application of the assignment problem case of pagcor's slot machine operation

7/28/2019 Application of the Assignment Problem Case of PAGCOR's Slot Machine Operation

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" ^.'^^^:.h-t loPerFescnts holnpli3don of 6"',ir.igr**t problern s a disrribution roblem o thecssc

. of PAC€OR's slot rnachineoperation a:orxi of its.Cariho Filt'plno brrnches n the pUif';ppi""r. p". ion"coofid3ntir{i,tyof ieveral pieces qf infomntion, thc pqrticiilar'braroh whEre the study took

'placeand rbe

operutios licrsonnelwhohelpid the aulhorobtain hcrequireddara iu"ot

x *-J h rid; p"C---

.-:

- PAGCOR'or the P.{lrnnle enus€mcot aad iaming Corporatiorl uscd o bc ihe'PhilippineCasino. operatorscorirorarioa duting.rh:. v{arc9s ears. sin; iE ,#b;;i;;i.-*r ir, .luly 19se, ,nccoR's'

,tI*-: l^ h.*ry*^It!- cqosistcotgrowtbandstrongpeionnancr. tL pp 8.98 billiou iocome.during' lhe [rst ninc monthsof 1997 laced its monibly incomeatan-averageof php 998 mfioo as comparedo thl' PT ?lz milliontverage,montbly amiDgst postid for thd'sarre *J iitlgx. Reverues ome rom hreet

fJtt 1T9*_j STs"ft-"P t!!9 g"qF"-a"a ltot g19!ines, Sualiyrng fees entranceecs), ;d rcqta1ncone .

' IIom cDrrywThrog operajous09asyS 9f gsrting facilitics to an opcratorwho b'rings oieign players nto the

_*5ryI?TTg.the J998amuatplanningco,afcr-ci, &mD"""Lb". s to rO, isz, l"p"rd'*dale-tevel. -l]|SjF. T*.challenged

to ctaft q slTtSq thst would enablePAGCOR to overoomc'tbe

dangersof lhe'currcnt ccfiouic conditionsrnd to mairitain ts inpressire'profitabiliry tbat bave srade t thi cotiltry's most

pofitableorporationn'1995 d id:'1996.'wi,llit'"n ii*g";;i;;"*;;#d*"' * pliiii6ti'n";.

ncreasingly become more oriented * optinizing pqrfqrmatr,?ewhile.bcing morelesponsive

to shifting iustomer:: " ;xefercnccs.:- ' . r ' : - ' .1: . . , : :

. : : . : ] - : ' , . - : . i , , : . : : - ' -. l i ,.. , . ,. : . ,

,-r_-_. ̂ ,.3: *, *tty .oryTti* ir-oy parrlcuG'Ur*O oi C-io o Fitipino tns V,comebe uU;ei i,finterestf he ut[or.Theraih r""" "f

rh";;;t u'oa]rt; iti#*,rifiti,rf,.*J*ffil;ilffi;l"j^gr$ r..tc rapi,outiue;abcarar,nini accarar,n,dpok;,;;s;:i;-;r'J;"birJ;;; il;.Ill tll

}]:o:q.*d"** to .2.27.LrLe othrCasrno. Filipino o[erations; be branch s rclenrlessly

mod€rDlzEgts facilities. ridcontiriuously mpro'r,ing',its pcrations.tAspart of the quest for'.supcrior' pcrf.oroaacc'.Ealascmrtrt rvould like to"*i*i.

if thc currgrtrtmix and plocemcntof slot roachines o 57' lea'trn8 ocauonsand their extended roupl arcstill favoiableos'far as-di"ld"g nct rcccipts s concerled.' Thc Slot vtachineSection, bqgroupresponsibleor tbeopcrationof slotrnachines,as not used be conieptsofassignmeilproblem o daermiit" rt" opi--o placemeniof machinesalthougb hecasino's present ystemof

. ti*tg andassigningmachinesalsoconsiders he q,pesof machinesan4 fJr eachmachine. hb actualdaily. sversge et receiptand numberof playeo.,"d of'pl"y

times.Even thoughno i"fbr.utiori"";.t""i

arUi,averuge etreceipts rom themachiniswasnude

"*it"'tt"tyrl"

"p".airi;"ff,[. uutho,** able o apply

theassignment'toblemby using theamountof oachine deoqrninations themiaimum ambuntof bet allowed

Ior cachpuuandby corsidering.otherictors_coolaininghe.equireddataprovided o him by theSlbt vlachineSectio' Tbus' from tbgfour ql"y!:t gr'"hi"c mixesiroviiea by theopgmtions Ln tn" Hungarinnmerhol:f 9$P1

(Quantitativesysteirs fo.rBusinessPlus) veriion 2.0, uiorpui"r prog; by yih-Long chang and TqF

t s.-sullivan,yieldedan ggrirounassigrunentrrtot mi"iinoi;itd;fig b"ationswir.han estimateddaily totolnet recciptofPhp 158,s54'8 r an'esiinat"dyeaily totalnet eceiptof'elp sz.ra milion This otalneJlec€.rpts 3.47 imes

T4*h Qt. totalnet ccciplthaic"n be realzi &ily, i, y*rly,from the currgot

mixandp lacemento fmach ioes. . '

' ' ' . . . ] . .:

PAGCOR'SFIRSTTEN YEARSUXOBNTIIE POST-EDSAMANAGEMENT.

' :- . . . . - .-- : . . . .PAGco\ or fte Philippine-AmusementndGamingCorporatioqsedo be he

' ' :Philippine CasinoOperatordColporatiohduring,the Marcosyears. t changed ts

Tanagementn July 1986. The first tbn years of operationunder the post-EDSA

manageqent asa p€riodiof emarkablbuccessesnd"esounding ictories.FromJuly. a '

1986 o December:996,thecorporation's'ccumulatedevenuewasPhp 60 billion. It

wasa periodcapPedearafteryqarby recordhchievementsndeffectivennovationsn

tha,ny sPects f its operations.n its tenthyear under he post-EDSAmanagement,t

t



:, ' brokethe ten-billion-pesooundaryine int::T"

the ten-billion-pes-ooundaryine in revenues s it posteda record-setting hp1l'24 billion totar ncome or 1996 The colporation,smpressive:erfor-J ;; irealized lrgughaggressiveurri.u, anddomesticmarketing fforts,andboostedn large

PartbyFpthrivingtourismindustryandstrongecono*,..-_ ?:---'-..

PAGCOR'Sevenue uadrupledo Php2.05billion n 1gg7 romthephp 536..64miltion total ncomet postedn July o December 986.Revenubhenconsist.ntlyo*to Php2-63billion n r9g8,php3.5gbllion in 19g9,php4.23b1rt"; ;;;;;,;;; ;;;

. b.iui.lnn 1991,Php6 I I billion n 1992,phpz.s9tbillion in lgg3, php7.57billion in199'4'Php9'42 illion n 1995, ndPhp |l.24birlion in 1996. n termsof yearlygrowth,

In 1995'PAGCoRoccupiedhe highestposition n the Securities ndExchangecommission'sist of top 5,000publicand=privateo.po*ri*r;;; of net ncome'surpassingwo Philippinegiantcompenigs:anMiguel corporationandphilippineLongDistanceandTelephbne ompany. n rlg6,pAccoR wasstiu ,rr. pr,ii-pii*;;;

,e:ofitabletl*n*t and,asof December f thesame ear,became neof *.

"o""roirggest mployers,mploying otalof 9,090base.

, -PAGCOR's three-shift,24-hour cagino operations table games and slot

machines) osredotal winnings.f

php56.07bilrion for the period r, ,r, ,nru *o:r:t-.ott

",-tlnu'Toge$erwrtf,

1n9php r 17 billion qualifying ee (entranceee)

collections nd Php 1'47billion from the lease f chipswasrringacilities or leaseofgaming acilities o an operator,whobring n foreignplayersnto thephilippines),thecorporation'sncomerom gaming perationsotaredHrp ss.zr uilion uro;; 6o;^;;b ranchcon t r ibu t ion inTab Ie l ' I ' - - - . - - - : . : . .

Table =L\coME FR'TIIGAMINGopERATIoNSIN'ILLI.N pEsos

BranchBranch

AngelesBaguioBacolodCagayan eOroCebuDavaoIloilo

Php ,689.57. 34t.221,432.25

1 .8. 3,163.60

1,454.12. 29.30

LaoagHeritageOlongapoPavilionSilahisTagaytay

Php372.694,734.85

'133.57

23,185..5220,378.331,126.32

Total , ;Php58,207.55Isabela tt n ' " * ; t t tP ro'tv t ))



./"'

,The ollowing-shoulde notedwith referenceoTable1:, , '

:

. ' . , ;March |2 , .79g2 : , . . ,

. Income rom-Baguio ranch ncludeswinningsduring heperiodJuly 1986 o

July16;1990 nIy. 1'

o .Income rom Cagayande Oro branch ncludeswinnings during the period

June to26,1993 nly.

. Income rom.Cebu perationsncludeswinnings romthe followingsatelliteI .:- aSltroSl̂ ebu eachClubCasino fromDecembei ,199t5q June ,1996;i SkyClubCasino fromJuly6, 1994 o September , 1996;Delta hilippine

.' :; ' Dieam-startedoperationson January26, 1996;and waterfront Mactan

o Income rom Iloilo branch ncludeswinningSduring he periodAugust1986

to December 987only.

o IncomeromIsabela ranchncludes'winningswing the:period ecgmber ,

1991o September5,l9g3only.

. Laoagbranch tarted perationsnApril 24,1992.

. Heritage ranch tarted perationsn AugustS,'lgg4.

. Tagaytay ranchstarted perationsn May 25,lg9l. .. ,

'Interestandother ncome mounted!o Php 1.32billion, bringing he otal ncome. I :

to Php 6a.02billion forthe periodJuly15 ,1986 o December31, 1996.,

Out of the original l0 Cas,inoilipino brancheshat PAGCOR startedout with in

19E6, wo were closed dorvn - Iloilo brancii in 1987 becauseof lack of viabiliw and

Baguio branch in the aftermathof the 1990 killer earthquake. n 1991, Tagaytay" ndt :

Isabela ranches ereopenedollowedby Laoag itn 992.However, sabela ranchwasclosed in September1993. ln responseo changingcustomerpreferences, ebu

operationspenedrvosatellite asinos one n the SlqyClub of the CebuPlazaHoteln

1994, nd anothern theCebuBeachClubUot.t in 1995.However,hese ere eplaced

by moremodernacilitiesat heDeltaPhilippine reamFloatingHotel n Mactan nd he. : l

WaterfrontMactan slandHotelright acrosshe MactanCebu nternational iqport.As

of December 996,PAGCORoperates2CasinoFilipinobranchesn thecountry.



' - ' 4. ' ,

' , . t ,

The financial riumphof manycasino.operations,he improved mageof casino

gaming ndustry,and the growingmarket or recreation ndamusementavegiven hecasino industry rvorldwidean even larger rgom for develoirmentand growth. Theindustry n theAsia-Pacffic egionreflects'this rendalthoughhe recentcurrency risisgenerally lowed

9o* the region'seconomy. AGCOR'sprospectsn the regionarpstill bright evell n the presence f 53 casinosscatteredn the Far Fastas of 1996.Thegamingmarlet in the region s estimatedo be cl.os-eo U.S, $ 7 billion annually"Evenwith its superbPlrfopance, PAGCoR hasbarelv appea ts shareof the market.The'.

' fhiltppin.ess,inavery ggodcompetitive ositionnol onlywrth ts Asianco.unteqp4rtsutalsowith casinosn theU.S-andErIope.wheremany. layersstill go to satisfy heirtastefor higlr-pricedgaming:Ttte Philippines'closenesso the main gamingmarketsn the

Ieglqn,gqod ouristdestinations,ndwarm; riendly,andEngiish-ppeakingeopleput it

in goodcompetition,-u :

.' In line wittl its expectatiooo, an even more promlsing ufure,pAGCOR isdeterrninedo mplerne5rtts expansio,l rojegts, arryout asustained verse4s arketing

offensive, nd"positiol.itsasinos s heworld's riendriest.. ,'Havins

lped its tamished mageof p1e-EDSA'yearsnto an inspiringtask,PAGCORasanihoredt *unaute n"a .;il nrion- to makeh. ,"**rajserve its mandateof raising fund; for the philippine go,r.*rn.rri, ,r.r"*;*;;;;endeavorsnd vin thenation's rustby conductingts affairswith utmostprobity.n its1998annualplanningconferencerom December to 10, 1997, opandmrddle-level:managers erechallengedo devise strategy-thatvould'enableAGCoRto overwhelmthe hazardsof the currentuncertain

economicatmosphere ndpreservets remarkableit the distinction s hephilippines'mostprofrtable

companyn 1995 nd n 1996.

.5



Igl-CAsE oF srlgr rvr"rcnnle HnaTroN INoNEoF pAcCoR,sc4.sri{oFILIPINOBRANCEES :

-_ -_

The subject,of his study s th9 slot'm4chine perationn oneof pAGCOR,s

casrnos'The branchs one of the newestadditions o the CasinaFiilipinoc-hain.t islocatedn anareawhere radeand ourism hriveby dayandexciternent bounds t'night.Dancing,dining nightclubs,discos,gourmetrestaurants,afes,and other centersof .

entertainmentbckono touristsand ocalsalike.

A few yearsago,the branchh4{ only 41 tables o: black ack, craps, oulette,baccarat,mini baccara!,1d studpoker. ts slot machineshen were2ztr.'Inline withPAGCOR'song-termgoalof modernizing ll its casinoL ngputting hematparwith the. :

best n the world,the branch odayhasmore han4l tablesandaddedbingoasanothertablegame' ts slotmachines ownumber277iThelranchalso ecentlynauguratedtsnew VIP Room o accommodatehe casino"s rolvingnumberof guests. he nervVIpRoom tself has ablegamesor big baccarat,mini bacc'arat,oulette,andsfudpgker.Allin all, henew oomhas15gameables ddedo theexistingabres.

Unlikemanycasingsn theU:S.,wherehegamin*^r.u is usually unoundedyslotmachines,hebranch. asa gaming'areaocatedat thebuilding's ground loor and a

slot machinearea ocatedat the basement. ccording o someoperationseople,casinoguestsvhoplaygenerally refera relativelyquietgamingarea hat s insulatedrom thenoise of slot machines.Slot machineplayers,on the other hand, geneially ike a"shrouded"ateawh'ereheycan play withoutbeingbothered y surpriseencounters,,with friends ndotheracquaintances.

' The slotmachineoperations under he direit responsibility f theSlotMachineSectionpleaseefer o Figure for theorganizationalhart).Thesection ead eportsothe branchmanager

nd s responsibleor theoverallmanagementf theslotmachineoperation' heassistanteads sist thesection eadn themanagementf theoperation.Thesupervisors,n theotherhand,are esponsibleor the proper ontrol.andonduct fslot machine operation.The senioi and junior techniciansperform the rrg.rlarmalntenancehecksand needed epairson the machines.The slot machineattendantspreparehedocumentationuringackpotwinnings, reditpayments,ndhopper efills.Theyalso ecord he dailyvolumeof players nd he daily engthof play imeson each



, , '" i I '

i

niachine.TheSlotMachineSection as okenattendantsho rove aroundhearea o sell

tokensto.slotmachinelayers. hey actuallylbring o the players he needed okens

Figure1-SLOT

M{CHIMSECTIONORGANIZATIONAL IIART

' 1 r ' J

to helpdecongesthe okenboothsof theTreasurySection.This system ot only helps nincreasinghe average lay timeson the machines ut also enhanceshe competence f

the casino to serve its customerswell. The network controllers ake care of the

maintenancendproperuseof slot machinenterfacecontrollers.',Theylsopreparehe

. routindSlot MachineSectioneports.

Like otherCalno Filipino operations,he branchs relentlessly odernizingts

facilitiesandcontinuouslymplgving ts-operations. s.part o{the qug.s!or superior

performance,anagement ould ike to evaluatef thecurrentmix andplacement f slot

machines o 5T leadin=gocationsand heir extended roupsare still favorableas far as

maximizing etreceiptss concerned.earlysix monthshavepassed ow since he ast

reassignmentf slotmachinesookplace n the area.The diagramn Figure2 represents

t}resevenstrategicpointsand the leading ocationsof slot machines n each strategic

point.The diagramalso hows heextendedgroupsforach eadingocation. able2



Figuri 2 - LAyouT oFsLOT MAcHIti{EAREA

Fl98

Fl75F188

F177

El47

ET46

ID130

cl16

c101

RestRooms

GCr222

G22sGl83

/A2II MO

Mrz A163

At544.139 ' ,

8124

Bl73

F43

8108 c10QC44 C68at_.

c27c26

SlotMachineSectionOffice

EntranceromParkingAre4 Treasury



' , '1"

't,

: , i l

tl, I

. ' l

9

STRATEGICPOINT ,

Tab|e2- LEAI}INGSLOTLOCATIONSWITHINA STBATEGIC OIM

LEADbIGSLOTTOCATIONS

c

D

G

At4:1otL,Al39, l54,AI55,A182,At63,A2l l , 70

8221, l0g,8173,123,8124,l38

clol, c116,cI00,44 , 68,c27,c?:6

DI17,D130, l31,DD7, I66,D96;D73,D63,D32

Et46,Et478162, 9l,E7 ,E57P.43,E46, 193, l68

F109, i77, l88; 175; 198,199,F 2 0 6 , F g l , F 2 l , F 2 0 , F l , F 4 9 ,

G222,Gt83,G225,G703

Table3- CUnnEl,frASSIGNMENT f"SlOr MACHINESN EACHLEADINGLOCATION

STRATEGrc OINT LEADINGSLOT OCATIONS MACHINETYPE

A 1 4a2t2A l39Al54A l55

At82Al63A 2 l lA70

B22lBl08Bl73Bl23D I L q

B l38

c10 tc l 1 6cl00

c68 .f a a

e26

Dl 17D l 3 0D r 3 lD97Dl66D%D73D63D3 2

PlORaiseDrawP 5 M a g 7 _ .Pl0 DoubleDragonPlO DoubleDragon'Pl0

DoubleDragonP10RaiseDrawP105-WayLotusP5 N{ag7

' PlORaise raw

P5 N{agicCashier

P10TripleCasb

PlO DiamoudWinners

Pl0 Wild RosePl 0 BlackGoldP10DoubleDragon

'P30BlaokGoldPl0 BlackGoIdP30RaiseDrawP5 DoubleTake

. P5Blpck & White

P5JewelChest ..P5JewelChest

P10BlackGoldP10BlackGold

'PlO DoubleDragonP30RaiseDrawP5.Double akePI0 TripleCash

' P5 ScoreboerdP5 ScoreboardP5 Scoreboard



10

Continued.. Table3 ,.

STMTEGICPOINT LEADING LOTLOCATIONS MACHINETYPE

G

. . .E t4$El47Et62 .

E9 l. E78

F.57843F.46El93Erer

F109'Ft77

_ Fl88Fl75n98

. Fl99F206

. . F 8 l

F2IF20 .

, F l'!4e

G222Gl83

. c225 '

G203,

Pl0 DoubleDragonPlO DoubleDragon

'

PlO DoublcDragmPlO TripleCashP5ScoreboardP5Scoreboard1

. P2GoldenCalesaP2GoldenCalesaPlO TripleCashPlO Diamond ine 87

PlO RaiseDrawPlORaiseDraw'PlO RaiseDraw'

. P5PokerRealP5Rapid5-WayP5SummerVacationP5 vlag7P2GoldenCalesa ' . .

. .P2GoldesCalesaP2GoldeirCalesaP5GirmevfakerP5TenGrandGame

' :. P5 JewelChest

P58 Ways lltimhtcP5PokerRealP58 WaysSuperior

TAbIC4 - NTIMBEROEMACHINES IN TIIE CURREM lflX AND ASSIGNMEI{T

MACHINEMIX NUMBEROF ACHINES IDENTITYCODE

Ia

6

8

I^

' 1

. tA

I

I

2I

). | ,

P30BlackGotdP30RaiseDrawPl0 RaiseDraw

PiODoubleDragon

P105-WayLohrsPI0 TripleCashPl0 DiamondWinnsrsPl0 Wild RosePl0 BlackGotdPIQDamondLine87P5Mag7,,P5MagicCashier

P5 DoubleTakeP5Black& WHteP5JewelChestP5ScoreboardP5 PokerReal '

,P5Rapid5-WayP5 SummerVacationP5 GamcMakerP5 TenGrandGameP5 8 WaysUltimateP5 8 WaysSuperiorP2GoldcnCalesa

3OBGI. 3ORDI,3ORD2

l0RDl, l0RD2, 0RD3, 0RDl,IORDs,IORD6IODDI, ODD2,1ODD3,OD}{,IODD5, ODD6, ODD7,ODDSroFwloTcr;0Tc2,l0Tc3,0TC4IODWIIOWRIIOBGI,OBG2,OBG3,OBG4IODLI5M1,5M2,5M3

5MCl.5DTI,5DT25BWl5JCt,5JC2,5tC35SBI, S82, SB3,SB4,SB5sPRI,5PR25RFI5SVI5GMI5TGGl5EU1sESI2GCI, GC2, GC3,GC4, GC5



11

TAbIC - AVEMGE MACHII{E DATA

MACHINE TYPE / C'ODE

NUMBEROFPLAYSPERMINUTE

P30BlackGotd 30BGP30RaiseDraw 30Rti

. PI0 DoubleDragon/ ODDPI0 BlackGotd lOBGPIODamondLine87 / t0DLPlO DamondWinners l0DWPlOWitdRose/ OWR

.. PI0RaiseDraw/ l0RDPlO5-WayLotus l0FWPlO TripteCash tbtCP5Double ake/SDTP5Black& Whire/5BWP5 TenCnandGamel5TGP5GameMaker/5GM .

P5Rapid5-Way/5RF.

P5Surnmer acation 5SVP58 WaysUltimate/5EUP5 8 WaysSuperior 5ESP5Scorebodrd5SBP5lvlagT 5MP5MagicCashier 5MCP5JewelChesr/5JCP5PokerReal 5pR

'

P2 GoldenCalesa 2GC

5

J

J

J

J

J

J

J

J

4A

44 'I

44

' T

+' 4

4444

' ,

TAbIE6_ 24-HOURAVERAGX NI]MBE[. OF PT,EYTNSPrR MACHIM TYPE

MACHINETYPE STMTEGIC POINTS

29132 ll 020t 922. 7l 9t228

l 92 l) \278

22T225232 l122225

1' )

6I AI t

) l

I U

7I

t tI N

2I J

z5

8t rI t

9I At a

2 ll r

l 6

2 lI J

t <

9l 2) l

l 5a ,

2A8

LV

l o

I Il 512

o

8t 0t66

I 320T42 l20l )

P30BlackGold. P30RaiseDraw

Pl0 DoubieDraeonPl 0 BlackGotd-PIODiamondiul:eFilPI0 DamondWinnersPl0 Wild RosePlORaiseDrawPl0 5-WayLohsP10TripleCashP5DoubleTakeP5Black& Whits

P5 TenGrandGameP5GameMakerP5Bapid5-WayP5SummerVacatiohP58 WaysUlrimareP5 8 WaysSuperiorP5ScoreboardP5Mag 7P5MagicCashier

. P5JowelChestP5PokerRealP2 GoldenCalesa

2 6 'z>

2 l. 7 ' , '25l4I I25 1272 4 . ,a /lL'

t l5t t

526a ,

2227

7zo

t 82822

2227' 6

' 2 8

z3

L I

25l 26

. 2 627

zvt2v

J

222 1zot <

z )

25t 7t 025

2U

t 0] U

1 29

20221 A

222829

2 l1' '

t o

2028232 1I t

l 9I 68

l 9

21t

. t t

1 2. A

I' t

l 567

l2

23)8

1 At n

. 8J

6-t J

)2

1 n

5t 4



t2

Table -il-loIJR AyERAGELAyrrMEs(inminutes)ERpLAyER ERrvrAclrrNE

MACHINETYPESTRATEGICPOINTS

. 6. l l

87

127

25)

l 0t5

' 3

l 5zv

6. 1 5

it .

l 02

125

'12

1 56

. 4. 7

. J

A

), 2

355

. 7J

2 l8

l 0. o

, 4l 0306)

l 4I 61 98

. J )

P30BlackGotdP30RaiseDraw

. PlO DoubleDraeon:P 0 BlackGoldPl0 Diamond ine87Pl0 DiamondWinnersPlOWild Rose ,

PlORaiseDrawPlO5-WayLoh6PlO TripleCash

' P5DoubteTakeP5 Bldik& White l

P5 TenGrandGambP5 GameMaker

P5 Rapid5-WavP5 SummerVaiationP5 8Ways JltimateP5 8 WaysSuperiorP5 ScoreboardP5Mag7 . . :P5 MagicCashier

. P5 Je'welChestP5 PokerRealP2 GoldenCalesa

' i

)7

l n

. 325)

l 2. J

1 I

. 2 0

l55

l425,'

' s' 5

23t o

)z v

25I 57

4035J I

J

2412293 l20

. .251 8

25t2

. 2 1

5. 2 2l 5l o

. 3 4

45.

. 3 2t7

. 2 8303025t (

J O

l ) . .

35J. '

2640

23' 5

27z5

l 4251 9 .27A Il l

)+

+z

249

'35

. ) t

6J.f

20to

740

. 3 5

r4', 2s.' 1 4

t235283538t t

25. Aza

25t v

, ll l

. , 1

z )

38z+

l 93923344 l4532

2 l, 6.32206

J J

2)

3 0 .453037

summarizeshe eadingocationswithina strategic ointwhileTable3 lists he current

T*-"no assignmentf srotmachinesn eachreading ocation. able ,,;; ; ;;.;of slotmachinesn thecurrenimix andassignment.able5 containsheaverage umberof playsper minuteof play time on eachmachine ased n .u.tn"; Table6provides he dataon 24-houraverageo.lume f prayers n ail machinesuk.rr;;;;r;strategic oint'Table7, on theotherhand, ontainshedataon 24-hour verageengthofplay timesperplayerpermachineypeat eachstrategic oint.Slotmacfune itendantstookthedatainTables6and7forthelastthree-ontn,]

machinemix andassignment.anagementasdeterminedhatslotmachines;;consistentlyttractcustomers. ithermachines f various ypesor machines f similart't'pesma1' herefore e groupedogethern sucha way thateithermix throughoutheareas positionedn roughlyhesame roportion s hoiemachinesssigned.; ,;.;;stra.teglcoint. As required'bymanagement,lot machineo**r,-o-nt* ;;t;"-;Filipinobranchmustahvays avealternativemachinemixes*rrn *n,.n to comparehe



13

of thegrr-entmix. Table 8 provides the alternativemixes of slot machines n the case

branihunderstud i . ' ' '

Table8 - ALTERNATIVE NIXES OF SLOT NTACHTNES ErNG CONSTDERED

MACHINEMIX MIX I MIX2 MIX3 MIX4

P30BlackGoldP30RaiseDrawPIORaileDawPl0 DoubleDragon.P105-WayLotus'.P.lOTripleCashP10DiamondWinnersPlOWild RosePIOBlackGoldPl0 DamondLine87P5Mag7 . I :

I 3l 2a

222J

2

2

7

22.2I

I2

, 2

2

P5MagicCashis .'P5DoubleTake '

P5Bldck& White'P5JewelChest ' .

P5Scoreboard :

P5 PokerReaI'P5Rapid5-WayP5Summer acationP5GameMakerP5TsnGrandGameP58 WaysLTltimateP5 8 WaysSupe.rioqP2GoldenCalesa

2I

' t' I

r ' ' lI

I: l

2I2II

30

22 .It

. t

II

tI

t 4 l o

The casino's resent ystem f mixing and assigning'slotmachineso strategic

pointsdoesnot use he conceptof the assignmentroblemas a distribution roblem.

Howevgr,he present ystem lsoconsidershe ypesof machines nd, or each'machine,

the-agtual

aily-averageet receipt,numberof players, nd engthof play times even

though t is reiativei,=- -

juOg*.otrf u"J not as mathematicallyigorousas the

assignmentroblem. hebranchoperationstaffprovided o information n the actual

daily averagenet rec-eipt ei machine ype to the author. t was ust describedas the

amount eft to the casinoafterdeductinghe amountof machinepay outs, ncluding

players'ackpots, nd he refilli, or amount eplenishedn a machine y the casinodue

tg pay outs, rom the amountcollectedn the dropbox. It was i:rtherspecifiedhat net

receiptsroma slotmachine ctually arywith machineUpe. n absencef actual igures

on net eceiptsromamachine,t washowever evealedhat he hold rate or all machine

tlpes s 8 percent n theaverage. hehold ateof a machines defined y the operations

staff as the ratio of the amountof casino'snet rvinnings,ncludingackpots, rom a



T4

machine o the amquntollected in the dropbox inside a machine.Asidefrom the fact

that customers assing lose o anyslotmachirieg1oupwill take he first emptymachine

!o play, there.isalsoa generalperceptionamongslot machineoperations eople hat:

customers suallyplay ongeron slot machinesocatedn theareasnear he okenboothsandnear he rest ooms. ,

,

TIIE PROBLEM

Ttie slotmachineoperationn the particularCasinoFilipino branchdescribedn

thispapers in theprbcessf appraising hetherhecurrentmix andallocation f itsslot

machiness Still relevant itt ief.rence to the presentprrfrrrnrm of customers. he

currentassignments already lose o six monthsoid andmanagementeels hat a review

of thepresentmix andassignmentf machiness already eeded. ssentially,hereare

two sidesof theproblemn the case.One s that of knowingwhethera new'mix and

assignmentf machiness neededn theslot machine rea: heother s that of knowing

what mix and assignments needed.Figure 3 is the schematicepresentation f the

problemn the case.

Figure3 - CASEDECISION PROBLEM ILLUSTRATED

Crurentmachinemix andassisnment

Evaluation f currentmixandassignmentf

slotmachines

newmix andassignmentf' I

slotmachine

Evaluation f alternativemixesandassignmentsf slotmachines

(Mix I, Mix 2,Mix 3, andMix 4)

Whichaltemative il l maximize aming otentihl?



15

' : j

MAJOR OBJECTTVE

:'

The major objectiveof the study s to recommend machinemixandassignment

thatwill maximize hedailynet receipts hatcanbe earnedrom the slotmachines{n the

casino,This can be doneeitherby using he casino'spresent ystemof mixing and

assigningmachines r by using hemoremathematicallyigoroirsassignmentroblemas

a distribution roblemor a special ype'of linearprogramming roblem'(Turbannd

Meredith, gg4)..This tudymadeuseof the attermethod.

AREAS OF CONSIDERATION

: '' " " : i : ; 1r r ' ' : t : ' - "

ihe iollowing iactorsareconsideredn thestudy:

o Thedesignatedtrategic olntsand he eading bcationsn eachstrategi.cgint.. :

oTheaveragenumberofplaysperminuteoneachmachine.

. Thecurrentmix andassignmentf slotmachinesn eacheadingslot qcation.

o The 24-houraverage umberof playerspermachineyBe n eachstrategicocation.

. The 24-hour average engthof play per playerper machine ype in eachstrategic

location.

. Thealtemativemixesof slot machines eingconsideredy thecasino.

average oldrateof 8 percentor all machines.

. Theminimumallowable mountof bet hat canbeplacedby aplayer or eachpull.

. The endency f customerso take hefirst emptymachine o playas heypassclose

to anystrategrcocation.

l Management;sinding hat slot machines sa graupconsistently ttracts ustomers.

o The branchf quest for superiorperformance eading to - high profitability and

customeratisfaction.

o I neorgaruzauonf thebranch'SlotMachineSection.



-:..'>

t6.

NTSCPTPTIONOF'THE METHOI)

^..

Accordingo Turqan ndMeredith 1994), istributionrobler.nsrespecialypesof linearprogramming roblems ndcanbesolvedby efficientcomputationuftror"d*.,because f their speciar truchne.one type of distributionprobrem, , tr,, ;r;;;;problem' t involves finding the bgst.one-to-oneatch or eachof thegrvennumberofcandidates'

to a numberof 'posilions""(Tunban ndMeredith,1994).parameterslike

:"::* benlfits 4re nvorvedn eachurrigom.nt,with theobjectiv.

"t;t*;;;;;;;osts r.maximizingbenefits.,:'.

.

- 1

"

"

1 :. ' j .

Asnmprtd'ii of theAssignmew roblem

describedin this paper s tlpical of a classofassumptionsf the assignment roblemcan be

TheAssignmentproblem asa Linear program

Th;assienmentroblemn thdcase anbeexpressedsa specialypeof linear

programming roblernwith the ollowing ormulation:

r l l l n

lMu"imizeTotalNetReceipt: X Z pr*,

i : l j . : 1 , , . u



17

Subject o the iinear constraints balancedcase):

n

E Xt : I i : l , 2 ,3 ,4 , . : ) ,r l l

j : l

' .

m.lrr

L x i :1 j :1 ,2 ,3 ,4 , . . . ;n

i : l : . ,

e valueof xi;: I

meanshere s a matchbetween andT; hevalueof x4 0 means here s

atch.om

' - - -Whe-Ig. I -- l ,. P4: thedaily average etreceiptassociaied ith anassignmentf i to7.

Xy= 8nassignmentf ttre rthslot machine o thelh leadingocation.

' . '

. 'Accordingto TgrbanandMeredith 1994), theaSsignmentroblem s'usually

balanced roblemwith n items o be assignedto objects." hismeanshat f thereare

57 slot machineso be assignedo SZ gading ocations,as n the casedescribbd y this

paper, there are 57! (57 factorial){iffere.ntsolutions q the problemor 4 05 x 10 76

solutions. urbanandMeredith 1994)call this the complete numerafionpproach. n

the caseunderstudy, his approachs impracticalbecause f unmanageablyargenumber

of solutions.

This paperemployedhe Hungarianmethodof solving he assignmentroblem

through he use of the QSg+ Version2.0 software Changand Sullivarl 1991).

Accordingo TurbanandMeredith 1994),he Hungarianmethod is the mostefFrcient

way of solving argeassignmentroblems." he procedures based n the following

theorem: lf onesubtractsor adds)a constant umber rom all entriesn anyrow or

column of the assignment. atrix, then the total cost of each of the n! possible

assignmentss reduced or increased) y the constantnumbersubtractedor added)"



t8

(Turban ndMeredith,1994). evinet.al. (lgg2) call theHungarianmethodheFlood's

lechrique.Figure4 showshe lowghartof theHungarianmethod.

' 'Figure4-FLOWCIIART

OFTIIE HTNGARIANMETIIOD

Arrangeproblemasa table

' . '

Subtract ll entrics romlargestory n able

Improvable olution:Identi$ smallest mcoveredcntr,v,

l. Subract t fromall cellswithout ines.

2. Add it to all cellswithintdrsectingines.

3. Cellswith one ine emainunchanged.

Result=

Improved olution

IdentiS optimalsolution(s)

y makingsssigmgnts ozrro.valuedcells n one-toooematches

Calculateostor -prolit ofassignrirenty .rcferringto original able

columns)

Source:TurbqnandMeredith.1994



20

assignmentroblemobjectivehasalwaysbeen o maximize he totalnet receiptof each

altemati-velot machinemii, It shouldbe notedagain hat hetotalnet eceipts omputed

by the four altemativeassignmentsreall basedon the minimum ailowablepmountof

betthat canbeplacedbya player or eachpull on a Slotmachi-ne.his s so because oinformationon the actuaidailyaverage et receiptpermachine fi wasprovidedo the

authorby theoperations taff.

The assignmenteneratedn Exhibit 3 is the computer inal solution or Mix 1.

The assignment eneratedn Exhibit 4 is for Mix 2. For.Mix 3, the assignments in

Exhibit5, and or Mix 4, n Exhibit6.' -

t ; r " ' - - - " . -

The assigiiiieni in Exhibit 3 yielde-da ma4rmum total riet receipt of Php

63,776.09 er 24-how d1y Mix I containsmore machipes

in lhe

Php 5- andPhi 2-

denominationsthanmachinesirithe.Php30-andPhp10-denominationsml

The assignr4entn Exhibit 4 lelded a maximum total nef receipt of Php'

, j

158,854.8er24-hour ay.Thisassignment asgeneratedsingMix 2. This alternative' mix containsmoremachinesn thePhp30-andPhp 0-denominationshanmachinesn

the owdrPhp5- andPhp2denominations,n otherwords,Mix 2 mraybe onsideredhe

oppositeversionofMix. ' ,

Exhibit 5 yielded he'assignmentor Mix 3. The maximum otal net receiptper

24-hourday basis s Php 115,882.Mix 3 is differen, Ao* the two:othermixes ust

describedabove. tt containsan almost equal number of machines n all the four

denominations.herea1e

14 Php30denominationmachines, 4 Php 0denomination

machines,15hp5-denominationachines,nd14Php2;denominationachinqs.

Exhibit 6 containshe computergenerated ssignmentor Mix 4. The total net

receipt or themix is Php125,362.7er24-h9ur ay,Mix 4 containsessof thePhp 10-

andPhp5-denominationachin'eshan hePhp30-andPhp2-denominationachines.

Of the ouralternativessignments,he assignmentor Mix 2 is themostsuperior

assignmentn termsof maximizinghe casino'sotalnet:receiptrom ts slot machines.

Even if the casino'scurrent mix and assignments included n the analysis, he

assignmentor Mix 2 is still the mostsuperior. ts maximum otal n9treceipt s actually

3.47 imesmoresup€riorhan hetotal net receipt hatcan be derived rom the casino's

currentmix andassignnlentf slot machines. he currentmix and assignmentf slot



2r

machinesn the casino s actually he most nferior assignmentn terms of maximizing

the otalnet ecei$thatcanbeearnedromtheslotmachines ivenall the factors hat.are

consideredn the solutionsanil the assumptionsf the assignment rgblemasa special

linearprognmming

problem. . ' . ::

^ - - * - -CONCLUSION ANI} RECOMMEI\DATION

, :

Bas€don the solutionsgenerated,t can be concludedhat the currentmix and

assigrurlentf slotmachinesn theCasinoFilipinofrancfrunderstudyshouldbe replaced

with a mix and assignmenthat can maximize he casino's otal net receiptfrom slot. . . - . :

machineoperation.Mix 2 is therecommendedmix thatcanyield anoptimum assignment

of machines. hetotalnet receipthat canbe reatized y the'casinof it uses his mix is

Php 158,854.8er24-hourdayorPhp57.98million p€ry€ar. t bansubstantially ive he

casino he needed oost n termsof maximizing ts total net receipt.As it is now, the

currentmix andassignmentf machinesn theslotmachine reahas he owest ealizable

totalnetreceiptof onlyPhp 4s,743.36ailyor php 16.2million per year:

. Table9 lists dootr the recommended ix and assignments f slot machines. he

hEavl clusteringof high denominationmachinesn leadingslot.locationsof strdtegic

pointsC, D, E, andF isvery noticeable. igure2 showshat the samestrategic ointsare

actuallyclose o the tokenbooths A i"*t rooms.Furthermore, ablesO na I revealo

that sJotmachinesocatedat strategic oints'C,D, E, and F have relativelymuch higher

utilization han heothers theyhavehighernumberof playersand onger engthof play

times'These'confirmhat the generalperception mongsiot machineoperations eople

that customers suallyplay longeron slot mzrchinesocated n the areasnear he token

boothsandnear herest ooms sactuallya reality.

Tebh RECOMMENDEDrx(Mir2)exo essrcrurltNT Fsr,or uecrnms

STRATEGICOINT LEADINGSLOT OCATIONS MACHINETYPE

4 Al4A2t2A139Al54

. Al55Al82Al63

PlO 5-Wayl-ohrP10 5-WayLohsP5 lvlagic CashierP5 Ten Graad GarnePJ Jcwcl ChestPlO WildRosePlO WildRose



22

Contiuued .. Tabl€ 9

STRATEGICOINT LEADING LOTLOCATIONS MACHINETYPE

D

A2l lNO

B22lBl08Bl73Bl23Bl24 :Bl38

c l0 l .c l 16cl00-_c44c68c27 ..c26 |

D l lTD l 3 0 'D l3 lD97Dl66D.86.

D73D63D32

El46El47El62E9 lE78

F,57f ,+ J

EA6tr I tJ

El68

FtosF171Fl88Fl75Fl98Ft99r/uoF8 lF2rF20

FIF49

0222cl83o225G203

P5 SWays Ultimate .. P5PokerReal

P2GoldeaCalesaP5MagTP2GoldenCalesaPlORaiseDaw.Pl0 RaiseDrawP5 GameL{aker

P30RaiseDtaw. P30RaiscDraw I

. P30 RaiseDrswPlO DiamondLine 87ElO RaireDrawP30RaiseDraw

.P30RaiseDraw'

. P30Black GoldP30Black6oldP30Black GoldP30BlackGoldP30Black GoldH]0BlackOold.P30BlackGoldP30Black GoldP30Black Oold

P30BlackGoldP30Black GoldP30BlackGoldP30Black GbHP30 RaiseDrawP30 RaiseDrawP30RaiseDrawP30 RaiseDrnwP30RaiseDraw

, P30RaiseDraw

Pl0 DoubleDragonPlO DoubleDragonP10TripleCash

. PlO Triple cashPl0 DamondWinnersPlO Diariond WinnersPlO Danrcnd WinnersP5 SummerVacstionP5 DoubleTakeP5 8 WaysSuperior

P10BlackGoldPlOBlackgold

P5 ScoreboerdP10DarnondLine 87P5Rald 5-WayP5Black & Whitc



REFERPNCES

B\rsiness ertiqq 2.0.Prentice-Hall: nglewoodCliffs, New Jersey' .

I-evin,RichardL, David S.Rubin,Jobl P. Stinson,andEveretteS. Gardner, r. (1gg2).

Ouantitativeooroacheso Manasement.6 ed McGraw-Flill: ew York.

)-

PAGCOR's'1996s*l Reoort.

-

, -

- - - , - : ^ - - ^ - ^ ^ - - l a l f t

. . :

. - : _.

.. . : . . : . : . : . .

. - . , j

Turban,EfraimandJackR. Meredith 1994).Fundamentalsf N{anagemdntcience. 6

. . ed. rwin:Bun Ridge, llinois.



24EXHIBITMATRIXOF DAILYAVERAGE ETRECETPTSinphitippineesos) F sLoT MACHINESN ALLSTRATEGIQOINTS

Machine ype

P30BtackGoldP30RaiseDrawP10DoubleDragon

:

P10BlackGoldP1 0Diamondine87P10DiamondWinnersP1 0WildRoseP10RaiseDrawP10SWayLotusP10TripleCashP5 DoubleTakeP5Black& White

'

P5TenGrandGameP5GamaMakerP5Rapid Way

'

P5Summer acationP5 I WaysUltimateP5I WaysSuperiorP5 ScoreboardP5 Mag7P5 MagicCashierP5JewelChestP5 PokarReatP2GoldenCalesa

259.20172.80252.00'252.00576.00144.00480.00240.00662.40115.20193.6072.00

384.00144.0064.00

224.O0040.00: 19.20

62.40160.00515.20403.20160.00278.40

B

345.60302.40100.80201.60

,120.0033.60

336.00168.0033.60

156.00772.8A

.102.40.176.0086.40

' '99.60

'336.00

528.00153.60'192.00

470.40332.80212.8064.00,

336.00

.c .

4,680.003,132.00

352.80672.O0

2,100.001,041.60. 79.201,440.00

777,601,670.401,190.40

480.00.680.00't44.OO

1,040.00460.80739.20

,

216.00739.20168.0066s.60979.20

. 940.80633.60

D

6,681.601,591.201,;411.20

720.O01,440.001,140.00

792.00604.S0684.00

1,008.001,478.40

790.401,344.00

920.00216.00345.60809.60268.80

1,000.00699.20e07.20787.20

1,196.80672.00

E

6,494.40.4p82.40

460.801,545.602,097.60

979.201,140.001,123.20

331.202,121.60

'1 ,771.20.

2,088.00614.40302.4048.00

1,126.40672.OO249.60792.W

1,000.001,200.0o1;224.O0

480.00592.00

F

3,456.009E.00

1,512.001,065.60

129.601,584.001,056.00

974.40369.60

2,688.001,624.00

470.40.480.00582.40384,00

1,568.001,030.401,176.00

665.80516.80640.00307.20760.00673.92

G

.86,40

316.80211.20201.60575.00$1.2A240.00180.00144.00252.0057.60

552.00160.00'

?6.80336.00

51.2048.0015.20.

288.0040.0038.40

240.0048.00

215.04



J.a

{+

f;.; .:.,

25EXHIBITDAILYAVEMGENETRECE|PTSh phitiryir,€eso6)FRoMTHECURRENTAsstcNMENroF sLor MAcHrNesteecumhg fii;;;;-;-#ril betperphy)

L€ading

SH€gic Sktft)int . L€tlns Macl*p Type

21-llopr 24-Hqr Ayora€B

A\€ragp Avefa€g NurnborNumber' .

llayTrne ofpbysd Phye6 (il mlrurtes) per Mirxrte

MiirirnumDrityAmountof Arerags

Eetper . N€tPhy Recsitrt

Hold ,'Rate

A .A14 p1oRei€€nw n . F,g .

B%,,

10 24o.m A212 PsMaez? ; .4 B% 5 160.mt3 9 pl0DoqbbDr?go.r.

.2 1 S.g

Ao h 10 2SZ.q 4154 plO Da.rbbDragon

. llg :lSRHlH'on 21 s ? s% ro zsz,FA{60 etO+WayLots

-- . -

?, ' r :

Fo' |?JITJ,* ?' , a 4, ;; . s 16000:B , {ir ;;il"n;;;*L n ,l ,

I Zn ir3

#.$t0e Horr i ;bca i i , . :i 3 ; , i

- ; ; , ,:10 1s6.oo1T3 pjoDiznondWnnera

: T ; 3. g%.. 10 g3.@, a1?3 Plowild Rce

; ; , 3 , B% ..10 so6.oo121. . plOBbckc,oH 21 1 3 s% io 2ot.6oi3g ploDo,rbt€Oragon14 j

3 g% 10 1OO.Bo cj0t P3oBbckcotd. ; ; ., 3 B% 30 4,680.00:lS .FSiHffi j ; ; il io 6126c44- '-o*"il; To ' :? i , :f * l:l$f6S. psBbck&White

15 n I OX 5 ,I8O.OOz| psJ€i , l€tch6t. . , i ; ; 4 . B% b grs.nD. ;fr, ::J#_.ffi ie ; ; # ; ;;;:.x

o13oproea.rc,oui3 S : ZA , ll, n;n131 pio Dotrbteragon 21 za ; ;; . jo 1,411.n

3:l if"ffi?tr il fr a s% 30 r,ss12oDe€ plorripr.c$h

fr."

3 3f .,i l,;#:#73 pSsqeboardx A 4 .B% g 1,0m.@

Bff f : f f i :2 : ,%4i ls r ,ooo.ooE - __llf prqoq,ur.o""s"r, ? _ . A*.._*: *_""3I _,_"***_rl*,;;H,SE147 plO DoubteDragon ;E162 p1oDoubh ragpn 6 g2 3 g% 10 4€o.eosJ plo rrif,ecasri 26 t 3 A; i 10 . 2,121.& : .EZB p5scoreboard.

15 ; 4 e% s 7g2.@57 Psscoreboard 15 33 . 4 B% 5 792.00€ . p2 GoldenCetes8 ,5"?

I g% 2 SC2.@4€ P2Gddencateea z5 n 4,

8% 2 5C2.@193 pjOTripb a6h n 34 3.B% : 10 2,121.&168 p10 Dinmoqrdin€Bz ; ; . 3 s% 10 [email protected] F1@ . p10RahoDrarv 14 n .. 3

.g% 10 gr4.4nn pio RabeOraw

F188 P10RdseDnrv14 a 3 8% 10 ez4.q

F't7s 'i p"i"In"J"ii

n; #

10;#.#lsB ps Raptd .Way 6

;; 4 B% s 3g4.oo19O p5SurnmerVatkxr . . n 3O 4 B% 5 1,56g.002oo P5Mag 19 fi 4 g% s s16.Bo . ., FBI pz c,oraen el€€a zT 3, 4 a% 2 673.g221 P2GoldenCate-

Zf 39 4 8%: . Z 673.92

. FT f ffi^,|;ff" 3e 4 o% 2 6r3.s2

; ,e i:ffStr;.,o n- L: i !# I ffi#:S ffiyl{#,"."

'! l3 i itr 3 'fr$G2o3psew.v ; l ; i i * :2 i : r

Tcrtal 45,74:1.36



26. t

EXHIBM3- QSB+SOFTWARESOLTIiTONTOAI,TERNATTVESLOTMECrrrr,rSMX I

- - - : - : - - - - -+- - : , l l - - - - -+ ' : - - - - - - -_ :_+__- I_ l : -__ i__: : : :_ ,_-_+________-_308G1 p11? t: .gg?? srci_

-i----i l ; ;--i----;;;; i-308c2 | ,! l9g., i .gg9a i isir I D1311 +10000RD1 E}1q i .1gga i i i i rr r ,Ds,t 1 +trez0RDt' I glgl i .111g i si t i r , l : c100 | +10400DD1 l ' I lgs i t l l t l i s-srvr, rtTs t, +1568oFtul. I l l1_ i, .ur, r4, i 5iq t , Fres | +15680rc1 I \ !77 i ; lFq! i iEur I Dr.66t +e20.0.0Dw1t l lgg i *1191,i srbr , t De6 l +13440wR1 | !\ t7 . i .1119 i si iz t , D73 | +r.3440BGr I l lg? i . l i t i i 6eirr I AzLz | +640.00Dt1 | !198 i *?gga i Sisr r F2o6 I +1176ul ' | 891 i . i igi i , iEir, l , BzzL .+336.0. sMcl | l lg i,

'* l?gg i ;&t , i , ; ios I +336.0 5t7c2 I !?? i .ii i i i idis r Brz3 | +335.0 sDrl I l fg i . lZZ! i idia | 8123, +336.0BwL l .E4G j +2088 i zcc.s I BLIA I +336.0

MaximumoBJ=,63776, .09r terat io ;==- ; . - ; ; ; - ; ; ; ; ; - - - ; : ; -

t - - - - - - -I

I uti l ruuary of, Assignments for SLOTMIX' page: 2- - - - - - - - - - - - - - - - - - - - : -

i ourect I rask-ia;;;7;;;;;-;;;; -.i--i l;- '-l;;;;;;;;;:

|- - - ; : : ; - - - -+ - - - : . : - - - - i : : :__ ' -____+__________+-__ ;______+___-__-___

IIIIIII

I 2Gc6 | I91 i *911.? 2ccr.s .riu:-i--=;;;;:;-| 2ec7 | I?1 i *gl l :? i zi ;czo I Flee | +673.eI zccs I I?0 i +ozi.g i ibczr 1 A13e | +278.4| zccs I Il i *gzl.? i ieczz I A154 I +278.4 2ccr0 I I1?_ i *gJg,? i ibczgI

A15s|

+278.4 2cc1r. t g??? i .?l : .q i ,gql t i B13B +336.0 2GcLz | -c1q3 i -?l i . i i leczs I ArB2 | +278.4| 2Gc13 I pgl i -gz?.g i zecza I c2o3; +215.0| 2Gc14 | !g? i +ot i .o i icczz t ezzs | +215.0 2cc15 | 94-! i +911.9 i iecze I A163 | +278.4 2Gc16 I ggg i -gl i :q i leczg I A211 | +278.4 2GcL7 | 9?7- i *gl l .q i zccgo l Az0 | +278.4. 2Gc18 I c26 i +633.6 I r ,

OBJ = 63776 .09 I te ra t l on = Z CpU second = 9 .5

III

I



27

EXHIBIT 4_ QSB+SOrrW.rNS SOT.UITON OALTERNATTVESLOTMACfttNE I,']DK

---iiiir-i--Eiii-'

i--:ilii--i---un"i-'i--::ri;;--i=

'308G2I p\!7 i .91?1 i Ioirbq i sis- | +4082.08G3 , pllg i .gg!i i ioino i Eat | .+4082

I08G4 | p,191 i -giii i ioiibl i eai r +4082oBGs I plg6 i *ggga i 5o*pq f E4G | +408208G6 |pgg i; i i i l i , I6ibd:i Eissr +4082f08c7 I 9?9 i .ggga i i6iiulo Ei;B | +4oBZ0BGBp?7_.i .ggg? i ,Io*Utl c6a | +31320BGe I gl1? i ;gqil i i6ibrz i iii | +3r.3208c10 Fl62 i .9124 i f'ffii- i iize r +1680 |0Bcr1 g?l i -gtZt i ioibz i Eit3 | +168.00ncr2r lgl i igqll i ioel I Fr.oe +151208c13 D?2 i .giii i ioiirz I F1?? | +15120RD1 9?g. i .:1la i iofrr I A14 | +662.4oRDz I ql91 i; l t i l i ioiwzl AzLz

.--:9T:___1 1r6 i *!rgz I r.orcr"rr,

' I.13?;A

I- - - - - - - - - - : : - - : : : : - - - - - - - I " ' ' l a I ru l L ; r ' I F l88 | +2698 |

' ;;;il;;-=;;-';il-i;;;:=-;;

:;;;;--

i

r -------- -* --- -- ___:::1 I:: - _::l !l__,1_ :::_.__::::1:::l- | 10rc2 | I1?l i : lSla--i---ui*r i c203 r +552.010Dwr I l l?g j - l : i1 i i igt i aiss I +403.210Dw2 llge'

i .1: i4 i ;; i i i Ci iz r +288.0

I lSBHi i?gt i ^:i:di iill r r?e- +160.0

t - --*---

I :TTI- :- :1 1*""i"- l;;;bffi ;;-'=;il; -;

ii -::::::--,1-iJ

-=-l;;;;;;;;:|

;;;;--l.;;;;

----;il;;il;;: i

I rLrwRr At 2 i .fgg.i i ;iii i Eiis i liSi:8 i r0wR2 r 1163 i ing9,9 i isvi i i6 i r +156810BGt i 11 i . lggg i ;* l i i r i is | +86.40108c2 I I1?- i :1969 i i igl I A1s4 | +384.010Dt1 | g1q3 : i *sJg,g i i iur i ei i r | +640.010D12 | g!! i 11109 Siqt i Fzo . l +r. r?6sMt I plgg i -! it:, i iEcl i ir i is .r 1336.0smcl | 11.3e iul:.1 i id,cz i eiir r +336.0

l___: l l , I F21 i +1624 | I r ,



28

EXI{IBIT 5- QSN+SOFTWARE OLUTTONOAI,TERNATTVESLOT MACHINE MIX 3

_ _ : + _ _ _ _ _ _ _ _ _ _ a _ _ _ i _ _ : _ _ _ + _ _ _ _ b - _ _ _ _ + _ __

' . - - - .

30BGL pll? i.qqgl--i---;ooo1r Froe--i----; ; ; i ;- l308G2 I plgg i .qqg? i ioppz i FL77 t +l5r.208G3 | l l t l i tgqg? i ioFwl i i ie' r +662.433833 R?2. r:e:l i iii!? i iziz | +662.408G5'l or6s, i -6gii i ioi6r i riee i

' i i l , i ; i. 308G6 '

r De6' : i *06!3' i iopilr i r, i ie t +'584r08c7 | g?l- i .eq!! i id i l i i r I F2L, I +10s60RDr I ll{q i *loa3 ,, ;igwh', i ;,;0 | +10560RD2".

I11I , i1lss2;, ; . i ioi idr

I Et68 | +15460RD3' I Ef62 "' j . t i i? i ioidz I E1g, | +15460RD4.I ggl - .' ! *4gq? i io6ir f croo I +210_0,oRD5' g_q. j . i9g? i io;; t i c; i . | +21000RD6". !?l . i *aoa? i sur-, I BzzL | +470.40RD7 | !11- i l4ggi i 6ir ' i r , ' ! Azlt I +5r.5,20RD1 | glgl i r i440 i si i i i r Fl | +1624__19P1. | :1tu i * iqio i iswi i Er.e3 | +2088

___:=1i:_33j_:_11::g?, terar ion = !r cpu second 1?.e101.6 i

_-__!____ly l : " o f Assignments or SLOTMIX3 page: 2 .- - - - - - . - l

:{s? i dii^ i:;i;:ii 1831 3l?3 1333:3sBl I c?gl i * isa.q t 2cc5 | 8123 | +336.0sB2lc??zi*iab.oircc6ir.rzi j+336.0sPRl I Dql i , i i igz , i ,cCi | 8138 | +336.0RFl I cgg

l. iof

g i tcce I lLsz, l

+278.4svr I Fl?e i * isoe i iccg r A154 | +278.4cMr I F?96 i *sai.a i z&io I AL55. +278.4rcl I Dg? i i isa+ i icc i i I F4e | +6?3.Eul r e1-r l i *s+o.o i zcai; I A163 | +278.4ESr. I Fs1 i i i i io i tcci l I cra3 I +215.0ccl , l F1?5 i *oi i .g , i tcai4 t Gzzs | +21s.0Gc2 ' l Azo i * i ie.q | | r



29

EXHIBIT 6 _ QSB+SOFTWARESOLUTION TO AI,TERNATIVE SLOT MACSII{E [fDT4

i--:::.:l__.i__l:::____,1::::1:::l:1-331:::___,1__l=lI 308G1 | plz | , .ggg? gonoe I E1e3 ----; ; ; ; ; 308c2 I p1g9 i . , t1 i ionor I clor I +1440 308G3 | 9l!1 i rqqg? i ionoz I c116 I +1440 308G4 | P?7- i *ggp? i iopor t F10e | +1512 308G5 I Ptq6 i .ggg? i i6ooz I Ft77 | +ls .2| 308G6 | p:g i, .g992 i , i6r.wrr A14 | +662.4 30BGz I p7l i *ggg? i i6rwz r A2L2 +662.4 30BGB I ggg- i -gqqi i i6rcr I FlBs | +2688 3Qnnr

| l l fq i . fgi? i i6owr r Fres I +1584 30RD2 | y\t7 i .1991 i i6wnr r Fzl | +1056 30RD3 | !1.92'i ' *1gg? i i6ecr I cz2z | +1056 30RD4 | l l l i .+9,2 i idpr,r I c100 I +2100 30RDs | !19 i 'l4qii

i irar r B22L | +470.4 30RD6 I !g? i *1gg? i i i icr I A21r | +5r.5.2 30RD7 | !19 , i .+gg? i 6i lrr I Fzo6 I +L6z4l_--: :P:__- 846 i * osi i i iwr I E16B +20RR-------

l--Y=:ir-l l l-: 1253627 rteration = ti--i"o-;;;;;; '= rz.azrzs

. .se^ | \ - rJsE/r ro t . I obJect I Task lcostr /prof .- -+ - - - - - - - - - -+ -srcL l 9Vg | +szs.z i zccs I BL23 | +336.0sBr | 9!g i i i tg.z i zd|o I BL24 I +336.0PRl I 9?7 i * iao.e i idd,z I erga | +336.0RFl I g! ! i ; l91gi icds I erss | +278.4svl I l l?e i i l luq i zccg I Azo | +278.4GMl I I?9 i +5s2..a. zddro I Ft . t +673.ercr I gg? i ;\14! i iddrl I r+g I +623.eEUl I l lge i *019.9 i z&ry t Alsz I +278.4ESL r Fsl i i r rzo i iddig I c1B3 | +215.0GcL | 9191 i +22a.+ zcci+ l czzs l +21s.0ec2 I !r 's i isgo.b i icdis I c2o3 | +21s.0:ilt'- i gl;: i l!j;i; i ;fti' I A,63! +zzs.ar

application of the assignment problem case of pagcor's slot machine operation

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