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Joseph Berry
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1 5..1 EXPEDTNG A PROJECT o 'o-' 600 E Project durtion (dys) Figure 6-6 Project cost vs. project durtion for smple crsh problem. Using Excel@ to Crsh Project T" llt ffiiii::#;#ltlti.*?*:j,'i#,rffi volved inl crshins. occsionllyrnurry ur. i""otu"j' tt- 6E"r*A;r]Fi"n become quite tedious. n this section, we demonstrte how use of Excel@ spredsheets cn gret ivities to crsh so tht project is completed To illustrte this, the dt ;6GTTGG--tt.---into-t-hespredsheetshown in Tble 6-2.Figure 6-7 shows the network digrm for this project bsed on the ctiv- 5 > E ]: do mke one chnge to the dt in-tqble 6'1. Nmely, here cn hndle not t ll, we mke this chnge to simplify our ensuing discussion At the top of the spredsheet is entered nd the clcugiven in Tble by dividing the incrementl cost of crshing the ctivity s much s possible by the mximum number of dys the ctivity cn be shortened. n column H the mximum mount ech ctivity cn be crshed is clculted by subtrcting the crsh durtion from the norml durtion. Column corresponds to our decision, nmely, how much to crsh ech ctivity. Then bsed on the vlues entered in column, the cost of crshing ech ctivity is clculted in column J. Finlly, in column K the ctul time to complete the ctivity is clculted by subtrcting the mount node in the networ occurs t ttme zero. you ttme ech event occurs to ensure tht the ode 1 is excluded becuse we s' see. we need to keep trck of the..- reltionships-in the network

n this section, we demonstrte how use of Excel@ spredsheets cn gret ivities to crsh so tht project is completed To illustrte this, the dt ;6GTTGG--tt.---into-t-hespredsheetshown in Tble 6-2.

2 r iw\fi h'rt CHAPTER 6 / ALLOCATNG RESOURCES TO THE PROJECT Tble 6.2 ple "crsh" Problem in Tble 6-1 Trnsferred to n Excel@ spredsheet e{il ${r 6' w :(F6-E6y(C6-D6) =C6-D6 {copy to cells H7:H12} =6*G6 {copy to celis J7:J l2} :C6-16 {copy to cells K7:K12} {copy to cells GZ:G12} digrm re not violted. we need to mke sure tht node 4 does not occur A-' until fter node 2 occurs. to rte how Excel's@ Solver cn be used to rmine which c. tivities to crsh so tht the entire project is completed withi the minimum costs. To begin, select Tools from the men., bind then Solve#,n. rr.*i rn".,u tht ppers. The solver Prmeters dilog box is now displyed (see Figure 6-8). The Figure 6'7 problem. AOA network of smple "crsh"

cells K7:K12} {copy to cells GZ:G12} digrm re not violted. we need to mke sure tht node 4 does not occur A-' until fter node 2 occurs.

3 6.1 EXPEDTNG A PROJECT. 189 Figure 6,8 Excel's Solver@ loded with dt nd constrints from crsh problem. Set S"t Treet fr"g"fg[eld Cell refers to the cell in the spredsheet tht we would like to either mlnlmlze or mxrmrze. n our cse, we would like tggre]f)t he totl cost of completing the project, which is clculted in cell B2. To specify this, we - enter 82 in the Set Trget Cell field nd then select the Min rdio brtton. Next we tell Excel{wht cells it cn chngel in order to find the solution with the minimumtotlprojectcffiedsheetshownintb1e6.2,thev. lf iii,:l;:l:',n:i"':h:"f ;':"'5;xi::'?ifr il'*hi+til'::il,t:'*1j ure 6-8, these rnges were entered in the $y Chnging Cells field. onweneedtoenteristhelimittionsorconstrintssso. cited with this sitution. Perhps the most obvious constrint is tht we wnt to complete rhe project within 20 dys (cell B1). Since node 6 (cell B21) corresponds to the event of the project being completed, we cn specify this constrint s follows: {-nzi=fl Another importnt set of constrints is needed to mke sure we don't crsh n c' tivity more thn the mximum number of dys tht it cn be crshed. Constrints to ensure this could be entered s follows: Altemtively, by e sheet's bility to del w constrint s 16 < H6 (ctivity ) 7 < H7 (ctivity b) B < HB (ctivity c) 19 < H9 (ctivity d) 10 < Hl0 (ctivity e) 11 < H11 (ctivity f) tz = Hlz (ctivity g) ploying shorthnd pproch tht cpitlizes on spred' h rnges, these seven constrints could be entered s single <H6:H7 Another ser of constrints is needed to mke sure tht the precedence reltionships specified in the network digrm re not violted. We do this by keeping trck of the

n our cse, we would like tggre]f)t he totl cost of completing the project, which is clculted in cell B2. To specify this, we - enter 82 in the Set Trget Cell field nd then select the Min rdio brtton.

4 19O o CHAPTER 6 / ALLOCATNG RESOURCES TO THE PROJECT event times of the nodes. For exmple, the event time of Gnnot occur fter unril ctivity hs been completed (ssuming,tt"i rtr" pr":"ffit.,, t time zero). time to The complete ctivity is its norml time less th" time it is Since crshej cell 817 corresponds to the event time for.,od" j, *"iffi"ri."lly ".o,r.riof we could this enter constrint s follows, Bl7>C6-t6 This constrint sys tht the event corresponding to node 2 cnnot occur until tivity fter c- hs been completed. constrintt fo@ffi.re$$could be creted in similr fshion. For theconsrrintsf exmple, or(fi 6Gj-6iiff?]-o-'.rldb. B1B>C7_t7 B19>B17+CB_8 The constrint for node 4 sys in effect tht the event corresponding to node occur 4 cnnot until fter the evenr coffesponding to node 2 (cell Bftj-*.,r^ plus the tkes time to it complete ctivity c. Moving on to node 5, nore tht this node hs.two_ rrows pointing to it. with A more node thn one rrow poinring to itrvill riri.uirr, for "..!_g ech Thus rrow. we need the following two constri",, f".6if"t) B20>B17+C9_t9 B2O>81B+CiO_10 This first constrint sys tht node 5 (cell B20) cnnot occur until fter node Z curred (cell hs oc- 817) plus the mount of time it tkes ro.o*pt.* u.,irriry d. The constrint second sys tht node 5 cnnot occur until fter node 3 (cell B1B) hs o..rrrr" the.qmoueof-time it tkes ft,r, to complete crivrry e. Nd9r hndled in similr wy to node 5 s follows: 821 >B19+C11 -tl1 B2>820+Ctz-t} Finlly, since it does not mke sense to crsh n ctivi nor does it mke sense for 4g5[to_oqcur t tdleg zero, we dd con- Using Excel's@ shorthnd o > 0 B17:B21 > 0 n this exmple we ssume thut th. ii"itioiii-b" Gt rr"ction of dy. f th,;the ctivities "-" :i ::Y:1:"^"1?:."_T: hd to t".r"rr,.j l'uhot. "irr,o dy ll, or not we could t esily dd dditionr constrints to the model ro r"r"., it ii;i#;:::'"' To enter these constrints, select the Add button i",rr. sofj"lt to th. Constrints section of the Solver Prmeters dilog tro*. rne entire set ot.orrrtruints needed follows: is s ( nn =nt < H6:HL2 817>C6-t6 nrs >c7 -t7 819>817+CB _B

riof we could this enter constrint s follows, Bl7>C6-t6 This constrint sys tht the event corresponding to node 2 cnnot occur until tivity fter c- hs been completed. constrintt fo@ffi.

5 EXPEDTNG A PROJECT i gzo>b1z+c9-19 B20 > BlB + C10-10 BZr > B19 + Cl1-11 nzr > B2o + cr?. - rrz :112 > 0 (B17:B21 > 0 After entering these constrints, the Solver Prmeters dilog box ppers s shown in Figure 6-8. Before finding the lest costly wy to crsh the projectdown to 20 dys' selejt the Qptions... brriton nd click on the Assume Liner Model check box nd then click bk. No* to find the lest cost solution, select the Solve button in the Solver prmeters diloe box. As is shown in Tble 6-3, Excel@ identified the sme solution Tbf e 6-3 Excel@ Spredsheet for Crsh Problem, 20-Dy lolution nd Cost (F6-E6V(C6-D6) {copy to cells G7:G12} -D6 {copy to cells H7:H12} :16*G6 [copy to cells J7J l2] =C6-16 {copy to cells K7:K12)

Before finding the lest costly wy to crsh the projectdown to 20 dys' selejt the Qptions... brriton nd click on the Assume Liner Model check box nd then click bk.

6 192 o CHAPTER 6 / ALLOCATNG RESOURCES TO THE PROJECT ; 700 ; 650 E ooo '6' o F Figure 6-9 Cost/durtion grph 3:'.:rr,T crshing Project ( -.,- Fst-Trcking Project tht we obtined erlier using the mnul pproch. Specificlly, the solution suggests crshing ctivity by one dy (cell 16). This results in completing the project by dy 20 (cell 821) t totl project cost of9430 (cell 82). Hving set up the spredsheet, we cn now quickly nd esily evlute the cost of ffi ffi tilru::ili:il:;.tt::,f;,':x.,n'l.':iti;i:r#u, :T #ryj;ffii".g. f, n ddition to crshing project in order to expedite it, project my lso Used primrily in the construction industry, the term refers tone of leted before the building phse is strted. Uzully design n phtt ; !v vsqrlvs ie finished before ;i --^---^-b r^rqv! the building is strted, sotetting them overlp reduces project durtion-if the fct tht design nd plnning re incomplete does not result in significnt mount of rework nd ghnge orders during the building phse. lrge proportion number of chnge orders in fst-trcked construction projects is not significntly different from tht for similr projects tht were not fst-trcked (Kurtulus nd Nrul, l9b2'). \7hen tsk durtions re estimted, n ssumption is mde tht tsk resources re set t "norml" levels. This is the "stndrd prctice" ssumption. Trditionlly, CPM project durtion estimtes lso include "crsh" estimte together with estimtes of the crsh time nd the resources required to shorten the durtion of project ctivities. By selectively choosing which ctivities to crsh nd by how much, we cn determine the minimum cost for ll possible project completion times. Both mnul nd spredsheet methods re illusffted. ffind REsouRcE LoAptNG From the first dy on the job, the PM is concemed with resowrceloding. Resource loding refers to the mounts of specific resources tht re scheduled for use on specific ctivities or projects t specific times. t usully tkes the form of list or tble. Figure 6'10 is n MSP generted ction pln nd Gntt chrt of project imed t producing

This results in completing the project by dy 20 (cell 821) t totl project cost of9430 (cell 82). Hving set up the spredsheet, we cn now quickly nd esily evlute the cost of ffi ffi tilru::ili:il:;.

Experiment 6: Friction

Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht