Decison Makig Under Certainty-Analytic Hieachy Pocess (AHP)
struced: Cel reference to he altenaive UA must be coumn-fixe coumn-fixedd (namey (namey,, $L8 and $N8) whereas oher efeences must be row-and-column-fixed (namely $L$4 and $L$5) Te vaidity of he formulas requires ha the (coumnfixed) iv' weighs of each matrix appear in he same coumn wih no inervening emp celsFo cels Fo exampe in Figue 143 the hree ARweighs in coumn L canno be broken beween wo coumns Te same applies o the AL-weighs in coumn N. On he oher hand thee are no esticions on he pacement of the A-weights because because tey tey are wand columnfixed in he formula You can embelish the formua o capture he names of the aenatives direcly Hee is how the formua for atenaive UA shoud be eneed
=$K&&TE($$*$$5N "##
Noe that the names of he aernatives are soed in K8K0 I is you responsibii responsibiiyy o make sue ha hese ces contain he names of he aenatives Te procedure for evauating aenaives can be exended readily o any numbe of hierarchy eves Once you develop he formula corectly for fo r the first atenaive the same formua is appicable o he remaining aernatives simpy by copying it ino (same coumn) succeeding rows. Jus remember ha al cel eferences in the fomua must be ow-andcolumnfixed excep for references o he altenatives which mus be coumnfixed onlyPobem 1 Set 41b asks you to deveop deve op he fomua for a hee eve poblem
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POBLE SET 48 Consider the data of Problem 1 Set 14.1a. Copy the weights logicaly nto the solution summary section o the spreadsheet c4AHxls, and then develop the formula or evaluating the irst aternative UA and copy it to evaluate the remaining two aternatives. The personne department at C& has narrowed the search for a prospective employee to three candidaes: Steve (S), Jane and Maisa M The final selection is based on three riteria personal interview experience (E), and reerences R The department uses matrix given beow) to establish the preferences among the three criteria. Ater interviewing the three candidates and compiing the data regarding their experiences and reereces the matrices £ and are constructed Which o the three canddates should be hired? Assess the consistency o the data
1 ( A=�! ' ) �( l ! ( ) t
E
R
J M
1
5
1
�
3 1
Ml4 5 J M
J M 1 1 3 = J 3 � 1 M!2 1 M1
2You are encouragd to use speadsh ch14AHPxls o vrify or cacaos.
12
x + x X +
Deision Mking Unde Risk
epesen e w alenaves nvesing n scks Nex, e w bances emanaing m cance evens 2 an 3 epesen e "bll an e "bea makes wi ei especve pbabies an pays Fm Fge 43, e expece -yea ens e w alenaives ae F sck F sck
000
00
6
- 2000
6
00
4 = $2,200 4 100
Base n ese cmpans y ecsn s inves in sck A._ n e emngy ecsin ey e "b an e "bea makes n e peceng example ae eee as ss nur wse cances ccence ae pbabilsic 6 vess 4) n genea, a ecsn pblem may incle n saes nae an alnaivs If p > 0 is e pbabliy ccence sae nae j an ; is e pay alenave gven sae nae j , 2, . j 2, . n) en e expece pay alenave is cmpe as
EV; By def ntion, p1
=
p
P2 + . .
·
+ + + ;p
Pn
m
2, ,
;
n
= 1.
e bes aenave s e ne asscae w EV max{EV ; } E minEV} epenng, especvey, n wee e pay e pbem epesens p incme) ss expense)
OBLE SET 4 You have been invited to pay the Fortune Wheel game on teevione wheel operate eectronicaly with two buttons that prouce har H or soft (S) spn o the wheeThe wheel tel i vie into white () an re R hal-circle region. You have been tol that the whee is esigne to top with a probability of 3 in the white region an .7 in the re regionThe payof you get or the game i
W R s
3
Draw the asocate eciion tree an pecy a coure of action Farmer McCoy can plant either corn or oybean. The probabilites that the next harvet prces of these commotie wil go up tay the same or go own are 25, 3 an 45 respectively If the prce go up the corn crop wl net 3, an the oybean wl net 1 I the prce remain unchange McCoy will (barely break even But i the prce go own the corn an oybean crop wl ustain loses o 35 an 5 repectivey Repreent McCoy' probem as a ecision tree. Which crop hou McCoy plant? You have the chance to invet in three mutual uns: utility aggresive growth an globaThe vaue o your invetment wl change epening on the market conton. ere a 1% chance the maret wll go own 5% chance it wl remain moerate an
12 8
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9.
a b
ecson Mkn Under Rsk
51�-
Draw t csn tr r t gam. D y vr cm t aa n ts gam? Acm Manactrng rcs lts wgt wt 8%, 1% 12%, an 4% ctvs accrng t t rsctv rbablts 3 25, an 05 Tr cstmrs an ar cntract t rcv batcs wt n mr tan 8%, 12% an 14% ctvs rsctvy. Acm wll b naz $1000 r rcntag nt t rcntag ctvs s gr tan sc n t cntract Cnvrsy, slyng gr qalty batcs tan rqr csts Acm $500 r rcntag ntA ssm tat t batcs ar nt nsct br smnt a Draw t asscat csn tr b Wc t tr cstmrs sl av t gst rrty t rcv tr rr? Trtar ans t n a nw lant n Aransas. T cmany can n a -sz ant n a small-s lant tat can b xan 2 yars atr g man cntns rvaT tm rzn r t csn rblm s 10 yarsTrtar stmats tat t rbabty r g an lw mans vr t nxt 10 yars s 75 an 25 rsctvy cst mmat cnstrctn a larg ant s $5 mln an a sma an csts $1 mlln. Exansn a small lant 2 yars rm nw csts $42 mllnT ncm rm t ratn vr t nxt 10 yars s gvn n t llwng tab:
4
B,
High demand Low demand
Alteraive
Estmad annal ncom (n $1000)
Fl-szd lan now Smallsd lant now Eandd an n yars
000 50 900
300 00 00
(a)
Dvl t asscat csn tr gvn tat atr 2 yars Trtar as t tn t xan r nt xan t small lant b Dvl a cnstrctn stratgy r Trtar vr t nxt 10 yars. (Fr smlcty, gnr t tm va mny.) Rwr Prbm assmng tat t annal ntrst rat s 10% an tat t csns ar ma cnsrng t tm va mny. Note: Y n cmn ntrst tabls t slv ts rbm) Rwr Prbm assmng tat t man can b g mm an w wt rba bts 2 an 1 rsctvlyExansn a small lant wll ccr ny man n t rst 2 yars s gT lwng tabl gvs t annal ncm Ignr t tm val mny
0 7
Alterative
Flsd lan now Small-sd an now Eandd ant n yars
High demand Medium demand w demand Esmad annal ncom n $1000)
1000 400 00
500 80 600
300 10 00
nray Elctrc C ss a t 20 rcs t srvc ts ctrc ntwr cm any wants t vl a rc rvntv mantnanc r t t. T rbablty a brawn n yar 1 s zrr r 2, t brawn rbabty s 03 an t
