Network Techniques - I. t 5 4

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Horatio Washington
5 years ago
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1 Performance:Slide.doc Network Techniques - I. t s v u PRT time/cost : ( Program valuation & Review Technique ) vent-on-node typed project-model with probabilistic (stochastic) data set as weights (inp) and time potentials (outp) PM time/cost : ( ritical Path Method ) ctivity-on-arrow typed project-model with discrete (deterministic) data set as weights (inp) and time potentials (outp) UT TM / ngineering Programs in nglish / -

2 Performance:Slide.doc PRT/PM Graph-restrictions t st π s s π t t t tv t ut π v v t su "Network" : onnected weighted directed graph with a single source and a single sink but with no loops and no negative weights. "One-to-one correspondence" : ach identified particle is presented in the model by its only single representative "dges as related pairs of nodes" : u π u t uv etween two nodes at maximum one single directed edge (arrow) is allowed UT TM / ngineering Programs in nglish / -

3 Performance:Slide.doc Program valuation & Review Technique (PRT) 98 : US Navy, Polaris Program, Farard Nodes : dges : events, states, "mile-stones", phases of progression ctivities ("sub-projects") with closely not identified (technical) contents (R&) Parameters (weights) : ims : Probabilistic variables ("time-spans") of b distribution based on triplex estimates Predict timing of milestones and overall execution time of a project, together with indices of uncertainty ("deviation"). To check feasibility of a Schedule. UT TM / ngineering Programs in nglish / -

4 Performance:Slide.doc P "Probability" / b distribution / P max T e = T min+ T m + T max n = s = ( T max - T min ) T min a T m m T e T max b T P "Probability" / Gaussian standard distribution / P max s s.98 T e = T m s s T UT TM / ngineering Programs in nglish / -

5 (PRT) Problem: What is the probability of matching the tu Schedule of the project below? Performance:Slide.doc I (a-m-b) m e ; n (--7) ; /9 (--7) ; /9 (-7-8) 7; /9 (--) ; /9 (--) ; /9 G (--) ; /9 F (--9) ; /9 9 9 H (--) ; /9 I (--) ; /9 µ e = a + m + b ν = σ = ( b - a ) µ T = ν T = /9 UT TM / ngineering Programs in nglish / -

6 Performance:Slide.doc P entral limit distribution / Gaussian standard distribution / P max σ σ z σ µ S = µ T = σ σ T Z = µ S - µ T - = = -. νt /9 P 9 % Z P Z P UT TM / ngineering Programs in nglish / -

7 Performance:Slide7.doc ritical Path Method (PM time ) 97 : US,. I. du Pont de Nemours, James. Kelly, Morgan R. Walker Nodes : links, relations, direct precedences dges : ctivities ("sub-projects") with well identified (technical) content, direct precedences (see:"dummy activities") Parameters (weights) : ctivity durations, elapsed times and deadlines ( deterministic variables ) ims : Identify project elements significant ("dominant"/"critical") in timing of a project. etermine mile-stones and deadlines for execution. Indicate degree of freedom ("float") of a schedule for parts- and total of a project. UT TM / ngineering Programs in nglish / -

8 Performance:Slide8.doc PM / PRT graph-structure - operative informations - F I 7 G H List of direct precedences G I F G,,I < H,G <,I,H < I H H F <,G G I I G <,,I H I <,H Operative informations UT TM / ngineering Programs in nglish / -

9 Performance:Slide9.doc (PM time ) Problem: duration () () 7 () () (possible) earliest (acceptable) latest F() (8) 8 8 I S F LS LF TF FF F IF 7 "ritical Path" : Sub-graph of a graph constituted by nodes and dominant edges between at which the earliest schedule equals to the latest one. ( " project elements with no float " ) Sub-graph constituted by the longest paths between the only source and the only sink. UT TM / ngineering Programs in nglish / -

10 Performance:Slide.doc "Total Float" ( of an activity ) : cceptable increment in duration of an activity ( or acceptable delay of its start ) with not jeopardizing the early finish of the project assuming that all its (dominant) predecessors can be performed by their early schedules. ( " no delay before, maximum delay after " ) "Free Float" ( of an activity ) : cceptable increment in duration of an activity ( or acceptable delay of its start ) with not jeopardizing the early schedule of any activity assuming that all its (dominant) predecessors can be performed by their early schedules. ( " no delay before, no delay after " ) "onditional Float" ( of an activity ) : cceptable increment in duration of an activity ( or acceptable delay of its start ) with not jeopardizing the early finish of the project assuming that all its (dominant) predecessors can be performed by their late schedules. ( " maximum delay before, maximum delay after " ) "Independent Float" ( of an activity ) : cceptable increment in duration of an activity ( or acceptable delay of its start ) with not jeopardizing the early schedule of any activity assuming that all its (dominant) predecessors can be performed by their late schedules. ( " maximum delay before, no delay after " ) ( Non-negative values interpreted only! ) UT TM / ngineering Programs in nglish / -

11 Performance:Slide.doc PM cost ( PM cost model ) Project osts Indirect irect Tmin ctivity / Sub-project irect osts ST Tmax ost Slope T min T max T UT TM / ngineering Programs in nglish / -

12 Performance:Slide.doc (PM cost ) Problem : What is the minimum of "direct" cost of the project below associating an overall execution time not longer than tu? I F G Normal time cost 8 8 rash time cost S d F G () () d () () 7 () 7 F() G() () () d () () () F() G() = + S = 9 + = 97 = + S F = 97 + = 8 UT TM / ngineering Programs in nglish / -

13 Performance:Slide.doc max Tmin irect osts of a Project / PM cost / min Tmin max Tmax min Tmax max min T min Optimal Project uration - Minimum Overall ost - T max ST Overall min Indirect irect T opt ST UT TM / ngineering Programs in nglish / -

14 Performance:Slide.doc PM time+ Problem: PM difficulties with overlapping Solution: Parameters on "dummy activities" ( t ) ( τ ) ( t ) ( τ ) ( τ ) ( t ) ( τ ) Negative parameters still forbidden. Further problems with open networks and fixed durations UT TM / ngineering Programs in nglish / -

15 Performance:Slide.doc (PM cost ) Problem* : What is the minimum of "direct" cost of the project below associating an overall execution time not longer than tu? I Normal time cost rash time cost S () () () () () () () () () () = + S = + = = + S + = + =? UT TM / ngineering Programs in nglish / -

16 Performance:Slide.doc (PM cost ) Problem* : What is the minimum of "direct" cost of the project below associating an overall execution time not longer than tu? I Normal time cost rash time cost S () () () () () () () () () () = + S = + = 7 ( > ) = + S = 7 + = 9 ( < )! UT TM / ngineering Programs in nglish / -

A scheme developed by Du Pont to figure out

CPM Project Management scheme. A scheme developed by Du Pont to figure out Length of a normal project schedule given task durations and their precedence in a network type layout (or Gantt chart) Two examples