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Spatial decision support for resource allocation. Integration of optimization, uncertaintyanalysis and visualization

Aerts, J.C.J.H.

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Citation for published version (APA):Aerts, J. C. J. H. (2002). Spatial decision support for resource allocation. Integration of optimization, uncertaintyanalysis and visualization. UvA.

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Download date: 30 Oct 2020

6.. Conclusion s

6.11 Sunimar \ of result s

Thee mam goal ut' this research w as to mteyralc optimization, uncertainix anal\ si> and visualizationn technique within an SDSS tor resource allocation problems. The S[)SS ih^s ( I ISS functionality to manage and process the spatial data and is mount to facilitate a discussionn on ill-struciured resource allocation problems. involving pnmarilv non-technical users.. Any ol ' the three techniques applied in this context should therefore meet the requirementt of hein:: iviinhiv. r<>ha\t and Minp/c.

Inn addition to main other studies in the area ot' spatial decision support, it is stated that an SDSSS for ill-structured resource allocation problems should be developed asiny a decision framework,, such as first described In Smion ( !')(>!)). 'I'llis thesis used a der i \a l i \e approach, thee framework for anaksis ( f I A i . tor structuraii: resource allocation problems (Fmdciscn andd Ouade 1 ^XA Rijsbcnnaii and Koudstaal IW)).

f l icc most common!) known natural resources arc water, land. o i l . natural LUS and coal. In thiss research, the locus was on the allocation of an area with multiple land uses, which is referredd to as multt site land use allocation (M l 1.'A i.

Answer ss to th e reseure h <|iit'stinn s

ll'iuitll'iuit I'S the \kiic <>j fhc uri <>t inii-^riiiin'j, dlS hii^af ofFim/i^tion tc<. huh/tiL^ within tin SPSS'.' SPSS'.'

M L l ' AA problems can be solved with optimization modeling, which Uses the concept oï dividingg an area into cells, defining the potential land use t\pes and searching the optimal distributionn lor these land uses across all cells subject to a set of criteria and constraints. An M l . l ' AA problem is usually complex and diff icult to soke. 'I he\ have the properu of a combinatoriall optimization problem, which is characterized In a ver\ large number ol" possiblee solutions.

(. 'omple\it\\ arises, tor instance, when spatial requirements are included in the model. \ n examplee o\^ such a requirement is to either maximize spatial i <.<m/\/(7/iV^ or spatial iuntiLi'iityiuntiLi'iity ot ' the allocated land use. ('otitiguitv requires all cells of equal land use to be

Conclusions Conclusions

c o n n e c t e d .. ( o i r ipac tncss requirement.- m c r c b encourage cel ls O; equal k ind i k e io he

a l l o c a t e dd next !>' one another , hut k m m u \ result 1:1 d i \ Hk>: patches < )p : inn /L i t I .M I mode ls

m c i u d u i i :: commun is requ i remen ts more d n k i c u l l In s o k e compared in M i m h i r m o d e k

m c u : d t n ee o i i k cnmp . i cmcss requ i rements . I h is research focused nu thukne: n i o d c k thai

i n c l u d ee u i i u p d v l i i c - r equ i remen ts K ' u i u x ' ihex , ;k ' easier to i m p l e m e n t as c o m p a r e d lo

c o n i m u i kk r equ i r emen ts . ,ir.u thus hcticr k k m the e.cr;ck;l eauh to i m d s imp le and runnel

t e c h n i q u e -- tor au S D S S

11 a:id n-c a l l o c a t i o n p r o b l e m s arc o i icn c h u r a c m n z e d b> ;hc c o n t l m t m e o b i c c m c s o| d = c

s takeho lde rss i n \ o h co. C o m m o m s know n c o m ! ml me oh |cc t i ses arc found w i i l l in

ó i ] U i a \ L ' : ^ k ' - .. on economic m l c r c - k amu im; ens l ronmcn ia ' . p ro tec t ion --toe e x a m p l e , to

dess c l o p akk .s t : aal of urban a i c a - w ith::] the \ i cn ius ot a nature resem c. 1 here tore , research

inn t in- , area a d d r c - ^ c - a una In ob iec f . . e app roach b\ dc \ c l o p m e o p t i m i z a t i o n m o d e k . w Inch

s m i u i t u n c o i i s hh n n n i i n i / e or m a x m n / c those oh m e l k e-, 1 i l k e seal el : toe used on

m i n i m i z i u uu dc \ c l o p m c r a costs ;uk l maxinuztme the compactness ot the a l located land i k e .

11 he ava i l ab le o p t i m i z a t i o n tcchaucucs ]or sob, me M i i A p rob lems mas be d m d e d in to

d i e u i i s t i c '' and d inea r u i tceer p r o e m i i i m i n ck l l IP) approaches. No te lhal the hulk o f the

l i t e ra tu ree in t i l ls area descr ibe n p i m i i / u t i o n t e c h n i q u e - toi soK me v ^ c / o - n c a l l ocu t i on

p r o b l e m - ,, i he c h a i i c m j c io i d n - l ' : . - k d e b ; laid '-\>'.\\ m develop; ; ïL I U-. o p t i m i z a t i o n

techn iquess as w el l as to sols e rclat is el;, u n e x p l o r e d nnn'n eve land use a l l oca t i on p r o b l e m s

H e u r i s t i cc approaches are robus t , las; and capable ok sob mu knee c o m b i n a t o r i a l p rob lems

suchh as M l I A - -but i hc \ do not euaruniee die o p t i m a l so lu t i on . I . xnmplcs arc S m i u k i l c d

. m n c a l m e .. ereeds euowmc: n h e o n l l r i i - and tabu search. So [a i . ihcre k l i t t le Inc ra lu re m

ww Inch S i m u l a t e d anneal im i has been spec i l ien I k app l i ed lo M l . I A p rob lems . ! he concept

id"" S i m u l a t e d annca l i ne o i a e m a l k o u n e s t r o m c h c n i k t r s and k -.een as a p r o m i s i n e

t e c h n i q u ee to x d c M i d \ p r o b l e m s because ot die strone. ana loev between eo inb ina to r i a l

o p t i m i z a t i o nn and die phys i ca l pioccss m ci > M a l k z a t i o m lo w h i c h il was ! : ; - ! app l i ed .

\ i o r e o \ e r .. research ck i i n i s that s imu la ted ar.ucalime. we lds tlte op t ima l so lu t ion koi spat ial

a l loea i io i ' .. p r o b l e m s w h e n the sn-cai ied ' l i c cz ime parameter" is - u f f i c i c i u k s l o w e d d u n n e

d iee o p t i m i z a t i o n process. I hesc luk l i nus w ere the reason lo r e x p l o n n e the poss ib i l i t i es ot '

upmkk me S i m u l a t e d auueahue lo an Ml I \ nmbken i

(( ' o iu ra rs lo s i m u l a t e d aunca lme i s \ i. there k a w k i n ianber o i ' 1 IP n i o d e b a\ a l iab le !or

sk ' l x inee resource a l l oca t i on p rob lems. \ ] o s i o l ' i l icse mode ls ami io n u n i m i / e d e \ c l o p m e n i

^os iss and encouraee con ipac lnes^ |v. p u r s u m e a low per imete i lo area rano o! an a l located

suee ^>\' land i k e . Some s | x \ a t i e I. I I ' n i o d e b lor s ine le site a l l oca t i on are Inund \ u t h i n

to res [ r \\ research where the ma in a i o b l e m ret'ers (n tu id i i i ü o p u n i a l harvest schedules.

Desp i tee I IP mode l s -as opposed t o a e u i k n c a l g o r i t h m s - I I ; L \ c the a d \ a n t a ee o l e x p b c i t b

euarantecm;ee an o p t i m a l s o l u n o n . ih.es are r c h m \ e l s s low . In order lo cope \s i th slow

p e r f o r m a n c e ,, most [ IP mode ls on i \ me lude kormula t io i i s io encouiauee compactness as

c o m p a r e dd to the more ' s t r i c t ' co iu ipu i i s r e q u i i c i n e u l s . Kescaieh showed thai modest size

pii ob i cms. up lo areas ok s x S ce lK can cas i b be sols ed w ith c o m mere ial 1 IP s o b e r s hke

(.. ' I ' ! I X or I i \ n < > .

11 12

CofiC^i.-Gfio o

/ ' / ' ( j / > / ( . 7 / ; / /

fourr different optimization modck were developed in this thesis in soke LUI M [ . l ' \ problem.. Ml i i i i^k'K proved, in both minimize i.k'\ clopment cnsis ^ IK ! maximize compactnesss nl ' tits.' allocated land use. the kuier through the incorporation of ;t neighborhoodd function.

Thee first model (Chapter 2 and model 1 in ('hapter ; l is based on a nondiuear approach and wass solved \\ nil I lie S \ algorithm (from here this model is referred In a> the S.\ model). 11 m\\ ok es die implementation o\ a compactness obi eel i\ e b\ mcludum a non-1 incai neighborhoodd timet inn. 'I he neighborhood function is based on ihe pnneiple thai u hen two neighboringg cells are alloeaied w uh land use o\ equal l\ pe. a 'ensi boniis' is subtracted t ioin ihee total de\ elopment costs. The method n ;h tested on ;i ^rid ot' ] U x in eelk. .nul performedd well h\ supporting the ereation oi larger patehes of land w ith similar land use. ['hereafter,, the SA model was applied on a ease studv area measuring . dO x .idi'.i eelk. 1 he easee stud) invoked a large open mining area in Spam, where the inn in problem was :.o restoree the area with new land use. The preferenee of the decision-maker tor either nf die twoo objectives -min imi / ing restoration eosts and ma \un i /mg compactness - is expressed throughh a 'weiglumgdaetor ' //. Simi lark tn the It) x Id application, the S.\ model generatedd eompaet patches of land use. However. reiat i \ek high \alues of beta nrodueed 'un-naturarr rectangular shapes in land use.

Ihee second, third and forth tnodek comprise a set ot' three Id ! ' models, using different compactnesss functions. The second model uses the principles of ihe non-linear S.\ model b\\ traiislormmg the nondineai" neighborhood function into lour additional linear constraints.. 1 he third model uses the 'buffer approach' developed in \\ ilhnnis and Re\clie ( l ( ) n hh l ^ ' S i . which was reformulated from a s/^g,V- into a mail! she f f \ model. I lie bufferr appioach assumes that each allocated land use in a cell must be bordered w ith buffer eelk.. I k min imi / ing the number of buffer eelk. cells with equal [and Use tend 1o cluster, sincee larger clusters of equal land use are 'cheaper' in its use of buffer eelk. The fisi model usess a method of aggregating cells, forcing land use of equal t\ pe lo be allocated in a minimumm amount of pre-defined blocks. A l l four models were applied on an S \ N Lind and provedd lo be capable of optimizing a mtilti site allocation problem. Similar to ihe SA model,, ihe eompaelness function has been made opcralional b\ using a weighting factored . al lowingg ihe decision-maker to interactive]), select ihe preferred weight for achieving eompaelnesss against cost.

11 k';

Conclusions Conclusions

WhatWhat is the efficacy of optimization techniques for solving MLLA problems in terms of size andand solution time?

Thee case study for allocating new kind use in a former mining area clearly showed that Simulatedd annealing is capable o\' solving large combinatorial optimization problems. involvingg large amounts of spatial data. When comparing the application to areas with differentt grid sizes (10 x 10. 50 x 50. 250 x 250 and 300 \ 300) it turned out that the optimizationn time of the SA-model increased rapidly with the number of grid cells. This is partlyy caused by the software we used, as we did not pay much attention to speeding up the sourcee code. .Although smaller grids are solved within seconds, larger grids required several hourss on an average PC' (Pentium 111 450 MHZ). Currently, SA applications larger than 100 \\ 100 cells are less practical lor use within an SDSS.

Al ll three LIP models showed a good performance in terms of speed for smaller grid sizes of XX x N cells. We initially set an arbitrary threshold of maximum 2 minutes solution time, whichh was met by all models running in multi objective mode, using low values for OL . Modell 2 tends to be the slowest variant. Model 1 was the fastest, followed by model 3 and 4.. Model 1 is a non-linear model equal to the SA model, which performed well using the builtt in non-linear integer solver of Whafs/ie.v/.'. The problem, however, is to verify the resultss of model I whether it is a global optimum (GO). Some model runs were verified as aa GO by comparing the result with the known GO results of models 2. 3 and 4.

Modelss 3 and 4 were applied on a 16 x 16 grid yielding solution times between 10 minutes andd two hours for different values of (( . Although Cova (1999) mentions a limited use o\' tee buffer method for small to modest ~~\/x allocation problems, it can be concluded that this approachh is relatively simple as compared to other existing methods. Therefore, only Model 33 has been applied to a larger area of 30 x 30 cells, involving 57855 constraints and 9600 integerr variables. It took eight hours of computing lime to solve this model.

Gridsizee 100

500 Gridsize - 100

Hii Gridsize 50

ss Gridsize- In

Gridsizee 8

Nonn linear IP: model Simulatedd annealing

Nonn linear IP: model What'sBcst!! (Hxcel

linearr IP, model 3: What'sBcst!! il xcel)

linearr IP. model 4: What'sBcst!! (1 seel)

linearr IP. model 2: What'sBcst!! (Excel)

Figur ee 6.1 Relationship between optimization model, grid size fin cells) and solver type.

114 4

Conclusions Conclusions

f u r t h e r m o r e ,, ' i 'Aas sSloWt l t h a t ' V m L U . l l e d a 111 i ca '.] 11 C Cat: i v c a - i k I! 1 IP I Ci 11C t l i e d l o f

problemss wah mad sizes i;p to k in v. 11 in eclk. 1 I I ' models can he \ ci> well incorporated forr problems up ic grids of i fi \ ! h cc ik I , H ^ T grid - i / c - up in ."')') \ M.IO f >r S.\ and N) \ 500 lor [ I I ' can he solved. ht;t require intense c computing lime and ,nv diff icult to manage inn a spreadsheet i' f igure <\ 1 I.

nn Jia/JJ .'. L iwrh nk-ai "rfinu^aimn !r< 7/<;/</;<( > ƒ/.; ,m/ SPSS far yr.M^rci aihn\i!i'>u

'' - - ' / / ^ . '

Hull1,, lik' SA and I.IP methods prosed in ! v suitable tor integration within an existing spatiall decision support system lor mining areas t Aslcrisinos 200(1) and it was demon-aa ruled that the) til into the computational step ol ' an SDSS. The SA and 1.11' models addressedd ihe mull i object i\ e character oi a resource allocation problem bv optimizing both diee objectives ol ' minimizing costs and maximizing compactness. 1 iie SA model was implementedd Mich that it u ;h easy to handle !or non-experts --the software mik needs in be acti\atcdd In one opini i i /a l ion 'but ion' and a "slide bar" lor indicating the compactness level,, expressing the usem preference tor closed patches ol land use. I he 1.1P models were operatedd 11 Mn'j \\ hat A/>('\/.' for I A eel. w Inch requires some training for no\ ices.

\\ I though the c ^ c studies tor both techniques \\ ere s imp hired to some extent -hv neglecting environmentall evaluation criteria and assuming simple hneai" relationships between costs andd geographical attribute--- it has been dcmonstiatcd thai opmni/a i ion technicjiies are capablee o! I/(.WL;"///C' allocation altcrnaliv es. ( >plimizalion techniques are therefore consideredd as applicable n the computational framework ol ' an SDSS. ihe model resultss cleark give direction to a final more realistic allocation plan, which ohviousk requiress more detailed mode ling. Ihe great t iexihil i lv ot' SA implies that it mux be Used lor moree realistic problems and it can be concluded that ihe use of SA withm an SDSS is a poww erful algorithm because ot' lis simplicity and robustness.

Thee developments m I IP modeling arc promising for resource allocation issues but computingg lime is still a draw back as compared to S \ modeling. W ith respect to the goal o\' thiss research, naniclv to hud 'rPuihu . rnl-na and prefcrahk \nnr>ir' optimization techniques,, it can be concluded thai currentk, a ticurisiic approach such as Simulated annealingg lias more advantages o\ cr LIP modeling. Research in the area oi resource allocationn and decision support has ccr iamh advanced the development of optimization tookk for single site allocation problemv I low ever, it can be concluded that the direct link K^\' existingg optimization techniques to SI )SS sv stems still needs further altcnlion as w ell as die speedd ami traiisparencv of these techniques.

(ff //,': /; /< i hahinc ,w MiiUtSfr fur i (,'/,- iihuiii'^ k,v >>i Jain /."','< rriaini'r far

anan SPSS ianj /<m aU<n anna.'

II o date, there have been levv examples rj ihe application of unccrtauitv melhods to

problemss thai exhibit a more decision-making character, while quite a tew studies point out

ihee importance ot' doing exaellv that. 1 'his is partiv Ar.c to the lechuieal character o\'

II 15

Conciusi Conciusi

i k c k a i u kk ana l ' ."uious.. '-A ii [i.-!: ,ac in ere:ore mkur.dcrs i iHH.; er eo imp.ercd :m> t l : ] t ï^-u.

I kk ,m N D S ^

Inn t h k the — . .1 e c : i c r k m c d m d h.k hec: i deve loped kor a u a k / m e :he a i k c r k i n k m t ik '

s : \ i t i . i ll k u p u k i data i k c e f> ' i ' a:i - p ! i n i ; / . i ; i i ' i ; mode l tui ' : e -oarce a l lo L ..iiu <:i ksues . 1 lic

o p i m u / u r . o : :: mode l i.scs l i ic M i n u l c t c d unncaluic. a i e o n t h m and k p r c - c t a c d as ;i L IC- IL IÜ

m e t h o dd : , ' i .1:1 M ) S v I lic m o d e l calc.Jaïcs the o p n m a l route ior a sk; n m based on a slope

map .. i l ic latte; * t" L LM [ 1; L ] ] \ d c r k c d k o m a dieata! e levat ion m o d e ; ( I ) k . \ h . Bo th the

m k c r l a m kk a m i b s k m e t h o d ami the >'pt 11111 / a l m n mode l Fit u i lo the c o m p u t a t i o n a l Step 4 o l

a i :: S | )SS

cc a i m c k a u i k a n a l \ s | s f o l l o w s ;I M o n t e ( a r k - approach UMIIL s c q u c ü t k l ( i:iu^--k[:

m.duher,, 1 M iS 1 m k ; k c and cji;u:k;1) the p i " p a - a ' ion o l the [)[ M error al l the A ; : \ to ihc

!! mai a i h v a t !

c k o rr f i e l d ,

d SS | . \ I . \ e

.. ' e - a h c l :hc o p m m / . k o n n iodek I 11^1. M-. 11:L1 ~O m o a n d con t ra : p e u i k . l l ie

liee 1)1 M was mode led i k i n c a spher ica l k u i o p a u m ui ;kc s ta t khea l package

.. C i S ' I A ' I ec i i c ra l cd a -et P;' M K I ccjualK p robab le i ' i k r maps, w i n c h w ere

iddevll '.o the o n m i n ! D I M . p r o d u c u k N i n c H a u h \ p rohah lc D l \ K I hem 5ni) -dope maps

AA ei e de: w cd h o m the -c l et' I )l \ A . I h o e w ere i k c d 11; ;: \ ion ie (. 'ar lo s i m u l a t i o n , w here

i l :: ^! H ! d o p e maps w cre ^LLP-CL] I;C:".I i \ i k cd a-> aiput lor t i ic o p t i m i z a t i o n mode l I l i k

dd :n "~n't cm .a l k p rohah lc re.d vat 1 e i k i1 ' - i maps* mr a iecuPon et a ski rar,

ii m a i b . p i o b a h m l x k iL i i tcs w c i c e a k a i a l c d across uü Min 11-i rea l iza t ions, aion- j w n i i me

s tandardd dc \ la tuat et ' t i ic p r o b a b n i n . 1'hc number et' M o n t e Ca r l o rea l iza t ions has been

p l o t l e dd a k i n i s i the s tandard d c \ l a t a k a n d shows con stanl \ al l ies lor the standard J e \ un ion

a l te rr 4 l t i t tea l i /a thMls . [\ w a - i h c r c k i c c o i l c l l k l c d thai NIH M o n t c ( a rk ' ( \ l ( b Mills are

su f f i c i en tt !o ea lcu la ic r chub l c p robab i l i t y maps for al localuiL1 a ski run w i t h she S i i n u i a l c d

a i i n c a h n cc mode l

[ ' ,,. .. ... a , a,, !,.,. u .. M , , ï , , ^ l l : I . P , ' , u i r u „ i | l i k U , > l l l , K T a i l > M h

a p | d k a b i i i t \\ w i i i n n aa S | ) s S i ie \ e k p e d lor a case s i u d \ 111 the Aus t r i an A l l 1 - . Here , l i ic

ii p r e l v e i i : was 10 kmd a i : aica lor eo i k t racn ih . : a new - k i i'nr:. I :ie siarl and ku i k i i

kk k-;ui on ol l i l e ski run w ere know n bc to re l j and . as w ell as the requ i red w id ik ok the ski l u n

Heto ree appk.n iL ' the \ H anab.s is . \\\j S i m u l a t e d anncahtiLL mode ! Iiad been ics icd I01 im

C'. ins|stene\.. and appeared ie p r o d i k c siabie resul ts Hence. au \ \ ar ianee 111 the results

acrosss Min \ 1 ( ' r u i k U S U I L e q u a l b probab le , 'nul s l i ch t ! } d i l l e r c n l . s lope mat"1-- - therefore

causedd b\ da II c r e i k c s ( read , aneertar.-.tv ) 111 the input data e l ' the mode! .

I k k e dd en the p r o b u b i h n i n k o i r n a t i o ' K l c r k cd f rom the M( anab s k . i l ie re was an unheal 1 er,

i iu t ll a rou te low aids the lelt o l the m idd le sect ion e l the area was s l m h i b pre fer red . In o u l c :

100 t m l h c r cp iann t \ t l i k obserx a l i o n . \\ e app l i ed a l oan p r o h a b i h k analys is \v three pairs o[

cel lss \ H ih rcc pans *n ' ce l ls w ere pk^ cd al d i f l e r c t i l l oca l ions 'A i th in l l ie u n c c i t a m m i d d l e

sec t ionn and were eva lua ted : k to w l ie iher i l i e \ were le in l lx bcinLi a l located a- a ski run

k r o mm d i k a n a b s i s . u c o u l d he eor.cladeLl that indeed the left o r ien ted route I r k -\ kaclie;

m in tt p r o b a b i h l x c o m p a r e d to live othci routes.

ii i d

Itt V'. a-. furthermore described how data uncertainty at'tccm die variability m the dcv cf ipmcu: costss for a ski run. liuscd on the original slope map. 'wo optimal ski run akcrnal iv cs and t.k'\\ clopmcut a i^N were calculated Using different star; locations and a:i cvani finish location.. Next. In!' these [\\n altcrnaliv c routes, average development a ^ b were calculated acrosss all ^00 mode I-realizations. Ii appeared that (hew a\ erugc costs were higher -hel ween S44(i.ni)(.ii and V i:\ i toit- as compared to (he dcv clopment a>--h calculated mi die h;h!> o!' thee original slope map This is considered to be valuable additional informa;;o:i to die user whoo mmht coiisidci' )ii\cslin<e in a more accurate dala set in order io enhance confidence m thee simulations for a ski run location and die associated cos;.

Ass a robustness analv -a-,, the basic v anogram model luis been altered mm 4 new v ariograui modelss bv changing ihc range- and sill parameters. I; appears thai an increased v aluc lor the rangee resuhs m a decrease m the \anat ion of' the prohahfi tv. Mencc. die most probable routee for a ski run becomes more distinct. Similar ohserv aliens .an be made tor .1 decrease ol' lhee sdi \ a hie, u Inch also results in a decrease of the \ ariacon in the probabilities.

\;.! i inn,ii (l lM)V) describes the significance and implications ol unccituintv analysis tor

higher-levell decision-making. The case sludv in \ustna shows these implications, and it

cann be concluded that the described uncertainl\ U IK IKMS approach mux contribute to an

SDSSS lor the lol low in:.1 reasons:

It pro\ ides additional prohabihl\ information as to where to construct a new ski

runn or lo exclude uncertain areas.

It is a relalivek simple, and thus understandable, technique. including lor non

technicall users.

It supplies additional information on the development costs mvohed 111 die

constructionn of' the ski rum

AA disudvanlage ol ' lhe uncertainly method is the total calculation tune, which lakes at leas; 1-dd hours. Mowe\er. as concluded 111 the mining ease sualv. it is expected dial (.'PI tune wi l ll conlinue to increase. enabling a direct implementation of ike \ K ' procedure within an SDSS S

I i n a l b .. unccrtaintv information such as described 111 this thesis ^ decisive \ov higher-level decision-makingg and should therefore be careful l\ managed. I he lesulls of die whole \ I ( ' proceduree can he regarded as a valuable generic melhod for an SDSS and wi l l enhance a moree balanced discussion of (he pros and cons of resource allocation problems.

Iff '/;(/, ' illt/lhiljs i ;//,! !\ iipni'n J In I i^tliiiiji. y ' l / f / o / lU!-;\ Th I ill! 1 .'

II he research a I so au1 dressed ihc need for techniques to v isuahzc uncci taint v a: an SDSS fnr resourcee allocation issues. \s a case stud\. the ui ban grow ih model SI .1 ] 11 w as applied onn a case s!ud\ to simulate urban e row th in Sanla Harbara. ( ah foi ma. I he model is designedd to aid dec is ion -makers m the field ol urban planning. \1 [hough s i [ ( 'I 1 f w as ma integratedd mlo a complete SDSS. the urban growth rcsidm produced h\ the model ear he regardedd as allocation alternatives such ,h normally generated within the computational Stepp 4 of an SDSS.

11 r

Ii ;-.c<.:: on a rap h k a l k \ hi :K]:ic^ u c s k x k h\ M a . 1 acinkT. ( ! l > ; ' 4 ; , ind me exper ience j a t n c d

i r u i nn o i l ie r \ k i k d i / a p o n -k in c\ -. :v. k l a m c!> snr:p:c mc i i i n d - w ere chosen h k \ i -mal i /me.

ii UK-^-1 ;u n:\ . csuk ' co lo r v;;m:-.i: i^: i ; . . ' K ' nar a p raph ica l \ a k n h l c . Uoth Piet la H K at e k i v w :i

üii i i ' . c rnkuk as i kc ï i i u - i ' o b \ i nns ' \ ku .d i / a : ; ; n t c k i i i k a i e v '1 ke I ks i ;s j - ka l k o a n p a : > i ' i '

cc where i ihH.it] u.'suli u i k l 'o u n c c r t a i n u are presented ii i ;i ' s k i ^ b\ ^iJt ' in iaac

]] l ic s c o k i d techn ique !s r c i c r r e d lo a-. 'u'LI>J1111LI" where mode l rcs i i l ' s .md its l a i c c r t a n m are

sequencedd in a l oop . l "-me. these iw i- k i s ] e t echn ique - , - c \ cral '. ana t i ons ! K I \ e hec:i apphed

i . k ; i kk d i t l c r c n t c o l o r sei ic ines ma! i k k k j a u u t i d n d o i n i a m m .

;; — /k \: ' k k V 'X S '

II hci'e k a c o m m o n nercement !ii;u k n a k / m e . . a k c r l a m k k a a i l i c : a - p c d m i k a k :

spat ia ll da la and mode l s w ; ih :n d . c k i o ü - m a k me p rob! e n k . i here k. how e\ e i . l i l de

lii !c; al m e k l die i In ; k k 'h ^ o j ' \ ^ ^ j h / m e n i k c r t a n i l k a i l ia Hi eh il k acknow 'edeed laai

h u m a nn pel c c p t i o i ; .aid n k c r p r c i a l i o i - - a t n a hk Pretor m dele: m m m c el tee: k eness

]] i i is r csca ich ha- c o n d u c t e d an expeu tnem amo i i c po ten t ia l i k c m o: j : i s l ) s S . b e t a k e t: k

re l c re i i ccss m i h k area atv ihe exper iments h\ LcKnc r and h u u e n t i c l d < I L , l ' ~ d i t u i u and

\ \\ a t kn i s i j i ii K 11. n Inch bo th e\ a h ink \ k n a l i / a l i o n techn iques har pm l ra \ me a i k k r t a i n k

ww nt i e x p e r i m e n t a l sur\ e\ s

Inn o rder i k q u i c h k de r i ve r e s p o n s ^ to the s m \ c \ . an cxpc i uncut was posted cm the

in ternett 1 or i h k . PA o \ [ s u n l i / a t i o n k k m i q u c s \\ ere a pp! icd to the Si 11 I I I results. \ e x k a

-ene- ,, o l quest m i k and s i a i c m c u k v, ae la e eed lo lae-e 'k sua k /a : a a k m lS ^ u e s k e n u a a e . In

taaierr lo ma in ta in o b i c c l i v i i \ t h rone h u n die - u t \ e \ . w C spin ihc sm \ c\ across n\ o separale

AA ebs i k ' s . each con ta i n UIL: quest a ' ik au e:i l iei ' o[ the tw i * \ k u a u / a t a m t nel ia Hi s

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ee | k n " k l p a n k u n t i t l e d u[ ata>l lk i . l a i d i/at na: k k i n n q U v ,ual t lic S . u I ; K , ; I U H N \ \ c :e

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d i k i e i c i l !! s i n \ c \ s . die q i l c s i a a k w e !e e\ ae! :> d":e s..,kie I k e d u k i k c ü : l l;e - u i \ e ' . da l n>H

exceedd 1 it mnnalcs.

AA ww/<//;.-.;// / / ; / , ;; ; S/ ) SS

\1]] ] k i r l i e i pan l s w ere ap|k i»ac! ied [ k " - a ' k i l \\ \ ia e-ni ; uk w i t h int.. mi nat ion en die :k' . i is a l du

M u d \\ Wal et lJ" ; a j i p r cac l i eu pet'-'üis no ïe turneü a t e rm c h e m i e io i i i i rdk ' i ' analyses

II fence, tlie lo la l ï e l u i u secre w as " ] " .

II l ie responses demons t ra ted d ia l a.:nos- al l p n r t i c i p n n k were aide ic i c c i k k . i / c i . i l km

e r o w t t ii t r om SI I d I I ] resul ts . ; i nJ that tlie> c c u l d i d e u i i l \ urban areas I rom an aerial

p i i o lo 'e ra id i .. \ e \ k we c\ ahtated w kcthcr a person c o u l d i e e o e n i / e the t^oiirax eil uueen ;un : \

ii IS

Cüficiusiüns Cüficiusiüns

withinn a -.pec i tic area, and to what extent lhc\ could quautifv the unccrtainiv tmm the representation.. Almost all participants recognized the iniceriainiv as presented \<, itli either method.. and made realistic estimation- oi the uncertain! v w hen e om pa red to the unccrtainiv figuress supplied hv the S I . I I TH model. The participants LI-I HLL static comparison (method 11 t estimated the uncerlaintv more accurate!} than those cv ahiaimg the toggling (method 2}.

Mostt participants responded to cither include roads i.5(i;'.,) t.^r slopes i.^l'V) as background informationn tor explaining uncertain!} in a projected urban growth region and its surroundingg areas. When examining the differences in responses between those evaluating methodd I as opposed to those evaluating method 2. it appeared that preference lor roads andd slopes was more prevalent lhan tor the other background options tor the 'method 2 participants'. .

Wi l l ii respect lo color schemes, slightly more than bO"., of all participants preferred the single-colorr scheme above the bi-color scheme. However, it appeared that participants evalnaimgg method 2 almost equally preferred the single and hi color schemes. Non-experts dislikedd the bi-color scheme more lhan experts did. and saw less improvemcni in the effectivv eness i>\' unceitainiv \ isuah/alion w ith bi-color schemes.

Inn a 'head lo head' comparison oï the two \ isi iali/ation techniques. ~2"n of all participants preferredd the static comparison technique above the toggling technique, f l ic preference tor staticc comparison is. however, less pronounced for those who oniv evaluated the higgling technique.. Apparent!}, the hitter group was more accustomed to the higgling technique. Kxpertss preferred static com pa rist in 60" <. to 40" a. vv In I e non-experts preferred static comparisonn in a more pronounced wa\ at S3'1,,. vcrstis ] "7",, tor toggling.

Sii mi lark lo findings b\ I.eitner and Hutten field ( 1 200(1). we fouiitl thai all participants indicatedd that embedding uncertamtv information tends to CIÜIHY rather lhan render a graphicall display more complex, hxperts, as well as non-experts, responded posilivel} to bothh techniques and considered the survc} lo be comprehensible. It can therefore be concludedd lhat lechniques as static comparison and toggling, the latter alihough somewhat lesss preferred by the parlicipants. can m fact be embedded within a map display and can improvee the efficiency of spalial decision-making for resource allocation issues. Color saturationn as a graphical variable prove- to be powerful variable tor representing uncertainty,, which is in accordance with similar findings in other research i Buttenficid and Beardd 1W4. MaeKaehren . I.eitner and Buttcnfield 1 W 200(1). Our experience is that aa web-based survey is a convenient and fast medium to conduct \ isuah/ation experiments andd seems to be a promising environment for additional research in this area.

6.26.2 Recommendation s fo r furthe r researc h

Thee futur e of Spatia l Decisio n Suppor t I-'\isliiiüü SDSSs are often developed as expert svslenis and built upon CIS lechitoloüv and softwaree as ArcA'iew or Arc In to. I'hese s} stems certain l_v hav e prov ed to support al local ion andd planning problems, hi man}- instances, however, these svstems were not applicable lo poorlv-sirueturedd decision problems because ihe\ are loo technical lor the User and the} lackk a structured approach such as a decision framework. Hence, main of these CIS based

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ConckiSiütis ConckiSiütis

Specifi cc Recommendation s Thiss research has Jcrnonsmatcd that it is possible hi integrate techniques derived from the terrainn of( 'dSciencc u ith concepts of decision sciences into an SDSS. I he main draw Iveks aree computing capacitv and cumpat ihi l in nt' the software components and its data. Computers,, however, are becoming increasingly taster, and M> the application lor larger endss in an SDSS is unlv a matter ut' time, (.'lever programmine ma} ;iUu subsianlialk reducee the e^rrijiuting time. I hcreforc. research en larger problems is iveommended a-- well ass further researeh into the application of heuristic algorithms to allocation problems <WW ilhanis MK\ Ke\cl le ll>ws. t.'o\ a h>lW|.

Ass recommended In ('ova ( W W j . this research favors the me ot' heuristic algorithms for solvingg opt imi/at ioi i programs for resource allocation and strongly recommends more researchh in this area. First. ihe\ are taster than I IP based models. Secondly, although :hc\ ^.\o^.\o not guarantee the opl innmi solution, [hey do sen e the purpose of an SDSS. namek to supporll the search for allocation alternatives h\ design me pol en Ma I sul m ions. Mils does not nnpkk l hat research on LIP models- should be ne nice ted. (>n the cent rare . ihe capabilities ot thee What s/Vee/.' M>1\ er m l:\ecl has opened opt in 11/at i on. and more particular linear programming,, to a w ider audience. I fence, -since computing capacilv is continuing to increase,, and the user friendliness of LIP sol\ ers is unpruv nig. these concepts wil l definite!}} have potential tor use in an SDSS.

I.. nccrlamtv propagation becomes more important as the use ot spatial data and looK increases,, and more importantk. spatial Jala and techniques become mure decisiv e in highei'-levv ckdecision-mahing. In this research, unk the influence of spatial input data has beenn discussed. I nccrtaint\. however. plavs a rule in alt aspects of the decision process. It iss stated (hat an SDSS should be equipped with took that suppuri an anaksis o f ihe unceriainlvv in the eencraled solution. New research on a more comprehensive unceriaii i i \ anaksiss in an SDSS jv, recommended, invok ing an as>essinenl ^>f the influence of uncertainlyy m the model formulations and evaluation criteria.

l i na l l v .. this thesis described a sui'v c} to evaluate the effectiveness ^>f visualization of uncertain!}} lor decision-making purposes. Since there is a v as! arrav of \ isuali/ution techniquess available lo communicate uneerlainl}. more c\penmci i lal research is needed to evaluatee those techniques on their c fleet IV encss. 1.\ peri menial surv ev s u I" SDSS users ma\ givee research m uncertamt} v isuahzation a 'face' as a giv es ev i deuce that those techniques aree iruk useful.

1:1 1