PROJECT ACTIVITY ANALYSIS WITHOUT THE NETWORK MODEL. E. Munapo

Transcription

1 ROJEC CIVIY NLYSIS WIHOU HE NEWORK MODEL E. Muapo Departet of Decsos Sceces Uversty of South frca, South frca BSRC hs paper presets a ew proceure for aalysg a aagg actvty sequeces projects. he ew proceure eteres crtcal actvtes, crtcal path, start tes, free floats, crash lts, a other useful forato wthout the use of the etwork oel. Eve though etwork oels have bee successfully use project aageet so far, there are weakesses assocate wth the use. etwork s ot easy to geerate, a ues that are usually assocate wth t ake the etwork agra coplex a uy actvtes have o eag the orgal project aageet proble. he etwork oel for projects ca be avoe whle stll obtag all the useful forato that s requre for project aageet. What are requre are the actvtes, ther accurate uratos, a ther preecessors. OSOMMING De avorsg beskryf uwerwetse etoe vr e otleg e bestuur va e sekwesële aktwtete va projekte. De voorgestele etoe bepaal krtese aktwtete, e krteke pa, aavagstye, spelg, verhasg, e aer groothee soer e gebruk va etwerkoel. De etoe fuksoeer bevrege e praktyk, e osel e astratewe ropslop va e trasoele etwerkoelle. South frca Joural of Iustral Egeerg May 00 Vol (): 8-9

2 . INRODUCION Networks have bee use successfully project aageet sce the 950s. Networks graphcally show the total aout of te eee to coplete a project, the sequece whch the tasks ust be carre out, the crtcal tasks that ee close atteto, a whch tasks ca be carre out sultaeously [] [4] [6] [8]. project aager ca also shorte the project urato by ag ore resources to certa tasks a attept to get the oe faster. he etwork agra has prove to be a useful tool for scheulg actvtes a project [] [7]. Whe uexpecte crcustaces cause slght chages uratos for exaple, a worker strke, resources supply probles, or uprectable weather such probles requre the rescheulg of actvtes a rap coputato. Chagg etworks are calle protea etworks [3], a for very large projects a slght elay ecsoakg ca be costly. he etwork agra ca be avoe whle stll obtag the sae scheulg ecsos. hs paper presets a ovel proceure for aalysg a aagg actvty sequeces projects. he proceure eteres crtcal actvtes, the crtcal path, start tes, free floats, crash lts, a other useful forato wthout usg a etwork oel. Eve though the etwork oel has bee use successfully so far project aageet, there are weakesses assocate wth t. etwork s ot easy to geerate, a ues that are usually assocate wth t ake the etwork agra coplex a they have o eag the orgal project aageet proble. Oe ca avo the etwork oel for projects a stll get all the useful forato that s requre for project aageet. What are requre are the actvtes, ther accurate urato estates, a ther preecessors. he propose proceure chages are oly corporate to the affecte actvtes; uaffecte actvtes are ot cosere. s a result of ths, techque calculatos are raply carre out, resultg teous ecsos. Coser a gve actvty show able below., ts r preecessors, a a accurate urato estate, as ctvty reecessor ccurate urato estate,,..., r,...,, r,,..., r,...,, r able where =,,...,,..., he ata able ca be use to etere the crtcal actvtes, crtcal path, start a e tes, free floats, crash lts, a other useful forato that s requre for project aageet wthout the use of a etwork agra.. GENERING HE LES END IME ( ) FOR CIVIY he latest e te ( ) for actvty ( ) s gve by [, r ] = ax,..., + () 8

3 where s the e te for j th of the r preecessors. I ths case j =,,..., r j 3. UDING LES END IMES Ieately after obtag ax, where s gve by all the preecessors ust have the sae e te value of [, ] ax,..., ax = r () he process s calle upatg, a chages the latest e tes of all preecessors to. 4. CRIICL CIVIIES ax he actvty gvg the largest e te ( ) s the crtcal actvty. he set of crtcal actvtes chroologcal orer s the crtcal path. hs path s coveetly trace fro the botto of the table, gog backwars. he latest start te of a actvty s the latest e te of ts preecessor. 5. GENERING HE ERLIES END IME EE FOR CIVIY he earlest e te EE for actvty s geerate fro EE where s s s [( ),( ),...,( )] = EE s EE s EEk sk (3) s s EEj a sj are the earlest e te a urato of the successor actvty j =,,..., k he upate e tes a crtcal actvtes are show respectvely.. able. 6. CRSHING CIVIY DURIONS Crashg refers to a techque use project aageet for the purpose of ecreasg the total project urato. Crashg s oe after a careful a thorough aalyss of all actvtes, ther sequeces a portace, so as to obta the ost coveet urato at the least atoal cost. here are several approaches to crashg a project scheule. Oe of these s the u cog weght label (MIWL) etho propose by Muapo et al. [5]. hs etho selects oly those actvtes that are affecte by crashg, a uses the to calculate the crash lt. It s effcet, but t oes ot ake start a e tes realy avalable, a t s also rectly base o the project etwork agra. he other a ost coo approach s the use of the sallest free float selecte fro all the ocrtcal actvtes as the crash lt. serous rawback of ths approach s that t uses all the ocrtcal actvtes to etere the crash lt. Soe of these ocrtcal actvtes are ot affecte by the crashg, a as a result ay gve very sall values. he techque propose ths paper s effcet, t selects oly those actvtes that are affecte by crashg, a t uses the to calculate the crash lt. Both actvty start a e tes are also ae realy avalable. Suppose actvty s selecte for crashg, a actvty s oe of the teral crtcal actvtes. he oral project urato ( ) s gve by or 83

4 ctvty reecessor ccurate urato estate r,,..., r r r,,..., r r r,,..., r r r,,..., r r Suppose actvty s crtcal: the t s eote by a astersk, as follows: r *,,..., r r or able = (4) he earlest e tes are upate as show able 3. ctvty reecessor ccurate urato estate r,,..., r r,,..., r * r,,..., r * r,,..., r 84 able 3

5 ssue the crash lt to be cl. he urato for the crtcal actvty cl uts, a the ecessary recalculatos ae are show able 4. s reuce by ctvty reecessor ccurate urato estate r,,..., r cl *,,..., r r cl cl *,,..., r r,,..., r r able 4 where j s the ew latest e te for the j th preecessor of. he project urato ters of cl, ( ), becoes cl cl cl = (5) hs urato s also equal to the project urato gve by the seco best crtcal path. he seco best crtcal path s the crtcal path that s obtae after gorg actvty. If the ew project urato s gve by, the cl = p or ew ew (6).e. cl = (7) or ew Whe eterg the ew crtcal path, there s o ee to start fro the frst oe. Soe of the actvtes are ot affecte by ths chage, a so they ee ot be use the coputatos. 85

6 7. NUMERICL ILLUSRION he forato gve able 5 s use to aswer the followg questos. 9 By usg actvty latest e tes, show that s crtcal, hece etere the project 9 urato ( ). Suppose actvty s selecte for crashg, copute the crash lt. or ctvty reecessor Durato ( ays) , , , , 0 30 able 5 7. Latest e tes he latest e tes are geerate as show able 6. he crtcal actvtes are: (8) Selecto of the crtcal actvtes s oe by startg fro the botto of able 6. he project urato s gve by ays (9) or =

7 ctvty reecessor Durato ( ays) * * , *, , *, able 6 87

8 7. Upatg the latest e tes able 7 s obtae by upatg the latest e tes. ctvty reecessor Durato ( ays) * * , *, , *, able 7 88

9 7.3 Earlest e tes he earlest e tes are geerate as show able 8. ctvty reecessor Durato ( ays) * * , * , , * , able 8 9 Fro able 6 the crtcal actvty, selecte for crashg, s reuce by cl, a recalculatos are oe ters of cl as presete able

10 ctvty reecessor Durato ( ays) * * , cl * , , cl * cl 0 450, cl able 9 he project urato ( ), whch s ters of cl, s gve by cl or = ( 750 cl) ays (0) he seco-best crtcal actvtes a ew project urato are etere by gorg 9 actvty, as presete able 0. 90

11 ctvty reecessor Durato ( ays) * * , , * , *, able 0 he ew project urato ( ew ), whch s also the urato for the seco-best crtcal path, s gve by ew = 670 ays () cl = or = = 80 ays () ew 9

12 9 Note: he oly actvtes that are use crashg actvty, out of the gve actvtes, are 8. CONCLUSIONS 0 a. he rest of the actvtes are ot affecte. he proceure presete ths paper eteres crtcal actvtes, crtcal path, start a e tes, free floats, crash lts, a all other useful forato wthout the use of a etwork oel. he project etwork agra oel s ot easy to raw, a ay case s ot ecessary. ll the forato that s requre for ecso-akg project aageet ay be effcetly extracte fro the avalable ata wthout the use of a etwork oel. Whe coputg the crash lt, oly a fracto of the actvtes s requre. Calculatos o ot ecessarly have to start fro the frst actvtes, a the ew start a e tes are always realy avalable. 9. REFERENCES. rora, H. & Kuar, S (k+) th shortest path fro k shortest paths a etwork, Gupta, O.. (e.), Matheatcs toay, C Vaya Saa Nh rust, heaba, Vol -, pp Busch, D.H. 99. he ew crtcal path etho, robus ublshg Copay, Chcago. 3. Kuar, S Iforato recyclg atheatcal ethos for protea systes: path-way approach, South frca Joural of Iustral Egeerg, Vol. 6, No., May 005, pp Vre, L. & ruper, M roject ecsos: he art a scece, Maageet Cocepts, Vea, V. 5. Muapo, E., Joes, B.C. & Kuar, S u cog weght label etho a ts applcato CM etworks, ORION, Vol. 4 (), pp O Bre, J.J CM costructo aageet, 5 th e., McGraw-Hll, New York. 7. Wsto, W.L Operatos research-applcatos a algorths, 4 th e., hoso/brooks/cole, Belot, Calf. 8. Woolf, M.B Faster costructo projects wth CM scheulg, McGraw-Hll, New York. 9