The Basics of Simulation
3URFHHGLQJVRIWKH:LQWHU6LPXODWLRQ&RQIHUHQFH :.9&KDQ$' $PEURJLR*=DFKDUHZLF]10XVWDIHH*:DLQHUDQG(3DJHHGV
7+(%$6,&62)6,08/$7,21 .3UHVWRQ:KLWH-U
5LFNL*,QJDOOV
'HSDUWPHQWRI6\VWHPV ,QIRUPDWLRQ(QJLQHHULQJ 8QLYHUVLW\RI9LUJLQLD &KDUORWWHVYLOOH9$ 86$ $%675$&7
'LDPRQG+HDG$VVRFLDWHV 'LDPRQG+HDG'ULYH (QFLQLWDV&$ 86$
6LPXODWLRQLVH[SHULPHQWDWLRQZLWKDPRGHO7KHEHKDYLRURIWKHPRGHOLPLWDWHV VRPHVDOLHQWDVSHFWRI WKH EHKDYLRU RIWKH V\VWHP XQGHU VWXG\ DQG WKH XVHU H[SHULPHQWV ZLWK WKH PRGHO WR LQIHU WKLV EHKDYLRU 7KLVJHQHUDOIUDPHZRUNKDVSURYHQDSRZHUIXODGMXQFWWROHDUQLQJSUREOHPVROYLQJDQGGHVLJQ,QWKLV WXWRULDOZHIRFXVSULQFLSDOO\RQGLVFUHWHHYHQWVLPXODWLRQ—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—OHDUQLQJ RU MXVWKDYLQJIXQ E\GRLQJ 7KHVHFRQGFDWHJRU\LQFOXGHVWKHDQDO\VLVDQGGHVLJQRIDUWLIDFWVDQGSURFHVVHV7KLVLVWKHWHFKQLFDO GRPDLQZKLFKHQJLQHHUVRSHUDWLRQVUHVHDUFKHUVGDWDVFLHQWLVWVDQGRWKHUVPRVWFRPPRQO\DVVRFLDWHZLWK VLPXODWLRQ&RQVLGHUIRUH[DPSOHWKHGHVLJQRIDQHZDLUFUDIW7KH:ULJKWEURWKHUVLQYHQWHGWKHZLQG WXQQHOLQRUGHUWRVLPXODWHDHURG\QDPLFSKHQRPHQDXVLQJVFDOHPRGHOV:LQGWXQQHOWHVWVDUHVWLOOXVHG WRFDOLEUDWHKLJKO\FRPSOH[DHURG\QDPLFFRPSXWHUVLPXODWLRQV 978-1-5386-3428-8/17/$31.00 ©2017 IEEE
505
:KLWHDQG,QJDOOV
6LPXODWLRQVWDQGVLQFRQWUDVWWRDQDO\WLFDODSSURDFKHVWRWKHVROXWLRQRIPRGHOV,QDQDQDO\WLFDODS SURDFKWKHPRGHOLVH[SUHVVHGDVDVHWRIHTXDWLRQVWKDWGHVFULEHKRZWKHV\VWHPVWDWHFKDQJHVRYHUWLPH :HVROYHWKHVHHTXDWLRQVXVLQJVWDQGDUGPDWKHPDWLFDOPHWKRGV—DOJHEUDDQGFDOFXOXV—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—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“DLDORQHIRUFDUVWHUHRSURGXFWV GLDOWZRIRUDOORWKHUSURGXFWV”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
,QSXWV2XWSXWVDQG6WDWH
(YHQWVLQWKHHQYLURQPHQWZKLFKDFWRQDV\VWHPDUHFDOOHGWKHLQSXWVWRWKHV\VWHP7KHVHLQSXWVFDXVH FKDQJHVLQWKHLQWHUQDOFRQGLWLRQRIWKHV\VWHPFDOOHGWKHV\VWHP VWDWH7KH RXWSXWVRIWKHV\VWHPDUH WKRVHPHDVXUHGTXDQWLWLHVZKLFKFDQEHGHULYHGIURPWKHV\VWHPVWDWHDQGZKLFKZHQHHGWRNQRZLQRU GHUWRDQVZHUWKHTXHVWLRQVSRVHGIRUWKHVLPXODWLRQVWXG\,QRWKHUZRUGVWKHLQSXWVFDXVHFKDQJHVLQ WKHV\VWHPVWDWHDQGWKHVHDUHUHIOHFWHGE\FKDQJHVLQWKHRXWSXW
506
:KLWHDQG,QJDOOV
PlaceCall
Yes No Car Stereo
Other
)LJXUH &DOOFHQWHUH[DPSOHORJLFIORZ
(QWLWLHVDQG$WWULEXWHV
,Q D SURFHVVRULHQWHG GLVFUHWHHYHQW VLPXODWLRQ LQSXWV DUH UHDOL]HG E\ WKH DUULYDO RI G\QDPLF HQWLWLHV 7KHVHHQWLWLHVIORZWKURXJKWKHV\VWHPDQGDUHWKHVWUXFWXUDOHOHPHQWVZKLFKHIIHFWWKHFKDQJHVLQWKHV\V WHPVWDWHYDULDEOHV:LWKRXWHQWLWLHVQRWKLQJZRXOGKDSSHQ,QGHHGRQHVWRSSLQJFRQGLWLRQIRUDVLPXOD WLRQUXQLVZKHQWKHUHDUHQRDFWLYHHQWLWLHVLQWKHV\VWHP ,QRXUH[DPSOHWKHHQWLWLHVDUHWHOHSKRQHFDOOV—FXVWRPHUVVHHNLQJLQIRUPDWLRQDQGSHUKDSVZDQWLQJ WRSODFHDQRUGHUIRUDSURGXFW7KHVWDWHRIWKHV\VWHPDWDQ\SRLQWLQWLPHFDQEHGHILQHGE\WKUHHVWDWH YDULDEOHV—WKHQXPEHURIFDOOVLQSURFHVVRQWKH,95XQLWDQGWKHQXPEHURIFDOOVRIHDFKW\SHLQSURFHVV RUZDLWLQJIRUVHUYLFH2EYLRXVO\WKHVWDWHFKDQJHVHYHU\WLPHDFDOORIHLWKHUW\SHDUULYHVRUGHSDUWVRQH RIWKHSURFHVVLQJXQLWV:KLOHIRUFRQYHQLHQFHZHZLOOPRQLWRUDODUJHQXPEHURIYDULDEOHVGXULQJWKH VLPXODWLRQ WKHV\VWHPLPDJH LQSULQFLSOHHDFKRIWKHVHYDULDEOHVFDQEHGHULYHGLIZHNQRZWKHLQSXWVWR WKHV\VWHPDQGWKHV\VWHPVWDWHDWDOOSRLQWVLQWLPHGXULQJWKHVLPXODWLRQUXQ (QWLWLHVKDYHDWWULEXWHV–FKDUDFWHULVWLFVRIDJLYHQHQWLW\WKHYDOXHVRIZKLFKDUHVSHFLILFWRWKDWHQWLW\ $WWULEXWHVDUHFULWLFDOWRXQGHUVWDQGLQJWKHSHUIRUPDQFHDQGIXQFWLRQRIHQWLWLHVLQWKHVLPXODWLRQ ,QRXU H[DPSOHHDFKHQWLW\KDVWKUHHDWWULEXWHV7KHILUVW 3URGXFWB7\SH LVWKHFODVVRISURGXFWUHTXHVWHGE\WKH FDOOHU:HQHHGWKLVDWWULEXWHLQRUGHUWRGHWHUPLQHWKHURXWLQJRIWKHFDOOWKURXJKWKHV\VWHP7KHVHFRQG 6WDUWB7LPH LVWKHWLPHWKDWWKHHQWLW\DUULYHVDQGHLWKHUUHFHLYHVDEXV\VLJQDORUMRLQVWKHDSSURSULDWH TXHXHWREHJLQZDLWLQJIRUVHUYLFH7KHWKLUG %HJLQB:DLW LVWKHWLPHWKHFDOOOHDYHVWKH,95XQLWDQG MRLQVRQHRIWKHTXHXHV:HQHHGWKHVHWZRDWWULEXWHVLQRUGHUWRGHWHUPLQHWKHV\VWHPWLPHDQGWKHGXUD WLRQRIZDLWLQJWLPHIRUHDFKHQWLW\ ,QPRUHFRPSOH[VLPXODWLRQVWKHUHFDQEHPDQ\GLIIHUHQWHQWLW\W\SHV7KHVHFDQUHSUHVHQWWUDQVDF WLRQV DVLQRXUH[DPSOH SK\VLFDOREMHFWVSHRSOHLQIRUPDWLRQ—DQ\WKLQJWKDWFDQFDXVHDVWDWHFKDQJH ,QGHHGDUWLILFLDOHQWLWLHVDUHXVHGWRLPSOHPHQWFRQWUROORJLF VXFKDVWKHWLPHWKHVLPXODWLRQHQGV LQWKH PRGHO
5HVRXUFHV
5HVRXUFHVUHSUHVHQWDQ\WKLQJLQDVLPXODWLRQWKDWKDVDFRQVWUDLQHGFDSDFLW\5HVRXUFHVDUHWLPHVKDUHG E\HQWLWLHVHQWLWLHVPXVWTXHXHIRUEXV\UHVRXUFHV RUEHGLYHUWHGHOVHZKHUH DQGHQWLWLHVW\SLFDOO\DUHGH OD\HGDIWHUWKHVHKDYHVHL]HGDUHVRXUFHDQGEHJLQSURFHVVLQJ&RPPRQH[DPSOHVRIUHVRXUFHVLQFOXGH ZRUNHUVPDFKLQHVQRGHVLQDFRPPXQLFDWLRQQHWZRUNDQGWUDIILFLQWHUVHFWLRQV
507
:KLWHDQG,QJDOOV
,Q RXU H[DPSOH ZH KDYH WZR UHVRXUFHV HDFKUHSUHVHQWLQJWKH VDOHV IRUFH IRU DJLYHQ SURGXFWW\SH The study question is to determine the capacity of each of these resources needed to satisfy the manager’s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—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
$FWLYLWLHVDQG(YHQWV
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
*OREDO9DULDEOHV
,I\RXDUHDSURJUDPPHUWKHQWKHLGHDRIKDYLQJJOREDOYDULDEOHVLVQRWKLQJQHZ7KHYDOXHVRIDJOREDO YDULDEOHDUHDYDLODEOHWRWKHHQWLUHVLPXODWLRQDWDOOWLPHVDQGFDQWUDFNMXVWDERXWDQ\WKLQJRILQWHUHVW,Q
508
:KLWHDQG,QJDOOV
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greater than zero, the we have not met the manager’s reTXLUHPHQW
5DQGRP1XPEHU*HQHUDWRU
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—WKHUROORIWZRGLFH7KH SUREDELOLW\GLVWULEXWLRQIRUWKHUROORIWZRGLFHLVVHHQLQ)LJXUH QH[WSDJH ,QRXUPRGHOWKHUROOZLOO EHWKHEDVLVIRUHYHU\UDQGRPGHOD\DQGHYHU\UDQGRPO\DVVLJQHGYDOXHLQWKHPRGHO:HKDYHIRXUUDQ GRPO\DQGRQHDVVLJQHGGHOD\VYDOXHVLQWKHPRGHO 7LPHEHWZHHQDUULYDOVRIFDUVDWWKHFDOOFHQWHU ',&( PLQV 7KHGHOD\DWWKH,95XQLW ',&( PLQV 7KHGHOD\IRUFDUVWHUHRFDOOSURFHVVLQJ ',&( PLQV 7KHGHOD\IRURWKHUSURGXFWFDOOSURFHVVLQJ ',&( PLQV 7KHSURGXFWW\SHUHTXHVWHGE\WKHFDOOHUFDOO DVVXPLQJRQDYHUDJHRIDOOFDOOVDUHIRUFDU VWHUHRSURGXFWV Car Stereo, if DICE d 4 otherwise ¯Other,
3URGXFWB7\SHB$WWULEXWH ®
7KH&ORFNDQG&DOHQGDU
7KHFORFNLVDJOREDOYDULDEOH &XUUHQWB7LPH WKDWFDUULHVWKHYDOXHRIWKHFXUUHQWWLPHLQWKHVLPXODWLRQ 7KHFDOHQGDULVDOLVWRIHYHQWVWKDWDUHVFKHGXOHGWRRFFXULQWKHIXWXUHLHDWFORFNWLPHVODWHUWKDQWKH FXUUHQWFORFNWLPH,QHYHU\VLPXODWLRQWKHUHLVRQO\RQHFDOHQGDUDQGLWLVRUGHUHGE\WKHHDUOLHVWVFKHG XOHGWLPHILUVW,Q6HFWLRQLWZLOOEHFRPHFOHDUKRZWKHFDOHQGDUZRUNVDQGZK\LWLVLPSRUWDQWLQWKH VLPXODWLRQ$WWKLVSRLQWMXVWUHPHPEHUWKDWDWDQ\JLYHQSRLQWLQWLPHHYHU\HYHQWWKDWKDVDOUHDG\EHHQ VFKHGXOHGWRRFFXULQWKHIXWXUHLVKHOGRQWKHFDOHQGDU
509
:KLWHDQG,QJDOOV
)LJXUH 'LVWULEXWLRQRIUROOLQJWZRGLFH
6WDWLVWLFV&ROOHFWRUV
6WDWLVWLFVFROOHFWRUVDUHDSDUWRIWKHVLPXODWLRQWKDWFROOHFWVVWDWLVWLFVRQFRQGLWLRQV VXFKWKHQXPEHURI XQLWVRIWKHFDSDFLW\RIDUHVRXUFHLQXVH RUWKHYDOXHRIJOREDOYDULDEOHVRUFHUWDLQSHUIRUPDQFHVWDWLV WLFV EDVHG RQ DWWULEXWHV RI WKH HQWLW\ 7KUHH GLIIHUHQW W\SHV RI VWDWLVWLFV FDQ EH FROOHFWHG—FRXQWV WLPH SHUVLVWHQWDQGWDOOLHV&RXQWVDUHYHU\VWUDLJKWIRUZDUGWKH\FRXQW,QRXUPRGHOZHGHILQHGIRXUFRXQWV DV JOREDO YDULDEOHV DQG ZH ZLOO FROOHFW VWDWLVWLFV RQ WKHVH 7LPHSHUVLVWHQW VWDWLVWLFDO FROOHFWRUV JLYH WKH WLPHZHLJKWHGYDOXHVRIGLIIHUHQWYDULDEOHVLQWKHVLPXODWLRQ$FRPPRQYDULDEOHWRWUDFNLVWKHXWLOL]D WLRQRIDUHVRXUFH,QRXUPRGHOZHFROOHFWIRXUGLIIHUHQWWLPHSHUVLVWHQWVWDWLVWLFV—WKHQXPEHURIEXV\ UHVRXUFHVRIWKHWZRUHVRXUFHVWKDWZHKDYHLQWKHPRGHODQGWKHQXPEHURIHQWLWLHVLQHDFKRIWKHFRUUH VSRQGLQJTXHXHV7KHVHDUHQRWVWULFWO\QHHGHGWRDVVHVVWKHPDQDger’s FULWHULDEXWSURYLGHDGGLWLRQDOLQ VLJKWUHJDUGLQJWKHSHUIRUPDQFHRIWKHFDOOFHQWHUZKLFKPLJKWEHXVHIXOLIWKHPDQDger’s requirements DUHQRWPHW7DOO\VWDWLVWLFVDUHFROOHFWHGRQHREVHUYDWLRQDWDWLPHZLWKRXWUHJDUGWRWKHDPRXQWRIWLPH EHWZHHQREVHUYDWLRQV,QRXUPRGHOZHFROOHFWDYHU\FRPPRQVWDWLVWLFZKLFKLVWKHDPRXQWRIWLPHWKDW DQHQWLW\VWD\VLQWKHV\VWHP6LQFHZHDVVLJQWKHYDOXHRIWKHHQWLW\DWWULEXWH6WDUWB7LPH &XUUHQWB7LPH ZKHQLWHQWHUVWKHFDOOFHQWHUWKHYDOXH &XUUHQWB7LPH–6WDUWB7LPH ZKHQWKLVHQWLW\GHSDUWVWKHV\VWHP LVWKHWRWDODPRXQWRIWLPHWKLVHQWLW\LVLQWKHV\VWHP$JDLQWKLVVWDWLVWLFSURYLGHVDGGLWLRQDOLQVLJKWRQ SHUIRUPDQFH $:$/.7+528*+7+(6(&21&(376 :KDWZHDUHJRLQJWRGRQRZLVZDONWKURXJKDFRXSOHRIVWHSVLQRXUVLPXODWLRQPRGHO$V\RXZLOOVHH ZHZLOOWUDFNWKHVWDWHRIWKHV\VWHPWKHHQWLWLHVRQWKHFDOHQGDUWKHYDOXHVRIDWWULEXWHVDQGVWDWHYDULD EOHVDQGWKHVWDWLVWLFVZHDUHFROOHFWLQJ
7KH6WDWHRI7KH6\VWHPDW1RRQ
:HDVVXPHLQLWLDOO\WKDWWKHUHDUHRQHFDUVWHUHRDJHQWDQGWZRDJHQWVIRURWKHUSURGXFWV)LJXUHVKRZV WKHLPDJHRIWKHV\VWHPDWQRRQ7KHFDOHQGDURIWKLVV\VWHPLVPDGHXSRIWKHHQWLWLHVWKDWDUHVFKHGXOHG WRFRPSOHWHDQDFWLYLW\ZLWKDVSHFLILFWLPHGXUDWLRQDVVKRZQLQ7DEOH7KHWZRTXHXHVDUHVKRZQ ZLWKWKHHQWLWLHVLQUDQNRUGHULQ7DEOHVDQG ZHDVVXPHWKHFDOOVDUHSURFHVVHG),)2LHLQWKHRUGHU RIDUULYDODWWKHTXHXH 1RWHWKDWWKHHYHQWWLPHVDUHXQGHILQHG(DFKHYHQWUHFRUGRQWKHWKUHHOLVWVDOVR LQFOXGHVWKHYDOXHVRIWKHHQWLWLHVDWWULEXWHVZKHQWKHVHDUHGHILQHG
510
:KLWHDQG,QJDOOV
WaitinginCarStereoQueue
Scheduled toArrive
InProcess IVRUnit
InProcess CarStereoSales Representative
InProcess OtherProductsSales Representatives
WaitinginOtherProductsQueue
)LJXUH 6WDWHRIWKHV\VWHPDWQRRQ 2WKHULPSRUWDQWLQIRUPDWLRQFRQFHUQVWKHFORFN&XUUHQWB7LPHZKLFKLVVHWWR 307KHVWD WLVWLFVWKDWZHDUHWUDFNLQJLQWKHVLPXODWLRQKDYHWKHYDOXHVOLVWHGLQ7DEOHas of noon. The “Time/Obs” FROXPQJLYHVWKHDPRXQWRIWLPHWKDWZHKDYHEHHQFROOHFWLQJWKHVWDWLVWLF ZKLFKLVVLQFH $0 IRU WLPHSHUVLVWHQWVWDWLVWLFVRUWKHQXPEHURIREVHUYDWLRQVIRUWDOO\VWDWLVWLFV 7DEOH 7KH&DOHQGDUDWQRRQ (QWLW\
(YHQW $UULYHDW&DOO&HQWHU &RPSOHWH6HUYLFH,95 &RPSOHWH6HUYLFH&DU 6WHUHR &RPSOHWH6HUYLFH2WKHU &RPSOHWH6HUYLFH2WKHU (QGUHSOLFDWLRQ
(YHQW7LPH 30 30 30
3URGXFWB7\SH FDUVWHUHR FDUVWHUHR
6WDUWB7LPH $0 $0
%HJLQB:DLW $0
30 30 30
RWKHU RWKHU
$0 $0
$0 $0
6WDUWB7LPH $0 $0
%HJLQB:DLW $0 $0
7DEOH &DU6WHUHR4XHXHDWQRRQ (QWLW\ (YHQW %HJLQ6HUYLFH %HJLQ6HUYLFH
(YHQW7LPH
3URGXFWB7\SH FDUVWHUHR FDUVWHUHR
7DEOH 2WKHU3URGXFW4XHXHDW1RRQ (QWLW\
(YHQW %HJLQ6HUYLFH %HJLQ6HUYLFH %HJLQ6HUYLFH %HJLQ6HUYLFH %HJLQ6HUYLFH
(YHQW7LPH
3URGXFWB7\SH RWKHU RWKHU RWKHU RWKHU RWKHU
6WDUWB7LPH $0 $0 $0 $0 $0
7DEOH 6WDWLVWLFVDWQRRQ 6WDWLVWLF 9DOXH %XV\6LJQDO&RXQW &RPSOHWLRQV &DU6WHUHR &RXQW &RPSOHWLRQV 2WKHU3URGXFW &RXQW ([FHVVLYH:DLW &DU6WHUHR &RXQW ([FHVVLYH:DLW 2WKHU3URGXFW &RXQW 5HSUHVHQWDWLYH8WLOL]DWLRQ &DU6WHUHR 5HSUHVHQWDWLYH8WLOL]DWLRQ 2WKHU3URGXFW
511
7LPH2EV
%HJLQB:DLW $0 $0 $0 $0 $0
:KLWHDQG,QJDOOV
$YHUDJH1XPEHU:DLWLQJ &DU6WHUHR $YHUDJH1XPEHU:DLWLQJ 2WKHU3URGXFW $YHUDJH:DLWLQJ7LPH %RWK7\SHV $YHUDJH6\VWHP7LPH
7KH6WDWHRI7KH6\VWHPDW 30
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e attribute value is set to “Other”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
(YHQW &RPSOHWH6HUYLFH,95 $UULYHDW&DOO&HQWHU &RPSOHWH6HUYLFH,95 &RPSOHWH6HUYLFH&DU6WHUHR &RPSOHWH6HUYLFH2WKHU &RPSOHWH6HUYLFH2WKHU (QGUHSOLFDWLRQ
(YHQW7LPH 30 30 30 30 30 30 30
512
3URGXFWB7\SH FDUVWHUHR RWKHU FDUVWHUHR RWKHU RWKHU
6WDUWB7LPH $0 30 $0 $0 $0
%HJLQB:DLW $0 $0 $0
:KLWHDQG,QJDOOV
7KH6WDWHRI7KH6\VWHPDW 30
Lets process one more event, just so we’ve got the idea. Looking at the calendar in Table 4, the next HYHQWUHFRUGKDVHQWLW\FRPSOHWLQJVHUYLFHDWWKH,95XQLW7KHFORFNLVDGYDQFHGWR HQWLW\ EHFRPHV WKH DFWLYH HQWLW\ DQG WKH UHFRUG IRU HQWLW\ LV UHPRYHG IURP WKH FDOHQGDU 1H[W WKH %HJLQB:DLWDWWULEXWHIRUWKLVHQWLW\LVVHWWRWKHFXUUHQWFORFNWLPH7KH3URGXFt_Type attribute is “Car Stereo”VRWKHHQWLW\LVVHQWWRUHFHLYHVHUYLFHIURPWKHFDUVWHUHRVDOHVUHSUHVHQWDWLYH)LQGLQJWKHVDOHV UHSUHVHQWDWLYHEXV\ZLWKDQRWKHUFDOODQGWZRFDOOVDOUHDG\ZDLWLQJHQWLW\MRLQVWKHTXHXHDWUDQN 7KHVWDWLVWLFVDUHXSGDWHGWRUHIOHFWWKHSDVVDJHRItime and that’s it. ,17(535(7,1*28738767$7,67,&6 /HWXVDVVXPHWKDWRXUPRGHOKDVUXQIURP $0WR 30$W 30ZHVWRSWKHVLPXODWLRQ and we have all of our statistics calculated. The “answer” for the simulatioQLVLQ7DEOH
7DEOH 6WDWLVWLFVDW 30 6WDWLVWLF 9DOXH %XV\6LJQDO&RXQW &RPSOHWLRQV &DU6WHUHR &RXQW &RPSOHWLRQV 2WKHU3URGXFW &RXQW ([FHVVLYH:DLW &DU6WHUHR &RXQW ([FHVVLYH:DLW 2WKHU3URGXFW &RXQW 5HSUHVHQWDWLYH8WLOL]DWLRQ &DU6WHUHR 5HSUHVHQWDWLYH8WLOL]DWLRQ 2WKHU3URGXFW $YHUDJH1XPEHU:DLWLQJ &DU6WHUHR $YHUDJH1XPEHU:DLWLQJ 2WKHU3URGXFW $YHUDJH:DLWLQJ7LPH %RWK7\SHV $YHUDJH6\VWHP7LPH
7LPH2EV
,WLVWHPSWLQJWRFRQFOXGHLPPHGLDWHO\WKDWWKHFDOOFHQWHULVJURVVO\XQGHUVWDIIHGDQGGRHVQRWQHDUO\ approximate the manager’s requirements. Seven out of (7+10+53)=70 (RU RIDUULYLQJSKRQHFDOOV DUHUHMHFWHGDWWKHVZLWFK RI RU RIFDUVWHUHRFDOOVDQGRIRWKHUSURGXFWFDOOVH[SHULHQFH ZDLWVORQJHUWKDWPLQ DQGWKHDYHUDJHZDLWLQJWLPHLVQHDUO\PLQXWHV—IDUWRRORQJIRUFXVWRPHUVDW LVIDFWLRQ,QGHHG,NQRZWKDW,ZRXOGKDQJXSORQJEHIRUHWKLVXQKDSS\DQGZRXOGSHUKDSVHYHQWU\DQ RWKHUUHWDLOHU:HFDQVHHWKDWWKHUHVRXUFHVDUHVWUHVVHG—WKHFDUVWHUHRUHSUHVHQWDWLYHLVEXV\RIWKH WLPHDQGQHLWKHURIWKHRWKHUSURGXFWUHSUHVHQWDWLYHVGUDZDEUHDWKHZKLOHQRWRQWKHSKRQH7KHVLWXDWLRQ RQWKLVGD\LVVRYHU\EDGWKDWWKHFRQFOXVLRQPD\EHZDUUDQWHG %XWFDXWLRQLVDGYLVHG6XSSRVHWKDWWKLVLVMXVWDQH[FHSWLRQDOO\EDGGay? Shouldn’t we really look DWWKHFDOOFHQWHURQPRUHWKDQRQHGD\EHIRUHZHMXPSWRWKLVFRQFOXVLRQ",QGHHGZHVKRXOGDQGWKLVLV DOZD\VWKHFDVHLQGLVFUHWHHYHQWVLPXODWLRQ7KHQXPEHUVJLYHQLQ7DEOHDUHDUDQGRPDQVZHUWRWKH SHUIRUPDQFHRIWKHV\VWHP7KLVLVEHFDXVHWKHUHDUHUDQGRPLQSXWVWRWKHV\VWHPWKDWJLYHXVWKLVDQ VZHU7KHDQVZHUJHQHUDWHGE\RQO\RQHUXQLVQRWUHDOO\DQDQVZHUDWDOO 7RPDNHWKHSRLQWOHWXVWDNHWKHIROORZLQJUROOVRIWKHGLFH
7+(%$6,&62)6,08/$7,21 .3UHVWRQ:KLWH-U
5LFNL*,QJDOOV
'HSDUWPHQWRI6\VWHPV ,QIRUPDWLRQ(QJLQHHULQJ 8QLYHUVLW\RI9LUJLQLD &KDUORWWHVYLOOH9$ 86$ $%675$&7
'LDPRQG+HDG$VVRFLDWHV 'LDPRQG+HDG'ULYH (QFLQLWDV&$ 86$
6LPXODWLRQLVH[SHULPHQWDWLRQZLWKDPRGHO7KHEHKDYLRURIWKHPRGHOLPLWDWHV VRPHVDOLHQWDVSHFWRI WKH EHKDYLRU RIWKH V\VWHP XQGHU VWXG\ DQG WKH XVHU H[SHULPHQWV ZLWK WKH PRGHO WR LQIHU WKLV EHKDYLRU 7KLVJHQHUDOIUDPHZRUNKDVSURYHQDSRZHUIXODGMXQFWWROHDUQLQJSUREOHPVROYLQJDQGGHVLJQ,QWKLV WXWRULDOZHIRFXVSULQFLSDOO\RQGLVFUHWHHYHQWVLPXODWLRQ—LWVXQGHUO\LQJFRQFHSWVVWUXFWXUHDQGDSSOL FDWLRQ 02'(/6$1'6,08/$7,21 $ PRGHO LV DQ HQWLW\ WKDW LV XVHG WR UHSUHVHQW VRPH RWKHU HQWLW\ IRU VRPH GHILQHG SXUSRVH ,Q JHQHUDO PRGHOVDUHVLPSOLILHGDEVWUDFWLRQVZKLFKHPEUDFHRQO\WKHVFRSHDQGOHYHORIGHWDLOQHHGHGWRVDWLVI\VSH FLILF VWXG\ REMHFWLYHV 0RGHOV DUH HPSOR\HG ZKHQ LQYHVWLJDWLRQ RI WKH DFWXDO V\VWHP LV LPSUDFWLFDO RU SURKLELWLYH7KLVPLJKWEHEHFDXVHGLUHFWLQYHVWLJDWLRQLVH[SHQVLYHVORZGLVUXSWLYHXQVDIHRUHYHQLOOH JDO,QGHHGPRGHOVFDQEHXVHGWRVWXG\V\VWHPVWKDWH[LVWRQO\LQFRQFHSW 6LPXODWLRQLVDSDUWLFXODUDSSURDFKWRVWXG\LQJPRGHOVZKLFKLVIXQGDPHQWDOO\H[SHULHQWLDORUH[SHU LPHQWDO,QSULQFLSOHVLPXODWLRQLVPXFKOLNHUXQQLQJILHOGWHVWVH[FHSWWKDWWKHV\VWHPRILQWHUHVWLVUH SODFHGE\D SK\VLFDORU FRPSXWDWLRQDOPRGHO 6LPXODWLRQLQYROYHVFUHDWLQJDPRGHOZKLFKLPLWDWHVWKH EHKDYLRUVRILQWHUHVW H[SHULPHQWLQJZLWKWKHPRGHOWRJHQHUDWHREVHUYDWLRQVRIWKHVHEHKDYLRUV DQGDW WHPSWLQJWRXQGHUVWDQGVXPPDUL]HDQGRUJHQHUDOL]HWKHVHEHKDYLRUV,QPDQ\DSSOLFDWLRQVVLPXODWLRQ DOVRLQYROYHVWHVWLQJDQGFRPSDULQJDOWHUQDWLYHGHVLJQVDQGYDOLGDWLQJH[SODLQLQJDQGVXSSRUWLQJVLPXOD WLRQRXWFRPHVDQGVWXG\UHFRPPHQGDWLRQV $33/,&$7,21'20$,16 :HPLJKWGLYLGHDSSOLFDWLRQVRIVLPXODWLRQEURDGO\LQWRWZRFDWHJRULHV7KHILUVWLQFOXGHVVRFDOOHGKX PDQLQWKHORRSVLPXODWLRQVXVHGIRUWUDLQLQJDQGRUHQWHUWDLQPHQW0DQ\SURIHVVLRQDOVKRQHWKHLUVNLOOV DQGOHDUQHPHUJHQF\SURFHGXUHVLQVLPXODWHGHQYLURQPHQWVZKLFKDUHVDIHIURPWKHFRQVHTXHQFHVRI LQ H[SHULHQFHDQGIDLOXUH3LORWVWUDLQLQIOLJKWVLPXODWRUVLQRUGHUWRH[SHULHQFHWKHFRFNSLWRIDSDUWLFXODU DLUFUDIW QXFOHDU SRZHUSODQW RSHUDWRUV URXWLQHO\ UHFHUWLI\ LQ FRQWUROURRP VLPXODWRUV SK\VLFLDQV OHDUQ QHZSURFHGXUHVHPSOR\LQJVLPXODWHGSDWLHQWV ZDUILJKWHUVOHDUQWDFWLFVRQVLPXODWHGEDWWOHILHOGV,QWKH UHDOPRIHQWHUWDLQPHQWZHKDYHDOOSOD\HGFRPSXWHUJDPHVWKDWVLPXODWHHYHU\WKLQJIURPGULYLQJDWUDLQ WR QDYLJDWLQJ WKH IDQFLIXO XQUHDOLWLHVRI YLUWXDO ZRUOGV 7KHHPSKDVLV KHUHLV H[SHULHQWLDO—OHDUQLQJ RU MXVWKDYLQJIXQ E\GRLQJ 7KHVHFRQGFDWHJRU\LQFOXGHVWKHDQDO\VLVDQGGHVLJQRIDUWLIDFWVDQGSURFHVVHV7KLVLVWKHWHFKQLFDO GRPDLQZKLFKHQJLQHHUVRSHUDWLRQVUHVHDUFKHUVGDWDVFLHQWLVWVDQGRWKHUVPRVWFRPPRQO\DVVRFLDWHZLWK VLPXODWLRQ&RQVLGHUIRUH[DPSOHWKHGHVLJQRIDQHZDLUFUDIW7KH:ULJKWEURWKHUVLQYHQWHGWKHZLQG WXQQHOLQRUGHUWRVLPXODWHDHURG\QDPLFSKHQRPHQDXVLQJVFDOHPRGHOV:LQGWXQQHOWHVWVDUHVWLOOXVHG WRFDOLEUDWHKLJKO\FRPSOH[DHURG\QDPLFFRPSXWHUVLPXODWLRQV 978-1-5386-3428-8/17/$31.00 ©2017 IEEE
505
:KLWHDQG,QJDOOV
6LPXODWLRQVWDQGVLQFRQWUDVWWRDQDO\WLFDODSSURDFKHVWRWKHVROXWLRQRIPRGHOV,QDQDQDO\WLFDODS SURDFKWKHPRGHOLVH[SUHVVHGDVDVHWRIHTXDWLRQVWKDWGHVFULEHKRZWKHV\VWHPVWDWHFKDQJHVRYHUWLPH :HVROYHWKHVHHTXDWLRQVXVLQJVWDQGDUGPDWKHPDWLFDOPHWKRGV—DOJHEUDDQGFDOFXOXV—WRGHWHUPLQHWKH GLVWULEXWLRQRIWKHVWDWHDWDQ\SDUWLFXODUWLPH7KHUHVXOWLVDJHQHUDOFORVHGIRUPVROXWLRQZKLFKJLYHV WKHVWDWHDWDQ\WLPHDVDIXQFWLRQRIWKHLQLWLDOVWDWHWKHLQSXWDQGWKHPRGHOSDUDPHWHUV:KHQPRGHOV FDQEHVROYHGDQDO\WLFDOO\WKLVLVDOZD\VWKHSUHIHUUHGDSSURDFK+RZHYHUIRUFRPSOH[V\VWHPVWKLVLV DOPRVWQHYHUWKHFDVH 6LPXODWLRQVDOVRPD\EHFDWHJRUL]HGDFFRUGLQJWRWKHLULPSOHPHQWDWLRQVWUDWHJ\&RQWLQXRXVV\VWHP VLPXODWLRQ0RQWH&DUORVLPXODWLRQGLVFUHWHHYHQWVLPXODWLRQ '(6 K\EULGVLPXODWLRQDQGDJHQWEDVHG VLPXODWLRQDOOKDYHWKHLUSDUWLFXODULPSOHPHQWDWLRQVWUDWHJLHV,QNHHSLQJZLWKWKHWKHPHRIWKLVFRQIHU HQFHZHUHVWULFWWKLVWXWRULDOWRIXUWKHUFRQVLGHUDWLRQRI'(67KURXJKRXWWKLVSDSHUZHZLOOEHUHIHUHQF LQJ LGHDV DQG WKRXJKWV IURP 6KDQQRQ ,QJDOOV DQG (FNHUVOH\ ,QJDOOV .DVDOHV DQG,QJDOOV :KLWH :KLWH DQG ,QJDOOV %DQNV HW DO 1HOVRQ /DZ DQG.HOWRQHWDO &$//&(17(5(;$03/( ,QRUGHUWRLOOXVWUDWHWKHFRQFHSWVGHYHORSHGLQWKHUHPDLQGHURIWKLVSDSHUZHZLOOUHIHUWRDVLPSOHH[ DPSOH—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“DLDORQHIRUFDUVWHUHRSURGXFWV GLDOWZRIRUDOORWKHUSURGXFWV”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
,QSXWV2XWSXWVDQG6WDWH
(YHQWVLQWKHHQYLURQPHQWZKLFKDFWRQDV\VWHPDUHFDOOHGWKHLQSXWVWRWKHV\VWHP7KHVHLQSXWVFDXVH FKDQJHVLQWKHLQWHUQDOFRQGLWLRQRIWKHV\VWHPFDOOHGWKHV\VWHP VWDWH7KH RXWSXWVRIWKHV\VWHPDUH WKRVHPHDVXUHGTXDQWLWLHVZKLFKFDQEHGHULYHGIURPWKHV\VWHPVWDWHDQGZKLFKZHQHHGWRNQRZLQRU GHUWRDQVZHUWKHTXHVWLRQVSRVHGIRUWKHVLPXODWLRQVWXG\,QRWKHUZRUGVWKHLQSXWVFDXVHFKDQJHVLQ WKHV\VWHPVWDWHDQGWKHVHDUHUHIOHFWHGE\FKDQJHVLQWKHRXWSXW
506
:KLWHDQG,QJDOOV
PlaceCall
Yes No Car Stereo
Other
)LJXUH &DOOFHQWHUH[DPSOHORJLFIORZ
(QWLWLHVDQG$WWULEXWHV
,Q D SURFHVVRULHQWHG GLVFUHWHHYHQW VLPXODWLRQ LQSXWV DUH UHDOL]HG E\ WKH DUULYDO RI G\QDPLF HQWLWLHV 7KHVHHQWLWLHVIORZWKURXJKWKHV\VWHPDQGDUHWKHVWUXFWXUDOHOHPHQWVZKLFKHIIHFWWKHFKDQJHVLQWKHV\V WHPVWDWHYDULDEOHV:LWKRXWHQWLWLHVQRWKLQJZRXOGKDSSHQ,QGHHGRQHVWRSSLQJFRQGLWLRQIRUDVLPXOD WLRQUXQLVZKHQWKHUHDUHQRDFWLYHHQWLWLHVLQWKHV\VWHP ,QRXUH[DPSOHWKHHQWLWLHVDUHWHOHSKRQHFDOOV—FXVWRPHUVVHHNLQJLQIRUPDWLRQDQGSHUKDSVZDQWLQJ WRSODFHDQRUGHUIRUDSURGXFW7KHVWDWHRIWKHV\VWHPDWDQ\SRLQWLQWLPHFDQEHGHILQHGE\WKUHHVWDWH YDULDEOHV—WKHQXPEHURIFDOOVLQSURFHVVRQWKH,95XQLWDQGWKHQXPEHURIFDOOVRIHDFKW\SHLQSURFHVV RUZDLWLQJIRUVHUYLFH2EYLRXVO\WKHVWDWHFKDQJHVHYHU\WLPHDFDOORIHLWKHUW\SHDUULYHVRUGHSDUWVRQH RIWKHSURFHVVLQJXQLWV:KLOHIRUFRQYHQLHQFHZHZLOOPRQLWRUDODUJHQXPEHURIYDULDEOHVGXULQJWKH VLPXODWLRQ WKHV\VWHPLPDJH LQSULQFLSOHHDFKRIWKHVHYDULDEOHVFDQEHGHULYHGLIZHNQRZWKHLQSXWVWR WKHV\VWHPDQGWKHV\VWHPVWDWHDWDOOSRLQWVLQWLPHGXULQJWKHVLPXODWLRQUXQ (QWLWLHVKDYHDWWULEXWHV–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—DQ\WKLQJWKDWFDQFDXVHDVWDWHFKDQJH ,QGHHGDUWLILFLDOHQWLWLHVDUHXVHGWRLPSOHPHQWFRQWUROORJLF VXFKDVWKHWLPHWKHVLPXODWLRQHQGV LQWKH PRGHO
5HVRXUFHV
5HVRXUFHVUHSUHVHQWDQ\WKLQJLQDVLPXODWLRQWKDWKDVDFRQVWUDLQHGFDSDFLW\5HVRXUFHVDUHWLPHVKDUHG E\HQWLWLHVHQWLWLHVPXVWTXHXHIRUEXV\UHVRXUFHV RUEHGLYHUWHGHOVHZKHUH DQGHQWLWLHVW\SLFDOO\DUHGH OD\HGDIWHUWKHVHKDYHVHL]HGDUHVRXUFHDQGEHJLQSURFHVVLQJ&RPPRQH[DPSOHVRIUHVRXUFHVLQFOXGH ZRUNHUVPDFKLQHVQRGHVLQDFRPPXQLFDWLRQQHWZRUNDQGWUDIILFLQWHUVHFWLRQV
507
:KLWHDQG,QJDOOV
,Q RXU H[DPSOH ZH KDYH WZR UHVRXUFHV HDFKUHSUHVHQWLQJWKH VDOHV IRUFH IRU DJLYHQ SURGXFWW\SH The study question is to determine the capacity of each of these resources needed to satisfy the manager’s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—LWLVDORJLFDODFWLYLW\:HDOVRDVVXPHWKDWWKH,95XQLWKDV VXIILFLHQWFDSDFLW\WRKDQGOHDVPDQ\FDOOVDVLWUHFHLYHVVLPXOWDQHRXVO\:HQHHGWRDFFRXQWIRUWKHGH OD\WLPHDVVRFLDWHGZLWKWKH,95SURFHVVLQJEXWGRQRWQHHGWRPRGHOWKH,95DVDUHVRXUFH7KH,95LV DSXUHGHOD\DFWLYLW\ 9HU\FRPSOH[UHVRXUFHVFDQEHPRGHOHGLQDVLPXODWLRQ,QDPDQXIDFWXULQJVLPXODWLRQIRUH[DPSOH FRQYH\RUVDUHDFRPSOH[UHVRXUFHW\SHWKDWPDQ\VLPXODWLRQSDFNDJHVRIIHU$OVRWUDQVSRUWDWLRQRSWLRQV VXFKDVWUXFNVDUHRIIHUHGDVUHVRXUFHV$WKLUGFRPSOH[UHVRXUFHLVDYDWRUFRQWDLQHUWKDWKDVD FRQWLQX RXV IORZRIPDWHULDOERWKLQDQRXWRIWKHUHVRXUFH'HSHQGLQJRQWKHWDUJHWPDUNHWRIWKHVLPXODWLRQ SDFNDJHPDQ\FRPSOH[UHVRXUFHVDUHDYDLODEOHWRXVH
$FWLYLWLHVDQG(YHQWV
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
*OREDO9DULDEOHV
,I\RXDUHDSURJUDPPHUWKHQWKHLGHDRIKDYLQJJOREDOYDULDEOHVLVQRWKLQJQHZ7KHYDOXHVRIDJOREDO YDULDEOHDUHDYDLODEOHWRWKHHQWLUHVLPXODWLRQDWDOOWLPHVDQGFDQWUDFNMXVWDERXWDQ\WKLQJRILQWHUHVW,Q
508
:KLWHDQG,QJDOOV
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greater than zero, the we have not met the manager’s reTXLUHPHQW
5DQGRP1XPEHU*HQHUDWRU
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—WKHUROORIWZRGLFH7KH SUREDELOLW\GLVWULEXWLRQIRUWKHUROORIWZRGLFHLVVHHQLQ)LJXUH QH[WSDJH ,QRXUPRGHOWKHUROOZLOO EHWKHEDVLVIRUHYHU\UDQGRPGHOD\DQGHYHU\UDQGRPO\DVVLJQHGYDOXHLQWKHPRGHO:HKDYHIRXUUDQ GRPO\DQGRQHDVVLJQHGGHOD\VYDOXHVLQWKHPRGHO 7LPHEHWZHHQDUULYDOVRIFDUVDWWKHFDOOFHQWHU ',&( PLQV 7KHGHOD\DWWKH,95XQLW ',&( PLQV 7KHGHOD\IRUFDUVWHUHRFDOOSURFHVVLQJ ',&( PLQV 7KHGHOD\IRURWKHUSURGXFWFDOOSURFHVVLQJ ',&( PLQV 7KHSURGXFWW\SHUHTXHVWHGE\WKHFDOOHUFDOO DVVXPLQJRQDYHUDJHRIDOOFDOOVDUHIRUFDU VWHUHRSURGXFWV Car Stereo, if DICE d 4 otherwise ¯Other,
3URGXFWB7\SHB$WWULEXWH ®
7KH&ORFNDQG&DOHQGDU
7KHFORFNLVDJOREDOYDULDEOH &XUUHQWB7LPH WKDWFDUULHVWKHYDOXHRIWKHFXUUHQWWLPHLQWKHVLPXODWLRQ 7KHFDOHQGDULVDOLVWRIHYHQWVWKDWDUHVFKHGXOHGWRRFFXULQWKHIXWXUHLHDWFORFNWLPHVODWHUWKDQWKH FXUUHQWFORFNWLPH,QHYHU\VLPXODWLRQWKHUHLVRQO\RQHFDOHQGDUDQGLWLVRUGHUHGE\WKHHDUOLHVWVFKHG XOHGWLPHILUVW,Q6HFWLRQLWZLOOEHFRPHFOHDUKRZWKHFDOHQGDUZRUNVDQGZK\LWLVLPSRUWDQWLQWKH VLPXODWLRQ$WWKLVSRLQWMXVWUHPHPEHUWKDWDWDQ\JLYHQSRLQWLQWLPHHYHU\HYHQWWKDWKDVDOUHDG\EHHQ VFKHGXOHGWRRFFXULQWKHIXWXUHLVKHOGRQWKHFDOHQGDU
509
:KLWHDQG,QJDOOV
)LJXUH 'LVWULEXWLRQRIUROOLQJWZRGLFH
6WDWLVWLFV&ROOHFWRUV
6WDWLVWLFVFROOHFWRUVDUHDSDUWRIWKHVLPXODWLRQWKDWFROOHFWVVWDWLVWLFVRQFRQGLWLRQV VXFKWKHQXPEHURI XQLWVRIWKHFDSDFLW\RIDUHVRXUFHLQXVH RUWKHYDOXHRIJOREDOYDULDEOHVRUFHUWDLQSHUIRUPDQFHVWDWLV WLFV EDVHG RQ DWWULEXWHV RI WKH HQWLW\ 7KUHH GLIIHUHQW W\SHV RI VWDWLVWLFV FDQ EH FROOHFWHG—FRXQWV WLPH SHUVLVWHQWDQGWDOOLHV&RXQWVDUHYHU\VWUDLJKWIRUZDUGWKH\FRXQW,QRXUPRGHOZHGHILQHGIRXUFRXQWV DV JOREDO YDULDEOHV DQG ZH ZLOO FROOHFW VWDWLVWLFV RQ WKHVH 7LPHSHUVLVWHQW VWDWLVWLFDO FROOHFWRUV JLYH WKH WLPHZHLJKWHGYDOXHVRIGLIIHUHQWYDULDEOHVLQWKHVLPXODWLRQ$FRPPRQYDULDEOHWRWUDFNLVWKHXWLOL]D WLRQRIDUHVRXUFH,QRXUPRGHOZHFROOHFWIRXUGLIIHUHQWWLPHSHUVLVWHQWVWDWLVWLFV—WKHQXPEHURIEXV\ UHVRXUFHVRIWKHWZRUHVRXUFHVWKDWZHKDYHLQWKHPRGHODQGWKHQXPEHURIHQWLWLHVLQHDFKRIWKHFRUUH VSRQGLQJTXHXHV7KHVHDUHQRWVWULFWO\QHHGHGWRDVVHVVWKHPDQDger’s FULWHULDEXWSURYLGHDGGLWLRQDOLQ VLJKWUHJDUGLQJWKHSHUIRUPDQFHRIWKHFDOOFHQWHUZKLFKPLJKWEHXVHIXOLIWKHPDQDger’s requirements DUHQRWPHW7DOO\VWDWLVWLFVDUHFROOHFWHGRQHREVHUYDWLRQDWDWLPHZLWKRXWUHJDUGWRWKHDPRXQWRIWLPH EHWZHHQREVHUYDWLRQV,QRXUPRGHOZHFROOHFWDYHU\FRPPRQVWDWLVWLFZKLFKLVWKHDPRXQWRIWLPHWKDW DQHQWLW\VWD\VLQWKHV\VWHP6LQFHZHDVVLJQWKHYDOXHRIWKHHQWLW\DWWULEXWH6WDUWB7LPH &XUUHQWB7LPH ZKHQLWHQWHUVWKHFDOOFHQWHUWKHYDOXH &XUUHQWB7LPH–6WDUWB7LPH ZKHQWKLVHQWLW\GHSDUWVWKHV\VWHP LVWKHWRWDODPRXQWRIWLPHWKLVHQWLW\LVLQWKHV\VWHP$JDLQWKLVVWDWLVWLFSURYLGHVDGGLWLRQDOLQVLJKWRQ SHUIRUPDQFH $:$/.7+528*+7+(6(&21&(376 :KDWZHDUHJRLQJWRGRQRZLVZDONWKURXJKDFRXSOHRIVWHSVLQRXUVLPXODWLRQPRGHO$V\RXZLOOVHH ZHZLOOWUDFNWKHVWDWHRIWKHV\VWHPWKHHQWLWLHVRQWKHFDOHQGDUWKHYDOXHVRIDWWULEXWHVDQGVWDWHYDULD EOHVDQGWKHVWDWLVWLFVZHDUHFROOHFWLQJ
7KH6WDWHRI7KH6\VWHPDW1RRQ
:HDVVXPHLQLWLDOO\WKDWWKHUHDUHRQHFDUVWHUHRDJHQWDQGWZRDJHQWVIRURWKHUSURGXFWV)LJXUHVKRZV WKHLPDJHRIWKHV\VWHPDWQRRQ7KHFDOHQGDURIWKLVV\VWHPLVPDGHXSRIWKHHQWLWLHVWKDWDUHVFKHGXOHG WRFRPSOHWHDQDFWLYLW\ZLWKDVSHFLILFWLPHGXUDWLRQDVVKRZQLQ7DEOH7KHWZRTXHXHVDUHVKRZQ ZLWKWKHHQWLWLHVLQUDQNRUGHULQ7DEOHVDQG ZHDVVXPHWKHFDOOVDUHSURFHVVHG),)2LHLQWKHRUGHU RIDUULYDODWWKHTXHXH 1RWHWKDWWKHHYHQWWLPHVDUHXQGHILQHG(DFKHYHQWUHFRUGRQWKHWKUHHOLVWVDOVR LQFOXGHVWKHYDOXHVRIWKHHQWLWLHVDWWULEXWHVZKHQWKHVHDUHGHILQHG
510
:KLWHDQG,QJDOOV
WaitinginCarStereoQueue
Scheduled toArrive
InProcess IVRUnit
InProcess CarStereoSales Representative
InProcess OtherProductsSales Representatives
WaitinginOtherProductsQueue
)LJXUH 6WDWHRIWKHV\VWHPDWQRRQ 2WKHULPSRUWDQWLQIRUPDWLRQFRQFHUQVWKHFORFN&XUUHQWB7LPHZKLFKLVVHWWR 307KHVWD WLVWLFVWKDWZHDUHWUDFNLQJLQWKHVLPXODWLRQKDYHWKHYDOXHVOLVWHGLQ7DEOHas of noon. The “Time/Obs” FROXPQJLYHVWKHDPRXQWRIWLPHWKDWZHKDYHEHHQFROOHFWLQJWKHVWDWLVWLF ZKLFKLVVLQFH $0 IRU WLPHSHUVLVWHQWVWDWLVWLFVRUWKHQXPEHURIREVHUYDWLRQVIRUWDOO\VWDWLVWLFV 7DEOH 7KH&DOHQGDUDWQRRQ (QWLW\
(YHQW $UULYHDW&DOO&HQWHU &RPSOHWH6HUYLFH,95 &RPSOHWH6HUYLFH&DU 6WHUHR &RPSOHWH6HUYLFH2WKHU &RPSOHWH6HUYLFH2WKHU (QGUHSOLFDWLRQ
(YHQW7LPH 30 30 30
3URGXFWB7\SH FDUVWHUHR FDUVWHUHR
6WDUWB7LPH $0 $0
%HJLQB:DLW $0
30 30 30
RWKHU RWKHU
$0 $0
$0 $0
6WDUWB7LPH $0 $0
%HJLQB:DLW $0 $0
7DEOH &DU6WHUHR4XHXHDWQRRQ (QWLW\ (YHQW %HJLQ6HUYLFH %HJLQ6HUYLFH
(YHQW7LPH
3URGXFWB7\SH FDUVWHUHR FDUVWHUHR
7DEOH 2WKHU3URGXFW4XHXHDW1RRQ (QWLW\
(YHQW %HJLQ6HUYLFH %HJLQ6HUYLFH %HJLQ6HUYLFH %HJLQ6HUYLFH %HJLQ6HUYLFH
(YHQW7LPH
3URGXFWB7\SH RWKHU RWKHU RWKHU RWKHU RWKHU
6WDUWB7LPH $0 $0 $0 $0 $0
7DEOH 6WDWLVWLFVDWQRRQ 6WDWLVWLF 9DOXH %XV\6LJQDO&RXQW &RPSOHWLRQV &DU6WHUHR &RXQW &RPSOHWLRQV 2WKHU3URGXFW &RXQW ([FHVVLYH:DLW &DU6WHUHR &RXQW ([FHVVLYH:DLW 2WKHU3URGXFW &RXQW 5HSUHVHQWDWLYH8WLOL]DWLRQ &DU6WHUHR 5HSUHVHQWDWLYH8WLOL]DWLRQ 2WKHU3URGXFW
511
7LPH2EV
%HJLQB:DLW $0 $0 $0 $0 $0
:KLWHDQG,QJDOOV
$YHUDJH1XPEHU:DLWLQJ &DU6WHUHR $YHUDJH1XPEHU:DLWLQJ 2WKHU3URGXFW $YHUDJH:DLWLQJ7LPH %RWK7\SHV $YHUDJH6\VWHP7LPH
7KH6WDWHRI7KH6\VWHPDW 30
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e attribute value is set to “Other”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
(YHQW &RPSOHWH6HUYLFH,95 $UULYHDW&DOO&HQWHU &RPSOHWH6HUYLFH,95 &RPSOHWH6HUYLFH&DU6WHUHR &RPSOHWH6HUYLFH2WKHU &RPSOHWH6HUYLFH2WKHU (QGUHSOLFDWLRQ
(YHQW7LPH 30 30 30 30 30 30 30
512
3URGXFWB7\SH FDUVWHUHR RWKHU FDUVWHUHR RWKHU RWKHU
6WDUWB7LPH $0 30 $0 $0 $0
%HJLQB:DLW $0 $0 $0
:KLWHDQG,QJDOOV
7KH6WDWHRI7KH6\VWHPDW 30
Lets process one more event, just so we’ve got the idea. Looking at the calendar in Table 4, the next HYHQWUHFRUGKDVHQWLW\FRPSOHWLQJVHUYLFHDWWKH,95XQLW7KHFORFNLVDGYDQFHGWR HQWLW\ EHFRPHV WKH DFWLYH HQWLW\ DQG WKH UHFRUG IRU HQWLW\ LV UHPRYHG IURP WKH FDOHQGDU 1H[W WKH %HJLQB:DLWDWWULEXWHIRUWKLVHQWLW\LVVHWWRWKHFXUUHQWFORFNWLPH7KH3URGXFt_Type attribute is “Car Stereo”VRWKHHQWLW\LVVHQWWRUHFHLYHVHUYLFHIURPWKHFDUVWHUHRVDOHVUHSUHVHQWDWLYH)LQGLQJWKHVDOHV UHSUHVHQWDWLYHEXV\ZLWKDQRWKHUFDOODQGWZRFDOOVDOUHDG\ZDLWLQJHQWLW\MRLQVWKHTXHXHDWUDQN 7KHVWDWLVWLFVDUHXSGDWHGWRUHIOHFWWKHSDVVDJHRItime and that’s it. ,17(535(7,1*28738767$7,67,&6 /HWXVDVVXPHWKDWRXUPRGHOKDVUXQIURP $0WR 30$W 30ZHVWRSWKHVLPXODWLRQ and we have all of our statistics calculated. The “answer” for the simulatioQLVLQ7DEOH
7DEOH 6WDWLVWLFVDW 30 6WDWLVWLF 9DOXH %XV\6LJQDO&RXQW &RPSOHWLRQV &DU6WHUHR &RXQW &RPSOHWLRQV 2WKHU3URGXFW &RXQW ([FHVVLYH:DLW &DU6WHUHR &RXQW ([FHVVLYH:DLW 2WKHU3URGXFW &RXQW 5HSUHVHQWDWLYH8WLOL]DWLRQ &DU6WHUHR 5HSUHVHQWDWLYH8WLOL]DWLRQ 2WKHU3URGXFW $YHUDJH1XPEHU:DLWLQJ &DU6WHUHR $YHUDJH1XPEHU:DLWLQJ 2WKHU3URGXFW $YHUDJH:DLWLQJ7LPH %RWK7\SHV $YHUDJH6\VWHP7LPH
7LPH2EV
,WLVWHPSWLQJWRFRQFOXGHLPPHGLDWHO\WKDWWKHFDOOFHQWHULVJURVVO\XQGHUVWDIIHGDQGGRHVQRWQHDUO\ approximate the manager’s requirements. Seven out of (7+10+53)=70 (RU RIDUULYLQJSKRQHFDOOV DUHUHMHFWHGDWWKHVZLWFK RI RU RIFDUVWHUHRFDOOVDQGRIRWKHUSURGXFWFDOOVH[SHULHQFH ZDLWVORQJHUWKDWPLQ DQGWKHDYHUDJHZDLWLQJWLPHLVQHDUO\PLQXWHV—IDUWRRORQJIRUFXVWRPHUVDW LVIDFWLRQ,QGHHG,NQRZWKDW,ZRXOGKDQJXSORQJEHIRUHWKLVXQKDSS\DQGZRXOGSHUKDSVHYHQWU\DQ RWKHUUHWDLOHU:HFDQVHHWKDWWKHUHVRXUFHVDUHVWUHVVHG—WKHFDUVWHUHRUHSUHVHQWDWLYHLVEXV\RIWKH WLPHDQGQHLWKHURIWKHRWKHUSURGXFWUHSUHVHQWDWLYHVGUDZDEUHDWKHZKLOHQRWRQWKHSKRQH7KHVLWXDWLRQ RQWKLVGD\LVVRYHU\EDGWKDWWKHFRQFOXVLRQPD\EHZDUUDQWHG %XWFDXWLRQLVDGYLVHG6XSSRVHWKDWWKLVLVMXVWDQH[FHSWLRQDOO\EDGGay? Shouldn’t we really look DWWKHFDOOFHQWHURQPRUHWKDQRQHGD\EHIRUHZHMXPSWRWKLVFRQFOXVLRQ",QGHHGZHVKRXOGDQGWKLVLV DOZD\VWKHFDVHLQGLVFUHWHHYHQWVLPXODWLRQ7KHQXPEHUVJLYHQLQ7DEOHDUHDUDQGRPDQVZHUWRWKH SHUIRUPDQFHRIWKHV\VWHP7KLVLVEHFDXVHWKHUHDUHUDQGRPLQSXWVWRWKHV\VWHPWKDWJLYHXVWKLVDQ VZHU7KHDQVZHUJHQHUDWHGE\RQO\RQHUXQLVQRWUHDOO\DQDQVZHUDWDOO 7RPDNHWKHSRLQWOHWXVWDNHWKHIROORZLQJUROOVRIWKHGLFH
