcent lnear tme algorthm for determnng the crtcal path that s smlar to the tradtonal CPM. In ths paper we wll develop mxed nteger lnear programmng models for determnng the crtcal path and the mnmum cost schedule n mxedtme constraned networs. 2 THE TWOPHASE METHOD In ths secton we present the essental ngredents of the twophase method developed by Chen et al. (1979) wrtten n the style of the standard algorthm. We adopt the followng basc notaton. Step3 ES = ts (j) ; where ts 1 < E ts. and EF = ES + t. () If (j) s tmewndow arc wth tme [L U ] then ES L = E f f f and EF = ES + t. E L E L E > U U For node j f EF has been calculated for all then E = j max{εf}. s : source node. Step4 (Stoppng rule) If = d stop EF = E d. Otherwse go d : destnaton node. to step 2. The longest path s found. A 1 A 2 A 3 : set of actvtes or arcs havng normal tmes. : set of actvtes or arcs havng a prescrbed schedule of start tmes (tmeschedule). : set of actvtes or arcs havng a prescrbed nterval of start tmes (tmewndow). Phase II : BacwardPass Procedure (Calculates the late start and fnsh tmes) Step 1 Set LF j = ES j. Step 2 For each arc(j) drected nto node j : () If ( j ) s normal tme arc wth tmes ts 1 ts 2... ts... ts v then LS j = LF j t j. ts : schedule departure tmes for actvty (j). () If ( j ) s tmeschedule arc then tw : tme wndow departure tme for actvty t (j) ; usually wrtten n [L U ]. : tme duraton of actvty (j). E : earlest occurrence tme event. ES : earlest start tme on actvty (j). LS ts = LF ts + t otherwse. ()If ( j ) s tme wndow arc [L U ] then.
3 U y = 1 for ( j) A 2. (6) LF U + t LS = LF L LF U y j s bnary j. (7) otherwse. [The restrctons (4) (7) ensure that the tmeschedule Step 3 For node f LS has been calculated for all j then For (j) A 3 L = mn {LS }. j E j  x t for (j) A 3. (8) Step 4 Stoppng rule: If j = s stop LF = L S otherwse go to Step 2. 3 MILP FORMULATIONS In ths secton the crtcal path problem wth mxedtme constrants wll be formulated as a MILP (Mxed Integer Lnear Program). We start wth a new MILP for determnng the earlest project completon tme and follow ths wth an MILP to determne the latest allowable occurrence tme. L x U for (j) A 3. (9) [The two above restrctons ensure that the tmewndow Determnng the latest allowable occurrence tme We have the followng addtonal notaton T : Project Completon date (due date). LS : Latest start tme of actvty (j). LSS : Latest start tme of actvty (j) A 2 A 3 ; Determnng the earlest project completon tme We begn wth some further notaton. Let: D = { d 1 d 2... d } for (j) A 2. [Start tme of actvty (j) ] LSS = LF t ; and LF ts t. N + = Neghbor set of (wth arcs drected out of ). Formulaton: 1 f actvty ( j) starts at tme d y = Maxmze L s (10) 0 else. subject to L d = T (11) : occurrence tmes on tmeschedule ; = 12 K (last number of tmeschedule). [The above restrctons ensures a completon tme of T] x : earlest start tme of actvty (j). Formulaton: Mnmze E d (1) subject to E S = 0 (2) [The above restrcton ensures a start tme s zero] E j  E t for (j) A 1. (3) [The above restrcton ensures that normal tme E j x t for (j) A 2. (4) x d y = 0 for ( j).(5) A 2 L j L t for (j) A 1. (12) [The above restrctons ensure that the normal tme For each and j N + ; (j) A L LS (13) and LS L + m z m (14) j [m s large postve nteger] z =1 (15) z s bnary. (16)
4 [The restrctons (13)(16) ensure that the event j gves the smallest latest start(j)] For (j) A 1 LS = L j t. (17) [The above restrctons ensure that the normal tme For (j) A 2 LSS = L j t (18) LS LSS (19) d y = LS 0 (20) y = 1 (21) Fgure 1 : Start and Fnsh Tmes. A 2 = {(13)(35)(46)(47)} and A 3 = {(34)}. Applyng the twophase method or usng the MILP s descrbed n Secton 3 yelds : Actvty t(j) E ES j EF j LF LS j (12) (13) (24) (25) (34) (35) (45) (46) (47) (56) (57) (68) (78) Table 1 : Start and Fnsh Tmes y s bnary for all j. (22) [The restrctons (18)(22) ensure that tme schedule For (j) A 3 LSS = L j t (23) LS LSS (24) L LS U. (25) [The restrctons (23)(25) ensure that tme wndow 4 EXAMPLE Consder the 8node networ dsplayed n Fgure 1 wth A 1 = {(12)(24)(25)(45)(56)(63)(68)(78)} The crtcal path of length 21 s : {(12) (24) (46) (68)}. 5 TIME COST TRADEOFF The modfed twophase method of Secton 2 can be used n the tradtonal way to resolve the tmecost tradeoff problem for networs wth mxedtme constrants. That s Step 1: Generate a prelmnary schedule usng normal resources (a modfed twophase method wth mxtme constrants). Step 2: Fnd the job along the crtcal path wth the least cost slope. Ths s the job that can be crashed wth least expense. If the cost of shortenng the schedule by one perod s less than the fxed ndrect cost for one perod then the job s expedted up to the pont where no further shortenng s possble (ether because the job duraton
5 cannot be reduced further or because some other job has become crtcal along a parallel path). [ The above two restrctons ensure that normal tme. For (j) A 2 (tme schedule arcs) : Step 3: Repeat Step 2 untl no further shortenng of crtcal jobs s uneconomcal. E j = ES +x. (32) (.e. reduce the savngs that would result). We can also use the followng MILP formulaton. l x u. (33) Consder a project networ wth n nodes labelled E j  ES 0. (34) n where node 1 represents the start of the project and node n the end of t. In addton to the earler notaton we let x : duraton of actvty (j). E : realzaton of event. a : cost slope of actvty(j). ES d y = 0. (35) y = 1. (36) y s bnary. (37) [the restrctons (32) (37) ensure that the tmeschedule l : Lower bound on the duraton of actvty For (j) A 3 (tme wndows arcs). (j). E j  ES x. (38) u : Upper bound on the duraton of actvty(j). l x u. (39) 1 2 D = { d d... d } for (j) A2. L ES U. (40) TW = [L U ] for (j) A 3. [the two above restrctons ensure that the tme wndow. y 1 = 0 f actvty( j) start to leave node to node else j The above MILP s easly solved by a pacage such as CPLEX. f : fxed cost (per unt tme). Example : Consder the project networ of Fgure 1 wth normal and crash cost data : We assume a lnear costduraton for each actvty. So we can wrte the cost of actvty(j) as Actvty Normal Crash c (j) Tme Tme = b + a x. The MILP formulaton s: Mnmze [ a x +f (En) + b ] (26) subject to For (j) A 1 (normal tme arcs). E 1 = 0. (27) E n E 1 T. (28) E j = ES + x. (29) l x u. (30) E j  ES 0. (31) t c t c Slope (12) (13) (24) (25) (34) (35) (45) (46) (47) (56) (57) (68) (78) Total Table 2 : Normal and Crash Data Suppose the ndrect cost assocated wth the project s $100 per day. Then the applcaton of the above method yelds :
6 Total tme Drecton Indrect Total Crash actvtes (46) (46) * (46)(24) (45)(68) Table 3 The optmal soluton s for a 19day schedule. 6 CONCLUSION Ths paper addresses project management problems n networs wth mxedtme constrants. We allow actvtes to be restrcted to tmewndow and tmeschedule constrants. We present mxed nteger lnear programmng models that can be effcently solved by avalable commercal software such as CPLEX. 7 REFERENCES Baer B.M /tme tradeoff analyss for the crtcal path method: a devaton of the networ flow approach Journal of the Operatonal Research Socety vol. 48 pp Chen YL. Rns D. and Tang K Crtcal path n an actvty networ wth tme constrants European Journal of Operatonal Research 100 pp De M. Dunne E.J.Ghosh J.B. and WellsC.E The dscrete tmecost tradeoff problem revsted European Journal of Operatonal Research 81 pp Demeulemeester E.L. Herroelen W.S. and Elmaghraby S.E Optmal procedures for the dscrete tme/cost tradeoff problem n project networ European Journal of Operatonal Research 88 pp Demeulemeester E. Reyc B.D. FoubertB. HerroelenW. and Vanhouce M.1998 New computatonal results on the dscrete tme/cost tradeoff problem n project networs Journal of the Operatonal Research Socety vol. 49 pp Fulerson D A networ flow computaton for project cost curves Management Scence 7 pp ILOG Inc. CPLEX Dvson 1997 Usng the CPLEX Callable LbraryVerson5.5. Kelley J Crtcalpath plannng and schedulng: Mathematcal bass Operatons Research vol. 9 no. 3 pp Phllps J.P. and Dessouy M.I Solvng the project tme/cost tradeoff problem usng the mnmal cut concept Management Scence vol. 13 no. 6 ppb359b377. Sunde L. and Lchtenberg S Netpresent value cost/tme tradeoff Internatonal Journal of Project Management vol. 13 no. 1 pp4549.
A 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 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 informationActivity Scheduling for CostTime Investment Optimization in Project Management
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
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 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 informationFormulating & Solving Integer Problems Chapter 11 289
Formulatng & Solvng Integer Problems Chapter 11 289 The Optonal Stop TSP If we drop the requrement that every stop must be vsted, we then get the optonal stop TSP. Ths mght correspond to a ob sequencng
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 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 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 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 informationAllocating Time and Resources in Project Management Under Uncertainty
Proceedngs of the 36th Hawa Internatonal Conference on System Scences  23 Allocatng Tme and Resources n Project Management Under Uncertanty Mark A. Turnqust School of Cvl and Envronmental Eng. Cornell
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 informationLogical Development Of Vogel s Approximation Method (LDVAM): An Approach To Find Basic Feasible Solution Of Transportation Problem
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME, ISSUE, FEBRUARY ISSN 77866 Logcal Development Of Vogel s Approxmaton Method (LD An Approach To Fnd Basc Feasble Soluton Of Transportaton
More 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 informationNONLINEAR OPTIMIZATION FOR PROJECT SCHEDULING AND RESOURCE ALLOCATION UNDER UNCERTAINTY
NONLINEAR OPTIMIZATION FOR PROJECT SCHEDULING AND RESOURCE ALLOCATION UNDER UNCERTAINTY A Dssertaton Presented to the Faculty of the Graduate School of Cornell Unversty In Partal Fulfllment of the Requrements
More informationA Computer Technique for Solving LP Problems with Bounded Variables
Dhaka Unv. J. Sc. 60(2): 163168, 2012 (July) A Computer Technque for Solvng LP Problems wth Bounded Varables S. M. Atqur Rahman Chowdhury * and Sanwar Uddn Ahmad Department of Mathematcs; Unversty of
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 informationResourceconstrained Project Scheduling with Fuzziness
esourceconstraned Project Schedulng wth Fuzzness HONGQI PN, OBET J. WIIS, CHUNGHSING YEH School of Busness Systems Monash Unversty Clayton, Vctora 368 USTI bstract:  esourceconstraned project schedulng
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 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 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 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 informationParticle Swarm Optimization for Scheduling to Minimize Tardiness Penalty and Power Cost
Partcle Swarm Optmzaton for Schedulng to Mnmze Tardness Penalty and Power Cost KueTang Fang and Bertrand M.T. Ln Department of Informaton and Fnance Management Insttute of Informaton Management Natonal
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 informationTo Fill or not to Fill: The Gas Station Problem
To Fll or not to Fll: The Gas Staton Problem Samr Khuller Azarakhsh Malekan Julán Mestre Abstract In ths paper we study several routng problems that generalze shortest paths and the Travelng Salesman Problem.
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 informationThreedimensional Gantt Chart Based Resourceconstrained Multiple Projects Scheduling and Critical Chain Identification
Threedmensonal Gantt Chart Based Resourceconstraned Multple Proects Schedulng and Crtcal Chan Identfcaton J. Q. Wang,, S. F. Zhang,, J. Chen,, S. Wang,, Y. F. Zhang, Insttute of System Integrated & ngneerng
More informationJ. Parallel Distrib. Comput.
J. Parallel Dstrb. Comput. 71 (2011) 62 76 Contents lsts avalable at ScenceDrect J. Parallel Dstrb. Comput. journal homepage: www.elsever.com/locate/jpdc Optmzng server placement n dstrbuted systems n
More informationCompiling for Parallelism & Locality. Dependence Testing in General. Algorithms for Solving the Dependence Problem. Dependence Testing
Complng for Parallelsm & Localty Dependence Testng n General Assgnments Deadlne for proect 4 extended to Dec 1 Last tme Data dependences and loops Today Fnsh data dependence analyss for loops General code
More 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 informationMultiPeriod Resource Allocation for Estimating Project Costs in Competitive Bidding
Department of Industral Engneerng and Management Techncall Report No. 20146 MultPerod Resource Allocaton for Estmatng Project Costs n Compettve dng Yuch Takano, Nobuak Ish, and Masaak Murak September,
More informationRealTime Process Scheduling
RealTme Process Schedulng ktw@cse.ntu.edu.tw (RealTme and Embedded Systems Laboratory) Independent Process Schedulng Processes share nothng but CPU Papers for dscussons: C.L. Lu and James. W. Layland,
More information9 Arithmetic and Geometric Sequence
AAU  Busness Mathematcs I Lecture #5, Aprl 4, 010 9 Arthmetc and Geometrc Sequence Fnte sequence: 1, 5, 9, 13, 17 Fnte seres: 1 + 5 + 9 + 13 +17 Infnte sequence: 1,, 4, 8, 16,... Infnte seres: 1 + + 4
More informationOptimal portfolios using Linear Programming models
Optmal portfolos usng Lnear Programmng models Chrstos Papahrstodoulou Mälardalen Unversty, Västerås, Sweden Abstract The classcal Quadratc Programmng formulaton of the well known portfolo selecton problem,
More informationSolution of Algebraic and Transcendental Equations
CHAPTER Soluton of Algerac and Transcendental Equatons. INTRODUCTION One of the most common prolem encountered n engneerng analyss s that gven a functon f (, fnd the values of for whch f ( = 0. The soluton
More informationMaintenance Scheduling by using the BiCriterion Algorithm of Preferential AntiPheromone
Leonardo ournal of Scences ISSN 5830233 Issue 2, anuaryune 2008 p. 4364 Mantenance Schedulng by usng the BCrteron Algorthm of Preferental AntPheromone Trantafyllos MYTAKIDIS and Arstds VLACHOS Department
More 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 informationgreatest common divisor
4. GCD 1 The greatest common dvsor of two ntegers a and b (not both zero) s the largest nteger whch s a common factor of both a and b. We denote ths number by gcd(a, b), or smply (a, b) when there s no
More 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 informationAryabhata s Root Extraction Methods. Abhishek Parakh Louisiana State University Aug 31 st 2006
Aryabhata s Root Extracton Methods Abhshek Parakh Lousana State Unversty Aug 1 st 1 Introducton Ths artcle presents an analyss of the root extracton algorthms of Aryabhata gven n hs book Āryabhatīya [1,
More informationScheduling a Single Mobile Robot for Feeding Tasks in a Manufacturing Cell
Schedulng a Sngle Moble Robot for Feedng Tasks n a Manufacturng Cell QuangVnh Dang 1, Izabela Ewa Nelsen 1, Kenn StegerJensen 1 1 Department of Mechancal and Manufacturng Engneerng, Aalborg Unversty,
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 informationFault tolerance in cloud technologies presented as a service
Internatonal Scentfc Conference Computer Scence 2015 Pavel Dzhunev, PhD student Fault tolerance n cloud technologes presented as a servce INTRODUCTION Improvements n technques for vrtualzaton and performance
More informationHeuristic Static LoadBalancing Algorithm Applied to CESM
Heurstc Statc LoadBalancng Algorthm Appled to CESM 1 Yur Alexeev, 1 Sher Mckelson, 1 Sven Leyffer, 1 Robert Jacob, 2 Anthony Crag 1 Argonne Natonal Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439,
More information2008/8. An integrated model for warehouse and inventory planning. Géraldine Strack and Yves Pochet
2008/8 An ntegrated model for warehouse and nventory plannng Géraldne Strack and Yves Pochet CORE Voe du Roman Pays 34 B1348 LouvanlaNeuve, Belgum. Tel (32 10) 47 43 04 Fax (32 10) 47 43 01 Emal: corestatlbrary@uclouvan.be
More informationAn Integrated Approach for Maintenance and Delivery Scheduling in Military Supply Chains
An Integrated Approach for Mantenance and Delvery Schedulng n Mltary Supply Chans Dmtry Tsadkovch 1*, Eugene Levner 2, Hanan Tell 2 and Frank Werner 3 2 1 Bar Ilan Unversty, Department of Management, Ramat
More informationINSTITUT FÜR INFORMATIK
INSTITUT FÜR INFORMATIK Schedulng jobs on unform processors revsted Klaus Jansen Chrstna Robene Bercht Nr. 1109 November 2011 ISSN 21926247 CHRISTIANALBRECHTSUNIVERSITÄT ZU KIEL Insttut für Informat
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 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 information1 Example 1: Axisaligned rectangles
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture # 6 Scrbe: Aaron Schld February 21, 2013 Last class, we dscussed an analogue for Occam s Razor for nfnte hypothess spaces that, n conjuncton
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 informationTesting and Debugging Resource Allocation for Fault Detection and Removal Process
Internatonal Journal of New Computer Archtectures and ther Applcatons (IJNCAA) 4(4): 9300 The Socety of Dgtal Informaton and Wreless Communcatons, 04 (ISSN: 09085) Testng and Debuggng Resource Allocaton
More information106 M.R. Akbar Jokar and M. Sefbarghy polcy, ndependent Posson demands n the retalers, a backordered demand durng stockouts n all nstallatons and cons
Scenta Iranca, Vol. 13, No. 1, pp 105{11 c Sharf Unversty of Technology, January 006 Research Note Cost Evaluaton of a TwoEchelon Inventory System wth Lost Sales and Approxmately Normal Demand M.R. Akbar
More information行 政 院 國 家 科 學 委 員 會 補 助 專 題 研 究 計 畫 成 果 報 告 期 中 進 度 報 告
行 政 院 國 家 科 學 委 員 會 補 助 專 題 研 究 計 畫 成 果 報 告 期 中 進 度 報 告 畫 類 別 : 個 別 型 計 畫 半 導 體 產 業 大 型 廠 房 之 設 施 規 劃 計 畫 編 號 :NSC 962628E009026MY3 執 行 期 間 : 2007 年 8 月 1 日 至 2010 年 7 月 31 日 計 畫 主 持 人 : 巫 木 誠 共 同
More information+ + +   This circuit than can be reduced to a planar circuit
MeshCurrent Method The meshcurrent s analog of the nodeoltage method. We sole for a new set of arables, mesh currents, that automatcally satsfy KCLs. As such, meshcurrent method reduces crcut soluton to
More informationSOLVING CARDINALITY CONSTRAINED PORTFOLIO OPTIMIZATION PROBLEM BY BINARY PARTICLE SWARM OPTIMIZATION ALGORITHM
SOLVIG CARDIALITY COSTRAIED PORTFOLIO OPTIMIZATIO PROBLEM BY BIARY PARTICLE SWARM OPTIMIZATIO ALGORITHM Aleš Kresta Klíčová slova: optmalzace portfola, bnární algortmus rojení částc Key words: portfolo
More information9.1 The Cumulative Sum Control Chart
Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s
More informationScheduling Home Hospice Care with LogicBased Benders Decomposition
Schedulng Home Hospce Care wth LogcBased Benders Decomposton Alza Hechng 1 and J. N. Hooker 2 1 Compassonate Care Hospce Group, alza.hechng@cchnet.net 2 Carnege Mellon Unversty, Pttsburgh, USA, jh38@andrew.cmu.edu
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 information8 Algorithm for Binary Searching in Trees
8 Algorthm for Bnary Searchng n Trees In ths secton we present our algorthm for bnary searchng n trees. A crucal observaton employed by the algorthm s that ths problem can be effcently solved when the
More informationRiskOriented Decision Making During Integrated Investment Management under Uncertainty
RskOrented Decson Makng Durng Integrated Investment Management under Uncertanty Valer Lovkn Abstract The model of decsonmakng durng ntegrated nvestment management under uncertanty, whch enables to dstrbute
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 informationInteger Programming Formulations for the Uncapacitated Vehicle Routing phub Center Problem
21st Internatonal Congress on Modellng and Smulaton, Gold Coast, Australa, 29 No to 4 Dec 2015 www.mssanz.org.au/modsm2015 Integer Programmng Formulatons for the Uncapactated Vehcle Routng phub Center
More information1.1 The University may award Higher Doctorate degrees as specified from timetotime in UPR AS11 1.
HIGHER DOCTORATE DEGREES SUMMARY OF PRINCIPAL CHANGES General changes None Secton 3.2 Refer to text (Amendments to verson 03.0, UPR AS02 are shown n talcs.) 1 INTRODUCTION 1.1 The Unversty may award Hgher
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 informationDynamic Constrained Economic/Emission Dispatch Scheduling Using Neural Network
Dynamc Constraned Economc/Emsson Dspatch Schedulng Usng Neural Network Fard BENHAMIDA 1, Rachd BELHACHEM 1 1 Department of Electrcal Engneerng, IRECOM Laboratory, Unversty of Djllal Labes, 220 00, Sd Bel
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More informationAn Evaluation of the Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products and Services
An Evaluaton of the Extended Logstc, Smple Logstc, and Gompertz Models for Forecastng Short Lfecycle Products and Servces Charles V. Trappey a,1, Hsnyng Wu b a Professor (Management Scence), Natonal Chao
More informationA Project Scheduling Method Based on Fuzzy Theory
Journal of Industral and ystems Engneerng Vol. No. pp 7080 prng 007 Proect chedulng Method Based on Fuzzy Theory hmad oltan * Rasoul Ha harf Unversty of Technology and Engneerng Research Insttute Mnstry
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 informationResearch Article A Time Scheduling Model of Logistics Service Supply Chain with Mass Customized Logistics Service
Hndaw Publshng Corporaton Dscrete Dynamcs n Nature and Socety Volume 01, Artcle ID 48978, 18 pages do:10.1155/01/48978 Research Artcle A Tme Schedulng Model of Logstcs Servce Supply Chan wth Mass Customzed
More informationMoment of a force about a point and about an axis
3. STATICS O RIGID BODIES In the precedng chapter t was assumed that each of the bodes consdered could be treated as a sngle partcle. Such a vew, however, s not always possble, and a body, n general, should
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a twostage stratfed cluster desgn. 1 The frst stage conssted of a sample
More informationNONCONSTANT SUM REDANDBLACK GAMES WITH BETDEPENDENT WIN PROBABILITY FUNCTION LAURA PONTIGGIA, University of the Sciences in Philadelphia
To appear n Journal o Appled Probablty June 2007 OCOSTAT SUM REDADBLACK GAMES WITH BETDEPEDET WI PROBABILITY FUCTIO LAURA POTIGGIA, Unversty o the Scences n Phladelpha Abstract In ths paper we nvestgate
More informationForecasting the Direction and Strength of Stock Market Movement
Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract  Stock market s one of the most complcated systems
More informationA Fault Tree Analysis Strategy Using Binary Decision Diagrams.
A Fault Tree Analyss Strategy Usng Bnary Decson Dagrams. Karen A. Reay and John D. Andrews Loughborough Unversty, Loughborough, Lecestershre, LE 3TU. Abstract The use of Bnary Decson Dagrams (BDDs) n fault
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 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 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 informationRobust Design of Public Storage Warehouses. Yeming (Yale) Gong EMLYON Business School
Robust Desgn of Publc Storage Warehouses Yemng (Yale) Gong EMLYON Busness School Rene de Koster Rotterdam school of management, Erasmus Unversty Abstract We apply robust optmzaton and revenue management
More informationCOSC 6385 Computer Architecture.  Pipelining (II)
COSC 6385 Computer Archtecture  Ppelnng (II) Sprng 2011 Performance evaluaton of ppelnes (I) General Speedup Formula: Tme Speedup = Tme = IC IC ClockCycle ClockClycle CPI CPI For a fxed applcaton lets
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 informationLesson 2 Chapter Two Three Phase Uncontrolled Rectifier
Lesson 2 Chapter Two Three Phase Uncontrolled Rectfer. Operatng prncple of three phase half wave uncontrolled rectfer The half wave uncontrolled converter s the smplest of all three phase rectfer topologes.
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 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 informationSIMULATION OF INVENTORY CONTROL SYSTEM FOR SUPPLY CHAIN PRODUCER WHOLESALER CLIENT IN EXTENDSIM ENVIRONMENT
SIMULATION OF INVENTOY CONTOL SYSTEM FO SUPPLY CHAIN PODUCE WHOLESALE CLIENT IN EXTENDSIM ENVIONMENT Eugene Kopytov and Avars Muravjovs Transport and Telecommuncaton Insttute, Lomonosov Street, ga, LV09,
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 informationWe are now ready to answer the question: What are the possible cardinalities for finite fields?
Chapter 3 Fnte felds We have seen, n the prevous chapters, some examples of fnte felds. For example, the resdue class rng Z/pZ (when p s a prme) forms a feld wth p elements whch may be dentfed wth the
More informationPAS: A Packet Accounting System to Limit the Effects of DoS & DDoS. Debish Fesehaye & Klara Naherstedt University of IllinoisUrbana Champaign
PAS: A Packet Accountng System to Lmt the Effects of DoS & DDoS Debsh Fesehaye & Klara Naherstedt Unversty of IllnosUrbana Champagn DoS and DDoS DDoS attacks are ncreasng threats to our dgtal world. Exstng
More informationQuality Adjustment of Secondhand Motor Vehicle Application of Hedonic Approach in Hong Kong s Consumer Price Index
Qualty Adustment of Secondhand Motor Vehcle Applcaton of Hedonc Approach n Hong Kong s Consumer Prce Index Prepared for the 14 th Meetng of the Ottawa Group on Prce Indces 20 22 May 2015, Tokyo, Japan
More informationEstimating projects duration in uncertain environments: Monte Carlo simulations strike back
Estmatng proects duraton n uncertan envronments: Monte Carlo smulatons strke back Stefana Tatton 1, Massmlano M. Schrald ( Tor Vergata Unversty of Rome, Dept. of Enterprse Engneerng, Va del Poltecnco,
More informationAnts Can Schedule Software Projects
Ants Can Schedule Software Proects Broderck Crawford 1,2, Rcardo Soto 1,3, Frankln Johnson 4, and Erc Monfroy 5 1 Pontfca Unversdad Católca de Valparaíso, Chle FrstName.Name@ucv.cl 2 Unversdad Fns Terrae,
More informationLevel Annuities with Payments Less Frequent than Each Interest Period
Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annutymmedate 2 Annutydue Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annutymmedate 2 Annutydue Symoblc approach
More informationEuropean Journal of Operational Research
European Journal of Operatonal Research 221 (2012) 317 327 Contents lsts avalable at ScVerse ScenceDrect European Journal of Operatonal Research journal homepage: www.elsever.com/locate/ejor Producton,
More informationOptimized ready mixed concrete truck scheduling for uncertain factors using bee algorithm
Songklanakarn J. Sc. Technol. 37 (2), 221230, Mar.Apr. 2015 http://www.sst.psu.ac.th Orgnal Artcle Optmzed ready mxed concrete truck schedulng for uncertan factors usng bee algorthm Nuntana Mayteekreangkra
More informationChapter 7. RandomVariate Generation 7.1. Prof. Dr. Mesut Güneş Ch. 7 RandomVariate Generation
Chapter 7 RandomVarate Generaton 7. Contents Inversetransform Technque AcceptanceRejecton Technque Specal Propertes 7. Purpose & Overvew Develop understandng of generatng samples from a specfed dstrbuton
More informationEVERY year, seasonal hurricanes threaten coastal areas.
1 Strategc Stockplng of Power System Supples for Dsaster Recovery Carleton Coffrn, Pascal Van Hentenryck, and Russell Bent Abstract Ths paper studes the Power System Stochastc Storage Problem (PSSSP),
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 informationSmall pots lump sum payment instruction
For customers Small pots lump sum payment nstructon Please read these notes before completng ths nstructon About ths nstructon Use ths nstructon f you re an ndvdual wth Aegon Retrement Choces Self Invested
More informationII. PROBABILITY OF AN EVENT
II. PROBABILITY OF AN EVENT As ndcated above, probablty s a quantfcaton, or a mathematcal model, of a random experment. Ths quantfcaton s a measure of the lkelhood that a gven event wll occur when the
More information