04 Radivojevic

7/28/2019 04 Radivojevic

1/17

39

FUZZY SYSTEM FOR VEHICLE DESIGN ROUTE

FAZI SISTEM ZA PROJEKTOVANJE RUTA VOZILA

Gordana RADIVOJEVI

Mihailo Pupin Institute, Belgrade, Serbia

1 INTRODUCTION

Dial-A-Ride system is type of transportation inwhich carrier owns car park and realize transporton relations and in time demanded by customers.Different versions of this kind of transportationare present in everyday use: transport of old andill people, transport in areas with low densitywhere there is no public transport, different typeof transportation in city municipal services etc.Static and dynamic case can be defined while

solving problems of design route and schedules.Static case considers that group of requests for

1 UVOD

Dial-a-Ride sistem je oblik prevoza u kome prevozilacposeduje vozni park i realizuje prevoz na relacijama iu vreme kako to zahtevaju korisnici. Razliitevarijante ovog oblika prevoza su prisutne usvakodnevnoj praksi: prevoz starih i bolesnih lica,

prevoz u oblastima sa malom gustinom naseljenostigde ne postoji javni gradski prevoz, razliiti oblici

prevoza u gradskim komunalnim slubama, i dr. Prireavanju problema projektovanja ruta i redova

vonje mogu se definisati statiki i dinamiki sluaj.Statiki sluaj podrazumeva da su skup zahteva za

Abstract: Dial-A-Ride system is type of transportation in which carrier owns fleet and realize transport onrelations and in time demanded by customers. Different versions of this type of transportation are presentin everyday use. Solving problem of design route and scheduling in real time is dynamic case of this

problem. In dynamic case, problems are being solved by dispatcher in real time. Dispatchers makedecisions based on subjective evaluation of present and future situation on transport network, personalexperience and intuition. Fuzzy system for design route of traffic devices for Dial-A-Ride system isdescribed in this paper. Two different approximate reasoning algorithms are developed within fuzzysystem: for choise of vehicle for realization of new request for transport and for defining route of vehicle.Developed fuzzy system has the possibility of usage in concrete conditions.

Key words:Dial-A-Ride, Transportation, Fuzzy Logic, Approximate Reasoning Algorithm.

Apstrakt: Dial-a-Ride sistem je oblik prevoza u kome prevozilac poseduje vozni park i realizuje prevoz narelacijama i u vreme kako to zahtevaju korisnici. Razliite varijante ovog oblika prevoza su prisutne usvakodnevnoj praksi. Reavanje problema projektovanja ruta i redova vonje u realnom vremenu jedinamiki sluaj ovog problema. U dinamikom sluaju se problemi reavaju odluivanjem dispeera urealnom vremenu. Dispeeri donose odluke na osnovu subjektivne procene trenutne i budue situacije natransportnoj mrei, linog iskustva i intuicije. U ovom radu je opisan fazi sistem za projektovanje ruta

saobraajnih sredstava za dynamic Dial-a-Ride system. U okviru fazi sistema razvijena su dva algoritmaaprosimativnog rezonovanja: za izbor vozila za realizaciju novog zahteva za prevozom i za definisanje

rute vozila. Razvijeni fazi sistem ima mogunost primene u konkretnim uslovima.

Kljune rei: dial-a-ride, transport, fazi logika, algoritam aprosimativnog rezonovanja.

UDC: 65.015.13:65.012.34

The International Journal ofTRANSPORT& LOGISTICSMeunarodni asopisTRANSPORT I LOGISTIKA


2/17

G. Radivojevi, FUZZY SYSTEM FOR VEHICLE DESING ROUTE T&L - 11/06

40

transport and data of traffic resources areknown in advance. Then design route and timeschedules are made for future period withknown parameters of transport process.Dynamic case considers solving problems ofdesign route and scheduling of traffic resourcesin real time.

Considering dynamic and static character ofthese problems, the approaches for theirsolving are different as well. Basiccharacteristic of solving problem in static caseare determination and that there is enough timefor making good solutions. In dynamic case,

problems are being solved by dispatchersdecisions in real time. Design route of trafficresources is mostly direct outcome of

dispatchers decision. Dispatcher makesdecisions based on subjective evaluation ofpresent and future situation on transportnetwork, personal experience and intuition.

The aim of this work is solving problem ofdesign route and scheduling for dynamic caseof Dial-A-Ride system. In the work is shownfuzzy system for design route based on usingfuzzy theory and approximate reasoningalgorithms.

The work is organized as followed. In first partis described Dial-A-ride system and is giventhe most significant overview of literature inarea of fuzzy theory and its use in traffic.Second part of the work contains postulate of

problem of design route for dynamic Dial-A-Ride system. Third part describes fuzzy systemfor design vehicle route. Fourth part containsfinal analyzing.

2 TRANSPORT SYSTEM DIAL-A-RIDE

In Dial-A-ride system carrier owns car parkwith which he transport passengers on certainarea. Transport is realized on relations and ontime demanded by passengers. The basic aimof transport is servicing of group of requestsfor transport in certain period of time. Thistransport system is used for transport of

passengers in areas with low density or fortransport of handicapped, old and sick peoplein big towns. Different versions of thistransport system are use in city municipalservices which deals with gathering anddistribution of goods and passengers.

prevozom i podaci o saobraajnim sredstvimaunapred poznati. Tada se projektovanje ruta ireda vonje radi za neki budui period sa

poznatim parametrima transportnog procesa.Dinamiki sluaj podrazumeva reavanje

problema projektovanja ruta i reda vonjesaobraajnih sredstava u realnom vremenu.

S obzirom na dinamiki i statiki karakter ovihproblema, razlikuju se i pristupi njihovomreavanju. Osnovne karakteristike reavanja

problema u statikom sluaju sudeterministinost i postojanje dovoljno vremenaza dobijanje kvalitetnih reenja. U dinamikomsluaju se problemi reavaju odluivanjemdispeera u realnom vremenu. Projektovanjeruta saobraajnih sredstava je uglavnom

direktna posledica dispeerske odluke. Dispe

eridonose odluke na osnovu subjektivne procene

trenutne i budue situacije na transportnojmrei, linog iskustva i intuicije.

Cilj ovoga rada je reavanje problemaprojektovanja ruta i redova vonje za dinamikisluaj Dial-a-Ride sistema. U radu je prikazanfazi sistem za projektovanje ruta, koji se zasnivana primeni fazi teorije i algoritamaaproksimativnog rezonovanja.

Rad je organizovan na sledei nain. U prvomdelu je opisan Dial-a-Ride sistem i dat jenajznaajniji pregled literature u oblasti faziteorije i njene primene u saobraaju. Drugi deorada obuhvata postavku problema projektovanjaruta za dinamiki Dial-a-Ride sistem. U treemdelu je opisan fazi sistem za projektovanje rutavozila. etvrti deo obuhvata zakljunarazmatranja.

2 TRANSPORTNI SISTEM NAZOVI VONJU

U Dial-a-ride sistemu prevozilac poseduje voznipark, kojim obavlja prevoz putnika na odreenompodruju. Prevoz se realizuje na relacijama i uvreme kako to zahtevaju putnici. Osnovni cilj

prevozioca je opsluivanje skupa zahteva zaprevozom u odreenom periodu. Ovaj transportnisistem se primenjuje za prevoz putnika u oblastimasa malom gustinom naseljenosti ili za prevozhendikepiranih, starih i bolesnih lica u velikimgradovima. Razliite varijante ovog sistema

prevoza se primenjuju u gradskim komunalnimslubama, koje se bave prikupljanjem idistribucijom robe ili putnika.


3/17


41

Gathering of requests for transport is realizedin dispatcher center. Each request for transportis described with stating and finishing point ofmovement and desired time of start of service.Maximization of number of services requests,minimization of transport distance,minimization of number of required vehicles,minimization of empty rides, etc. can be theaim of carrier when design route andscheduling. Criteria for design route can bevarious and depend on work organization andcarrier business politics.

Dial-A-Ride system has static and dynamiccase. Static case is when requests for transportare gathering today for tomorrow. Design routeand scheduling for the next day are made on

the behavior of previous working day.Dynamic case is when design route andscheduling are made in real time. User callsdispatcher center and makes a request fortransport. Dispatcher makes immediatedecision on request realization based onvehicles schedules and conditions on transportnetwork, or the request is dropped if all thevehicles are busy.

Previous studies in this area consider greatnumber of papers dealing with design route and

scheduling of traffic resources. Bodin andGolden (1981) give classification of problem ofdesign route and scheduling of traffic resources

based on basic characteristics of transportprocess: service time, number of depots onnetwork, size and structure of car park,capacity of vehicle resources, limitations insystem, etc. There are different versions fortransport system Dial-A-Ride in previousstudies: one or more depots of fleet, one ormore vehicles in fleet, homogeneous orheterogeneous fleet, existing of time intervals

or time moments that describe time of servicebeginning or finishing, static or dynamic case,etc. Stein (1978) and Psaraftis (1980, 1983)have studied transport systems Dial-A-Ride inwhich there are no time windows and onevehicle service. Sexton and Bodin (1985)dealed with static case of transport systemDial-A-Ride with defined time intervals andlarger number of vehicles servicing the users.In their work, Solomon and Desrosiers (1988)give overview of various problems in designroute and scheduling of traffic resources withexisting time intervals.

Prikupljanje zahteva za prevozom se realizuje udispeerskom centru. Svaki zahtev za prevozom

je opisan izvorom i ciljem kretanja i eljenimvremenom poetka opsluge. Pri projektovanjuruta i reda vonje, cilj prevozioca moe bitimaksimizacija broja opsluenih zahteva,minimizacija rastojanja prevoza, minimizacija

broja potrebnih vozila, minimizacija praznihvonji, i dr. Kriterijumi projektovanja ruta mogu

biti razliiti i zavise od organizacije rada iposlovne politike prevozioca.

Dial-a-ride sistem ima statiki i dinamikisluaj. Statiki sluaj je kada se zahtevi za

prevozom prikupljaju danas za sutra. Na krajuradnog dana se radi projektovanje ruta i redavonje za sledei dan. Dinamiki sluaj je kada

se projektovanje ruta i reda vonje radi urealnom vremenu. Korisnik se javljadispeerskom centru i prijavljuje zahtev za

prevozom. Dispeer odmah donosi odluku orealizaciji zahteva, na osnovu rasporeda i stanjavozila na transportnoj mrei, ili zahtev dobijaotkaz, ako su sva vozila zauzeta.

Dosadanja istraivanja u ovoj oblastiobuhvataju veliki broj radova koji se bave

projektovanjem ruta i redova vonjesaobraajnih sredstava. Bodin i Golden (1981)

daju klasifikaciju problema projektovanja ruta ireda vonje saobraajnih sredstava, premaosnovnim karakteristikama prevoznog procesa:vreme opsluge, broj depoa na mrei, veliina istruktura voznog parka, kapacitet saobraajnihsredstava, ogranienja u sistemu, i dr. Udosadanjim istraivanjima postoje razliitevarijante za transportni sistem Nazovi vonju:

jedan ili vie depoa voznog parka, jedno ili vievozila u voznom parku, homogen ili heterogenvozni park, postojanje vremenskih intervala ilivremenskih momenata koji opisuju vreme

poetka ili zavretka opsluge, statiki ilidinamiki sluaj, itd. Stein (1978) i Psaraftis(1980, 1983) su izuavali transportne sistemeNazovi vonju u kojima ne postoje vremenskiintervali i kada opslugu obavlja samo jednosaobraajno sredstvo. Sexton i Bodin (1985) suse bavili statikim sluajem transportnogsistema Nazovi vonju sa odredjenimvremenskim intervalima i veim brojem vozila,koja opsluuju korisnike. Solomon i Desrosiers(1988) u svom radu daju pregled razliitih

problema projektovanja ruta i reda vonjesaobraajnih sredstava sa postojanjemvremenskih intervala.


4/17


42

Development of fuzzy logic and use of fuzzysystems in manipulation of processes haveconsequence in use of fuzzy theory in traffic andtransport. In their book, Teodorovi and Kikuchi(1991, 1994) describe use of fuzzy theory intraffic. Kikuchi and Donnely (1992), Teodoroviand Pavkovi (1992), Vukadinovi andTeodorovi (1994), Teodorovi and Radivojevi(1997) also researched use of fuzzy theory insolving problems of design route and scheduling.

3 STATEMENT OF THE PROBLEM

In this work, the dynamic Dial-A-Ride systemwill be examined, where design route is made inreal time. Carrier owns fleet and realizes

transport in certain area, on relations and in timedemanded by customers. Dispatcher center isequipped with multi-line switching office(center) and radio-station. User can requesttransport to dispatcher center of carrier by

phone, maximum t* minutes (i.e. 30 minutes)before desired start of transport. After noticingthe request, dispatcher must immediately makedecision about realization of request, telling theuser number of vehicle which will make thetransport or the user is being dismissed if all thevehicles are busy. Vehicles are equipped with

radio-stations, so that they are in non-stopconnection with dispatcher center during workday.

During work day, dispatcher center gathersrequests for transport nonstop, and isimmediately giving them to specified vehicles torealize. Based on present location of eachvehicle on the network and previously assignedrequests, dispatcher decides to which vehiclewill be assigned for transport. Request fortransport given to one vehicle, cannot be shifted

to some other vehicle to realize. Vehicle whichhas do new ride, goes from present location tolocation which is beginning of new requestimmediately after receiving information. Therecan be more passengers in vehicle at the sametime. Dispatcher decides sentence of exiting of

passengers, apropos defining route of vehicle.Giving first transport request, specified vehiclestarts its route, which in first step considers

beginning and the end of first request. When thevehicle is given second request, its route isexpanding, and sentence of exiting of

passengers is being decided by dispatcher.

Razvoj fazi logike i primena fazi sistema uupravljanju procesima imali su za posledicu

primenu fazi teorije u saobraaju i transportu.Teodorovi i Kikuchi (1991, 1994) u svojojknjizi opisuju primenu fazi teorije u saobraaju.Primenom fazi teorije u reavanju problema

projektovanja ruta i reda vonje bavili su seKikuchi i Donnely (1992), Teodorovi iPavkovi (1992), Vukadinovi i Teodorovi(1994), Teodorovi i Radivojevi (1997, 2000).

3 POSTAVKA PROBLEMA

U ovom radu e biti razmatran the dynamic Dial-A-Ride system, kod koga se projektovanje rutavozila radi u realnom vremenu. Prevozilac

poseduje vozni park, kojim obavlja prevoz naodreenoj teritoriji, na relacijama i u vreme kakozahtevaju korisnici. Dispeerski centar

prevozioca je opremljen telefonskom centralomsa vie linija i radio-stanicom. Korisnici mogu datelefonski prijave svoj zahtev za prevozomdispeerskom centru prevozioca, najkasnije t*minuta (npr. 30 minuta) pre eljenog vremena

poetka prevoza. Dispeer odmah poevidentiranju zahteva mora da donose odluku orealizaciji zahteva, saoptavajui korisniku brojvozila koje e obaviti prevoz ili korisnik dobija

otkaz ako su sva vozila zauzeta. Vozila suopremljena radio-stanicama, tako da su u tokuradnog dana u neprekidnoj vezi sa dispeerskimcentrom.

U toku radnog dana dispeerski centarneprekidno prikuplja zahteve za prevozom iodmah ih dodeljuje odreenim vozilima narealizaciju. Dispeer na osnovu trenutne lokacijesvakog vozila na mrei i prethodno dodeljenihzahteva, odreuje kom vozilu e dodeliti novizahtev za prevozom. Zahtev za prevozom, koji je

dodeljen jednom vozilu, ne moe se kasnijedodeliti nekom drugom vozilu na realizaciju.Vozilo, koje treba da obavi novu vonju, odmah

po prijemu informacije odlazi iz trenutne lokacijeu lokaciju, koja je poetak novog zahteva. Uvozilu se istovremeno moe nai vie putnika.Redosled izlaza putnika iz vozila, odnosno,definisanje rute vozila, odreuje dispeer.Dodeljivanjem prvog zahteva za prevozom,odreeno vozilo zapoinje svoju rutu, koja u

prvom koraku obuhvata poetak i kraj prvogzahteva. Kada se ovom vozilu dodeli drugizahtev, njegova ruta se proiruje, a redosledizlaza putnika iz vozila definie dispeer.


5/17


43

Realization of transport requests is made oncertain transport network. Transport networkis city area, which consists of group ofnodes city junctures and group of streetsconnecting these junctions (nodes). Basiccharacteristics of transport network are:

M - number of nodes on the network,Xp, Yp - coordinates of node p on the

network,Dpq - distance between nodes p and q,TTpq - travel time between nodes p and q.

Carrier owns homogenous fleet with onedepot on transport network. Vehicles are

minibuses, which provide simultaneoustransport of many passengers. On thebeginning of work, all the vehicles are in thedepot. Vehicle exits the depot when isassigned for the first transport request. Ifduring the drive vehicle gets new request, itgoes to accomplish it ... Vehicle returns to thedepot when the last passenger exits thevehicle, it means when it realized all assignedtransport requests. Vehicles don't have limitedtime shift, but work during whole day.Characteristics of car park are:

N - number of vehicles,NC - capacity of vehicles,TC - coefficient of maximum increase of

travel time,D - depot location on transport network.

Coefficient of maximum increase of traveltime TC is defined by carrier's business

politics. It is the measure of quality ofrealized transport services, because it limitsthe time which each passenger can be in thevehicle. On figure 1 is shown transportnetwork on which the transport is beingrealized.

Transport of one passenger on specifiedrelation in specified time is considered astransport request. On figure 2 is showntransport request i.

Realizacija zahteva za prevozom se obavljana odreenoj transportnoj mrei. Transportnamrea je gradsko podruje, koje sastoji odskupa vorova - gradskih raskrsnica, i skupaulica, koje povezuju te vorove. Osnovnekarakteristike transportne mree su:

M - broj vorova na mrei,Xp, Yp - koordinate vora p na mrei,Dpq - rastojanje izmeu vorova p i q,TTpq - vreme putovanja izmeu vorova

p i q.

Prevozilac poseduje homogen vozni park sajednim depoom na transportnoj mrei. Vozila

su mini busevi, koji obezbeuju istovremeniprevoz vie putnika. Na poetku rada svavozila se nalaze u depou. Vozilo izlazi izdepoa kada dobije prvi zahtev za prevozom.Ako u toku vonje vozilo dobije novi zahtev,odlazi da primi njega, ... Vozilo se vraa udepo kada poslednji putnik izae iz vozila tj.kada je realizovalo sve dodeljene zahteve za

prevozom. Vozila nemaju ogranienjetrajanja radnog vremena ve rade u tokucelog dana. Karakteristike voznog parka su:

N - broj vozila,NC - kapacitet vozila,TC - koeficijent maksimalnog poveanja

vremena putovanja,D - lokacija depoa na transportnoj mrei.

Koeficijent maksimalnog poveanja vremenaputovanja TC je odreen poslovnompolitikom prevozioca. To je mera kvaliteta

ostvarenih prevoznih usluga, jer se na ovajnain ograniava vreme koje svaki putnikmoe provesti u vozilu. Na slici 1 je

prikazana transportna mrea na kojoj serealizuje prevoz.

Pod zahtevom za prevozom se podrazumevaprevoz jednog putnika na odreenoj relaciji uodreeno vreme. Na slici 2 je prikazan zahtevza prevozom i.


6/17


44

0

X

Y

D

p (x , y)p p

q (x , y )q q

TTpq

Dpq

Figure 1 Transportna mrea na kojoj se realizuje prevoz putnika

slika 1 Transportna mrea na kojoj se realizuje prevoz putnika

t

EPTi DPTi LPT i

APT i ADTi

EDTi DDTi LDTi

DTTi

MTTi

TW

ATTi

Figure 2 Characteristics of transport request i

slika 2 Karakteristike zahteva za prevozom i

Characteristics of transport request are:

i+ - i-th passenger's origin,

i-th - passenger's destination,DPTi - desired pick-up time of the i-th passenger,EPTi - earliest pick-up time of the i-th passenger,LPTi - latest pick-up time of the i-th passenger,APTi - actual pick-up time of the i-th passenger,DDTi - desired drop-off time of the i-th passenger,EDTi - earliest drop-off time of the i-th passenger,LDTi - latest drop-off time of the i-th passenger,ADTi - actual drop-off time of the i-th passenger,DTTi - direct travel time of the i-th passenger,MTTi - maximum travel time of the i-th passenger,ATTi - actual time of the i-th passenger,

TW - time window in which request service must start.


7/17


45

When user makes the transport request inmoment TPi, he defines transport relation (i

+,i-) and desired pick-up time. Based on TWcarrier determines earliest (EPTi) and latest(LPTi) pick-up time. Difference betweenearliest pick-up time and time of requestmust be greater or equal the time needed fordirect ride from depot to node of passengersorigin:

EPTi - TP i TTDi (1)

where TTDi is time needed for direct ridefrom depot D to node of passengers origini+. This condition provides that new transporttime cannot be dismissed cause the vehiclecant reach from depot to node i+ by earliest

pick-up time.Based on data given by user, carrier definesall the other characteristic of travel request.Direct Travel Time (DTT i) is time oftraveling between nodes i+ and i-. Maximumtravel time is defined by relation:

MTTi = TC. DTTi (2)

Time moment of earliest and latest drop-offtime are defined by relations::

EDTi = EPTi + DTTi (3)

LDTi = LPTi + MTTi (4)

Actual pick-up time (APTi) and actual drop-off time (ADTi) of request realization (i) aredefinined in moment from deciding whichvehicle will service the request and sentenceof exiting of passengers from vehicle.Relations for actual moments of pick-up anddrop-off time of request realization must be:

EPTi APTi LPTi (5)

EDTi ADTi LDTi (6)

It means pick-up and drop-off time must bewithin time defined intervals. ATT irepresents actual time for realization ofrequest and the relation is:

DTTi ATTi MTTi (7)

Kada korisnik prijavljuje prevoziocu zahtev zaprevozom u trenutku TPi, on definie relaciju prevoza(i+, i-) i eljeno vreme poetka opsluge zahteva. Naosnovu TW prevozilac odreuje najranije (EPTi) inajkasnije vreme (LPTi) poetka opsluge. Razlikaizmeu najranijeg momenta poetka opsluge imomenta prijave zahteva mora biti vea ili jednakavremenu trajanja direktne vonje od depoa do vora

poetka zahteva:

EPTi - TPi TTDi (1)

gde TTDi vreme trajanja direktne vonje od depoaD do vora poetka opsluge i+. Ovim uslovom seobezbeuje da novi zahtev za prevozom ne moedobiti otkaz jer vozilo ne moe da stigne iz depoau vor i+ do najranijeg momenta poetka

realizacije zahteva.Na osnovu podataka, koje zadaje korisnik, prevozilacdefinie ostale karakteristike zahteva za prevozom.Vreme direktnog putovanja (DTTi) je vreme

putovanja izmeu vorova i+ i i-. Maksimalno vremeputovanja se odreuje prema relaciji:

MTTi = TC. DTTi (2)

Vremenski momenti najranijeg i najkasnijeg zavretkarealizacije zahteva se odreuju preko relacija:

EDTi = EPTi + DTTi (3)

LDTi = LPTi + MTTi (4)

Stvarni momenti poetka (APTi) i zavretka(ADTi) realizacije zahteva (i) se odreuju utrenutku donoenja odluka o vozilu koje erealizovati zahtev i redosledu izlaza putnika izvozila. Za stvarne momente poetka izavretka realizacije zahteva moraju da vaerelacije:

EPTi APTi LPTi (5)

EDTi ADTi LDTi (6)

tj. vreme poetka i zavretka zahteva mora biti udefinisanim vremenskim intervalima. ATTi

predstavlja stvarno vreme trajanja realizacijezahteva i vai relacija:

DTTi ATTi MTTi (7)


8/17


46

Ratio between actual time of request realization(ATTi) and direct travel time on that relation (DTTi)is always minor or equal to coefficient TC andrepresents quality value of accomplished transportservices by carrier.

4 FUZZY SYSTEM

For solving problem of design route andscheduling for the dynamic Dial-A-Ride system,this work developed fuzzy system based on useof fuzzy logic. Two approximate reasoningalgorithms are developed within fuzzy system,which provide making decision on realization oftransport request in real time. The dynamic Dial-A-Ride system represents the system in which

user makes phone calls and generate the transportrequest. Dispatcher decision making is in realtime and immediately after receiving the requestdispatcher must make decision on which vehiclewill realize the request and a new route of thevehicle. With first approximate reasoningalgorithm comes decision on which vehicle willrealize new transport request. Secondapproximate reasoning algorithm decides newroute of vehicle, after adding new transportrequest.

In everydays tasks, while deterring travel timebetween two nodes on the network, dispatchersnever use phrases like "time travel is 13 minutesand 22 seconds". Considering the existence ofuncertainty indefiniteness in executing transport

process, it is not possible to precisely determinetravel time on transport network. The mostcommon phrases used are approximation ofnumeric value (travel time is around 13minutes) or linguistic form (travel time is

short). Dispatchers evaluation is based onexperience and subjective evaluation of time

travel. Thats why in this work time travels ontransport network and time moments, whichdescribe transport request, describe with fuzzynumbers. Based on approximate values andlinguistic forms, all time characteristic can beshown by fuzzy numbers. For example, desired

pick-up time is DPTi, earliest pick-up time andlatest pick-up time are EPTi and LPTi. Indeveloped fuzzy system, desired time of pick-uptime DPTi is presented by triangle fuzzy numberwhere earliest and latest pick-up time representsinterval of fuzzy group trust left and right limitof fuzzy number. Desired time of pick-up time of

Odnos izmeu stvarnog trajanja realizacije zahteva(ATTi) i vremena direktne vonje na toj relaciji(DTTi) uvek je manji ili jednak koeficijentu TC i

predstavlja meru kvaliteta ostvarenih prevoznihusluga prevozioca.

4 FUZZY SYSTEM

U ovom radu je za reavanje problemaprojektovanja ruta i reda vonje saobraajnihsredstava za the dynamic Dial-A-Ride systemrazvijen fazi sistem, koji se zasniva na primeni fazilogike. U okviru fazi sistema su razvijena dvaalgoritma aproksimativnog rezonovanja, koji urealnom vremenu obezbeuju donoenje odluke orealizaciji zahteva za prevozom. The dynamic Dial-

A-Ride system predstavlja sistem u kome sekorisnici telefonom javljaju i prijavljuju svoj zahtevza prevozom. Odluivanje dispeera je u realnomvremenu i odmah po prijemu zahteva dispeer morada donese odluku o vozilu koje e realizovatizahtev i o novoj ruti tog vozila. Prvim algoritmomaproksimativnog rezonovanja se dolazi do odluke ovozilu koje e realizovati novi zahtev za prevozom.Drugi algoritam aproksimativnog rezonovanjaodreuje novu rutu vozila, posle dodavanja novogzahteva za prevozom.

U svakodnevnom radu dispeeri, pri odreivanjuvremena putovanja izmeu dva vora na mrei,nikada ne koriste fraze oblika: vreme putovanjaiznosi 13 minuta i 22 sekunde. S obzirom na

postojanje neizvesnosti i neodreenosti uizvravanju prevoznog procesa, nije mogue

precizno definisanje vremena trajanja putovanja natransportnoj mrei. Najei oblici izraavanjadispeera su aproksimacija numerike vrednosti(vreme putovanja je oko 13 minuta) ililingvistika forma (vreme putovanja je malo).Procena dispeera se zasniva na iskustvu isubjektivnoj oceni vremena putovanja. Zbog togase u ovom radu vremena putovanja na transportnojmrei i vremenski momenti, koji opisuju zahtev za

prevozom, opisuju fazi brojevima. Na osnovuaproksimativnih vrednosti i lingvistikih formi, svevremenske karakteristike se mogu predstaviti fazi

brojevima. Na primer, eljeno vreme korisnika zapoetak opsluge zahteva je DPTi, a najraniji inajkasniji trenutak poetka opsluge su EPTi i LPTi.U razvijenom fazi sistemu se eljeno vreme poetkaopsluge DPTi predstavlja trouglastim fazi brojem

gde najraniji i najkasniji trenutak poetka opslugezahteva predstavljaju interval poverenja fazi skupa

tj. levu i desnu granicu fazi broja. eljeno vreme


9/17


47

request realization DPTi is a value with thehighest importance because customer hasbiggest wish that pick-up time of requestrealization is in that moment.

In the moment of receiving new transportrequest, dispatcher knows the position of all thevehicles on transport network and characteristicsof new request. Vehicle position considers

planned route, present location of each vehicleand time when the vehicle is on present location.On figure 3 is shown the vehicle position on thenetwork when receiving new request i.

poetka realizacije zahteva DPTi je vrednost sanajveim stepenom pripadnosti jer korisnik imanajveu elju da poetak realizacije zahteva budeu tom trenutku.

U trenutku prijave novog zahteva za prevozomdispeer zna raspored svih vozila na transportnojmrei i karakteristike novog zahteva. Podrasporedom vozila se podrazumeva planirana ruta,trenutna pozicija svakog vozila i vreme kada sevozilo nalazi na trenutnoj poziciji. Na slici 3 je

prikazan raspored vozila na mrei u trenutku prijavenovog zahteva i.

Depo

i

i+

i-

Figure 3 Position on the network when receiving new request i

slika 3 Raspored vozila na transportnoj mrei u trenutku prijave zahteva za prevozom i

When new transport request is received,dispatcher makes decision which vehicle willrealize it and on new route of that vehicle. Whenmaking decision, dispatcher can use varioustactics, which depend on carrier business politicsor on present situation on transport network.When dispatcher makes a decision, his thinkinglooks like: if ... then ... Criteria which determinedispatchers decision can be various: number ofavailable vehicles on network, present use ofvehicles, distance of vehicle from pick-up placeof new request, time which the vehicle would

wait for start of realization of new request...etc.

Kada se prijavi novi zahtev za prevozom dispeerdonosi odluku o vozilu koje e ga realizovati i onovoj ruti tog vozila. U donoenju odlukedispeer se moe rukovoditi razliitim taktikama,koje zavise od poslovne politike prevozioca ilitrenutne situacije na transportnoj mrei. Kadadispeer donosi neku odluku njegovorazmiljanje je oblika: if ... then ... Kriterijumi,koji opredeljuju dispeera da donese nekuodluku, mogu biti razliiti: broj raspoloivihvozila na mrei, trenutno angaovanje vozila,udaljenost vozila od mesta poetka novog

zahteva, vreme koje bi vozilo ekalo na poetakrealizacije novog zahteva, ... itd.


10/17


48

Dispatchers decision making can hardly bedescribed with some exact mathematic model,which will provide decision making in varioussituations. When dispatchers describe madedecisions, they rather use qualitative thanquantitative phrases. Experience and "intuition"are in the basis of dispatchers decision makingin certain situation. Qualitative or fuzzy natureof human way of thinking leads to use of fuzzylogic systems, which can be modeled onexperience and behaviour of dispatcher whenmaking a decision. Approximate reasoningalgorithms are group of rules which describedispatchers behaviour in various situation ofdecision making. One rule describes system ofdispatchers way of thinking like: if ... then ... Itis necessary to determine criteria for defining

group of rules based on which a decision ismade.

Modeling of dispatchers reasoning can be donebased on one, two, three or more criteria.Criteria of deciding can have different describedvalues: small, medium, big. Based onexperience, dispatchers concludes whether

present distance of vehicle from pick-up place isshort, medium, or long, and whether vehiclestime waiting for new request realization is short,medium or long. Dispatcher makes decision

with certain preference. Dispatchers preferencecan be described as strong of will to make acertain decision. Dispatchers preference for adecision can be very weak, weak, medium,strong or very strong. Dispatchers reasoninglooks like this: if the distance of vehicle is shortand time waiting is medium, then the preference

is strong. Group of rules provides makingdecisions in various situations of system.

Fuzzy system for design route in transportsystem Dial-A-Ride considers following steps:

Step 1: Prepare of set of input valuesStep 2: Choice of vehicle for realizationof new requestStep 3: Design new vehicle routeStep 4: Calculation of working indices

Step 1: Prepare of set of input values

Group of input values considers data on transportnetwork, data on new transport request and dataon car park. Data on transport network arenumber of nodes on network and distance andtravel time between all pairs of nodes.

Odluivanje dispeera se veoma teko moe opisatinekim egzaktnim matematikim modelom, koji biobezbedio donoenje odluka u razliitimsituacijama. Pri opisivanju donetih odluka dispeerivie koriste kvalitativne izraze od kvantitativnih. Uosnovi dispeerskog zakljuivanja je iskustvo ioseaj za odluku u odreenoj situaciji.Kvalitativna, odnosno, fazi priroda ljudskog nainarasuivanja upuuje na primenu fazi logikihsistema, kojima je mogue modelirati iskustvo i

ponaanje dispeera pri odluivanju. Algoritmiaproksimativnog rezonovanja predstavljaju skup

pravila, kojima se opisuje ponaanje dispeera urazliitim situacijama odluivanja. Jedno praviloopisuje sistem dispeerskog rasuivanja obilika: if... then ... Za definisanje skupa pravila potrebno jeodrediti kriterijume, na osnovu kojih se donosi neka

odluka.

Modeliranje dispeerskog rasuivanja se moeuraditi na osnovu jednog, dva, tri ili viekriterijuma. Kriterijumi odluivanja mogu imatirazliite opisne vrednosti: malo, srednje, veliko.Dispeer na osnovu iskustva zakljuuje da jeudaljenost trenutne pozicije vozila od poetkanovog zahteva mala, srednja ili velika, i da je vremeekanja vozila na poetak realizacije zahteva malo,srednje ili veliko. Dispeer sa odreenom

preferencijom donosi odluku. Preferenecija

dispeera se moe opisati kao jaina elje da sedonese odreena odluka. Preferencija dispeera zaneku odluku moe biti veoma slaba, slaba, srednja,

jaka ili veoma jaka. Rasuivanje dispeera jeoblika: ako je udaljenost vozila mala i vremeekanja vozila srednje tada je preferencija jaka.Skup pravila obezbeuje odluivanje u razliitimsituacijama sistema.

Fazi sistem za projektovanje ruta vozila utransportnom sistemu Nazovi vonju obuhvatasledee korake:

Step 1: Priprema skupa ulaznih veliinaStep 2: Izbor vozila za realizaciju novogzahteva za prevozomStep 3: Projektovanje nove rute vozilaStep 4: Izraunavanje pokazatelja rada

Step 1: Priprema skupa ulaznih veliina

Skup ulaznih veliina obuhvata podatke o transportnojmrei, podatke o novom zahtevu za prevozom i

podatke o voznom parku. Podaci o transportnoj mrei

su brojvorova na mrei i rastojanje i vremeputovanja izmeu svih parova vorova.


11/17


49

Customers, who makes new request, definetransport relation and desired pick-up time. Theearliest and the latest drop-off time of newrequest are based on that.

Data on car park are number of availablevehicles, location of vehicles on network androute of each vehicle with previously giventransport request. When new transport request isreceived, it is necessary to update condition of allvehicles, so that present location, time of presentlocation and planned route are known for eachvehicle. Dispatcher must choose the vehicleswhich are potential candidates for realization ofnew request according to characteristic of newtransport request and location of vehicle on the

network. Choise of vehicle is being done obeyingthese rules:

Giving new request to vehicle must mewithin allowed capacity of vehicle (NC

passengers). Vehicle must begin realization of new

request in given time interval (EDTj ADTj LDTj).

Increasing of time travel, based on input andoutput new request from vehicles, must notinfluence on requests time limits, previously

given to vehicle.

This results with smaller group of availablevehicles which can realize new request. Whenchoosing vehicle, dispatcher uses the rules thatvehicles that are already on the transport networkshould be aquired. If those vehicles cannotrealize new request, than the vehicle from thedepot is called. In this work, group of availablevehicles is divided in three groups:

First group vehicles that already haverequests and in the moment of receiving ofnew request are on the transport network

Second group vehicles which realizedgiven requests and in the moment ofreceiving of new request are in the depot

Third group vehicles that had no givenrequests and ih the moment of receiving ofnew request are in the depot.

When choosing vehicles, the advantage havevehicles from the first, then the second and then

the third group. This allows one vehicle to realizelarger number of requests.

Korisnik, koji prijavljuje novi zahtev, zadajerelaciju prevoza i eljeni vremenski interval

poetka opsluge. Na osnovu toga se definienajranije i najkasnije vreme zavretka opslugenovog zahteva.

Podaci o voznom parku su broj raspoloivihvozila, raspored vozila na mrei i ruta svakogvozila sa prethodno dodeljenim zahtevima za

prevozom. Kada se prijavi novi zahtev zaprevozom neophodno je izvriti auriranje stanjasvih vozila, tako je za svako vozilo poznatatrenutna lokacija, vreme trenutne lokacije i

planirana ruta vozila. Prema karakteristikamanovog zahteva za prevozom i poziciji vozila namrei, treba izvriti izbor vozila, koja su

potencijalni kandidati za realizaciju novog

zahteva. Izbor vozila se radi uz potovanjesledeih ogranienja:

Dodeljivanje novog zahteva vozilu mora biti uokviru dozvoljenog kapaciteta vozila (NC

putnika). Vozilo mora poeti realizaciju novog zahteva

u zadatom vremenskom intervalu (EDTj ADTj LDTj).

Poveanje vremena putovanja, koje nastajeulazom i izlazom novog zahteva iz vozila, nesme da utie na vremenska ogranienja

zahteva, koji su ranije dodeljeni vozilu.

Ovime se dobija manji skup raspoloivih vozila,koja mogu realizovati novi zahtev. Pri izboruvozila dispeer koristi pravilo da treba

prvenstveno angaovati vozila, koja ve rade natransportnoj mrei. Ako ta vozila ne mogu darealizuju novi zahtev, poziva se vozilo iz depoa. Uovom radu skup raspoloivih vozila deli se u trigrupe:

Prva grupa - vozila koja imaju dodeljenezahteve i u trenutku prijave novog zahteva senalaze na transportnoj mrei.

Druga grupa - vozila koja su realizovaladodeljene zahteve i u trenutku prijave novogzahteva se nalaze u depou.

Trea grupa - vozila koja nisu imaladodeljenih zahteva i u trenutku prijave novogzahteva se nalaze u depou.

Pri izboru vozila prednost se daje vozilima izprve grupe, zatim iz druge i tree grupe. Ovime

se obezbeuje da se jednim vozilom realizuje tovei broj zahteva.


12/17


50

Step 2: Choice of vehicle for realization

of new request

In this work, Choice of vehicle for realizationof new transport request is made with use offuzzy logic. The approximate reasoningalgorithm for vehicle choosing is developedwhich allows making good decision by groupof rules. Criteria for choosing vehicle forrealization of new request are:

Distance from present location to nodeof origin of new request, and

Vehicles waiting time for start ofrealization of new request.

Distance from actual position of vehicle to thespot of start of new request can be described by

fuzzy groups "short distance", "mediumdistance" or "long distance". The same way,vehicles waiting time for start of realization ofrequest is described by fuzzy sets "shortwaiting", "medium waiting" and "longwaiting".

Preference intension of decision maker can beshown by preference index PI whose value isfrom 0 to 1. When the value of preferenceindex is 1, decision maker is sure that he will

pick up that vehicle. With decrease of

preference index, the will of decision maker forchoosing the vehicle also decreases. Preferenceof decision maker can be very weak, weak,medium, strong and very strong. These levelsof preference can be shown by adequate fuzzysets.

Approximate reasoning algorithm for choosingof vehicle consists of 9 rules:

Rule 1:

If the distance is SHORT and waiting is SHORT

Then the preference is VERY STRONGRule 2:

If the distance is SHORT and waiting isMEDIUMThen the preference is STRONG

Rule 3:

If the distance is SHORT and the waiting isLONGThen the preference is MEDIUM

Rule 4:

If the distance is MEDIUM and the waiting isSHORTThen the preference is MEDIUM

Step 2: Izbor vozila za realizaciju novog zahteva

za prevozom

Izbor vozila za realizaciju novog zahteva zaprevozom izvren je u ovom radu primenom fazilogike. Razvijen je algoritam aproksimativnogrezonovanja za izbor vozila, koji skupom pravilaomoguava donoenje kvalitetne odluke. Priizboru vozila cilj je da se minimizira dodatnavonja i ekanje vozila. Kriterijumi izbora vozilaza realizaciju novog zahteva za prevozom su:

Rastojanje od trenutne pozicije vozila dovora poetka novog zahteva, i

Vreme ekanja vozila na poetakrealizacije novog zahteva.

Rastojanje od trenutne pozicije vozila do mesta

poetka novog zahteva moe se opisati faziskupovima malo rastojanje, srednje rastojanjeili veliko rastojanje. Na isti nain, vremeekanja vozila na poetak realizacije zahtevaopisuje se fazi skupovima malo ekanje,srednje ekanje i veliko ekanje.

Jaina preferencije donosioca odluke moe bitiiskazana indeksom preferencije PI ija jevrednost od 0 do 1. Kada je vrednost indeksa

preferencije 1 donosilac odluke je siguran da eizabrati to vozilo. Sa opadanjem indeksa

preferencije opada i jaina elje donosiocaodluke za izborom vozila. Preferencija donosiocaodluke moe biti: veoma slaba, slaba, srednja,

jaka i veoma jaka. Ovi nivoi preferencije se moguprikazati odgovarajuim fazi skupovima.

Algoritam aproksimativnog rezonovanja zaizbor vozila se sastoji od sledeih 9 pravila:

Pravilo 1:

Ako je rastojanje MALO i ekanje MALOTada je preferencija VEOMA JAKAPravilo 2:

Ako je rastojanje MALO i ekanje SREDNJETada je preferencija JAKA

Pravilo 3:

Ako je rastojanje MALO i ekanje VELIKOTada je preferencija SREDNJA

Pravilo 4:

Ako je rastojanje SREDNJE i ekanje MALOTada je preferencija SREDNJA


13/17


51

Rule 5:

If the distance is MEDIUM and the waiting isMEDIUMThen the preference is MEDIUM

Rule 6:

If the distance is MEDIUM and the waiting isLONGThen the preference is WEAK

Rule 7:

If the distance is LONG and the waiting isSHORTThen the preference is MEDIUM

Rule 8:

If the distance is LONG and the waiting isMEDIUMThen the preference is WEAK

Rule 9:

If the distance is LONG and the waiting is LONGThen the preference is VERY WEAK

Approximate reasoning algorithm applies for allavailable vehicles by schedule of belonging of

priority group: first is applied for vehicle fromfirst group, then from second and then from thirdgroup. Each vehicle gets preference index value,as output value of approximate reasoningalgorithm, and thats value of rankness ofdispatchers will to give him a request. Vehiclesfrom each group are ranked based on preference

index value. At this step of fuzzy system, it ispossible to make choise of vehicle for realizationof new request according to maximum PreferenceIndex value in priority group of vehicles. Whenthere are no available vehicles in all groups orwhen no vehicles can fulfill conditions forreceiving new requests, than the transport requestis dismissed.

Step3: Design new vehicle routeWhen a vehicle is chosen to realize new request,then the vehicle new route is projected, which

will consider request i. On figure 4 is shown theroute of vehicle which considers nodes k, j, h, l,m. On the figure is shown new request i, whichshould be added to existing route.

Pravilo 5:

Ako je rastojanje SREDNJE i ekanje SREDNJETada je preferencija SREDNJA

Pravilo 6:

Ako je rastojanje SREDNJE i ekanje VELIKO

Tada je preferencija SLABAPravilo 7:

Ako je rastojanje VELIKO i ekanje MALOTada je preferencija SREDNJA

Pravilo 8:

Ako je rastojanje VELIKO i ekanje SREDNJETada je preferencija SLABA

Pravilo 9:

Ako je rastojanje VELIKO i ekanje VELIKOTada je preferencija VEOMA SLABA

Algoritam aproksimativnog rezonovanja seprimenjuje za sva raspoloiva vozila poredosledu pripadnosti prioritetnoj grupi: prvo se

primenjuje za vozila iz prve grupe, zatim iz drugei na kraju iz tree grupe. Kao izlazni podatakalgoritma aproksimativnog rezonovanja, za svakovozilo se dobija vrednost indeksa preferencije,odnosno, mera jaine odluke dispeera da mudodeli zahtev. Na osnovu vrednosti indeksa

preferencije u okviru svake grupe se radirangiranje vozila. U ovom koraku fazi sistema

mogue je izvriti izbor vozila za realizacijunovog zahteva prema maksimalnoj vrednostiindeksa preferencije u prioritetnoj grupi vozila.Kada nema raspoloivih vozila ni u jednoj grupi,odnosno, kada ni jedno vozilo ne ispunjavauslove za preuzimanje novog zahteva, tadazahtev za prevozom dobija otkaz.

Step3: Projektovanje nove rute vozilaKada se neko vozilo izabere za realizaciju novogzahteva, tada se projektuje nova ruta vozila, kojae obuhvatiti zahtev i. Na slici 4 prikazana je rutavozila, koja obuhvata vorove k, j, h, l, m. Naslici je prikazan novi zahtev za prevozom i, kogatreba dodati na postojeu rutu.

k

i+ i

-

j h l mi+

new request i

Figure 4 Planned vehicle route and new request islika 4 Planirana ruta vozila i novi zahtev za prevozom i


14/17


52

Node whish is origin of request i+ is added to theroute immediately after actual location, and nodei- can be added to the vehicles route on different

ways. Various versions of adding node i- presentsvarious vehicles routes. For each route isnecessary that increasing of time travel, made byoutput of request i from vehicle, doesnt react onrequests time limits, already given to the vehicle.If increasing of time travel leads to violating timelimits of other requests, then that combination is

being dismissed.

Criteria for design new route are:

Average increase of travel time, and Average increase of accomplished requests

route (passengers), which are in the vehicle

Average increase of requests travel time can besmall, medium orbig and can be presented

by adequate fuzzy groups. Average increase ofaccomplished requests route can also be small,medium or big and is described by fuzzygroups. Preference rankness of decision maker isshown by Preference Index, whose value can befrom 0 to 1. With increase of preference, willrankness of decision makers to choose specifiedroute of vehicle also increases.

Approximate reasoning algorithm for designroute of vehicle, developed in this paper, consistsof 9 rules:

Rule 1:

If the increase of time is SMALL and theincrease of route is SMALLThen the preference is VERY STRONG

Rule 2:

If the increase of time is SMALL and theincrease of route is MEDIUMThen the preference is STRONG

Rule 3:

If the increase of time is SMALL and theincrease of route is BIGThen the preference is STRONG

Rule 4:

If the increase of time is MEDIUM and theincrease of route is SMALLThen the preference is MEDIUM

Rule 5:

If the increase of time is MEDIUM and theincrease of route is MEDIUMThen the preference is MEDIUM

vor koji je poetak zahteva i+ dodaje se na rutuodmah posle trenutne lokacije, a vor i- moe sena razliite naine dodati na rutu vozila. Razliitekombinacije dodavanja vora i- predstavljajurazliite rute vozila. Za svaku rutu neophodno jeda poveanje vremena putovanja, koje nastajeizlazom zahteva i iz vozila, ne utie navremenska ogranienja zahteva, koji su

prethodno dodeljeni vozilu. Ako poveanjevremena putovanja dovodi do krenja vremenskihogranienja drugih zahteva, tada se takombinacija odbacuje.

Kriterijumi projektovanja nove rute vozila su:

Proseno poveanje vremena putovanja, i Proseno poveanje preenog puta zahteva

(putnika), koji su u vozilu.

Proseno poveanje vremena putovanja zahtevamoe biti malo, srednje ili veliko i moe se

predstaviti odgovarajuim fazi skupovima.Takoe, proseno poveanje preenog putazahteva moe biti malo, srednje ili veliko iopisuje se fazi skupovima. Jaina preferencijedonosioca odluke se izraava indeksom

preferencije, ija je vrednost od 0 do 1. Saporastom indeksa preferencije raste i jaina eljedonosioca odluke za izborom odreene rute

vozila.

Algoritam aproksimativnog rezonovanja zaprojektovanje rute vozila, razvijen u ovom radu,sastoji se od sledeih 9 pravila:

Pravilo 1:

Ako je poveanje vremena MALO i poveanjeputa MALOTada je preferencija VEOMA JAKA

Pravilo 2:

Ako je poveanje vremena MALO i poveanjeputa SREDNJETada je preferencija JAKA

Pravilo 3:

Ako je poveanje vremena MALO i poveanjeputa VELIKOTada je preferencija JAKA

Pravilo 4:

Ako je poveanje vremena SREDNJE ipoveanje puta MALOTada je preferencija SREDNJA

Pravilo 5:

Ako je poveanje vremena SREDNJE ipoveanje puta SREDNJE

Tada je preferencija SREDNJA


15/17


53

Rule 6:

If the increase of time is MEDIUM and theincrease of route is BIGThen the preference is WEAK

Rule 7:

If the increase of time is BIG and the increase ofroute is SMALLThen the preference is WEAK

Rule 8:

If the increase of time is BIG and the increase ofroute is MEDIUMThen the preference is VERY WEAK

Rule 9:

If the increase of time is BIG and the increase ofroute is BIGThen the preference is VERY WEAK

Criteria values for each route are determinedbefore entering the approximate reasoningalgorithm: average increase of travel time andaverage increase of accomplished request's routein vehicle. We enter the approximate reasoningalgorithm with these criteria values. Value of

preference index for each route, which can becreated by giving new request to vehicle, comesas output value of algorithm. The route that hashighest value of preference index is taken fornew vehicle's route. If vehicle chosen in previousstep didn't have any possible route that fulfill

request's time limit in vehicle, then the samemodel step is repeated for the next ranked vehiclefrom the same or next priority group. If there isno route that fulfill request's time limit in vehiclefor all available vehicles, than the transportrequest i must be dismissed.

Step 4: Calculation of working indices

At the end of work you get group of realized andgroup of dismissed transport requests and routeof vehicles through which vehicles were goingduring the day as output value of fuzzy system.

Quantitative characteristics of carriers workorganization are indices of requests servicesquality and indices of fleets work.

Indices of requests services quality arecalculated for every accomplished request andconsider: total time of requests accomplishment,travel time, standing time, coefficient of timeincrease and coefficient of increase of distance.An index of car fleet work are calculated forevery vehicle separately and considers indices ofexploitation of accomplished route and indices ofexploitation of time: accomplished distance with

Pravilo 6:

Ako je poveanje vremena SREDNJE ipoveanje puta VELIKOTada je preferencija SLABA

Pravilo 7:

Ako je poveanje vremena VELIKO i poveanjeputa MALOTada je preferencija SLABA

Pravilo 8:

Ako je poveanje vremena VELIKO i poveanjeputa SREDNJETada je preferencija VEOMA SLABA

Pravilo 9:

Ako je poveanje vremena VELIKO i poveanjeputa VELIKOTada je preferencija VEOMA SLABA

Pre ulaza u algoritam aproksimativnog rezonovanja,za svaku moguu kombinaciju rute odreuju sevrednosti kriterijuma: proseno poveanje vremena

putovanja i proseno poveanje preenog puta,zahteva u vozilu. Sa ovim vrednostima kriterijumaulazi se u algoritam aproksimativnog rezonovanja.Kao izlazni podatak algoritma dobija se vrednostindeksa preferencije za svaku rutu, koja moe nastatidodavanjem novog zahteva vozilu. Za novu rutuvozila se uzima ruta koja ima najveu vrednostindeksa preferencije. Ako vozilo, koje je izabrano u

prethodnom koraku, nije imalo ni jednu moguu

rutu, koja zadovoljava vremenska ogranienjazahteva u vozilu, tada se ovaj korak modela ponavljaza sledee rangirano vozilo iz iste ili sledee

prioritetne grupe. Ako ni za jedno od raspoloivihvozila ne postoji ruta, koja zadovoljava vremenskaogranienja zahteva u vozilu, tada zahtev za

prevozom i mora dobiti otkaz.

Step 4: Izraunavanje pokazatelja rada

Na kraju rada, kao izlazni rezultat fazi sistema dobijase skup realizovanih i skup otkazanih zahteva za

prevozom i rute vozila, kojima su se vozila kretala u

toku dana. Kvantitativne karakteristike organizacijerada prevozioca su pokazatelji kvaliteta opslugezahteva i pokazatelji rada voznog parka.

Pokazatelji kvaliteta opsluge zahteva seizraunavaju za svaki realizovani zahtev iobuhvataju: ukupno vreme realizacije zahteva,vreme prevoza, vreme stajanja, koeficijent

poveanja vremena i koeficijent poveanjapreenog puta. Pokazatelji rada voznog parka seizraunavaju za svako vozilo i obuhvataju

pokazatelje iskorienja preenog puta ipokazatelje iskorienja vremena: preeni put sa


16/17


54

passengers, accomplished distance withoutpassengers, travel time with passengers, traveltime without passengers, standing time, etc.Values of group of indices are got at the end ofthe day, based on which working effects andquality of given transport services can beevaluated.

6 CONCLUSION

In this work is presented fuzzy system for designvehicle's route in dynamic Dial-A-Ride system.Fuzzy system was tested on large number ofnumeric examples, which represents one carrier'swork day. Test showed that developed fuzzysystem can be successfully applied in defined

conditions. Executing of fuzzy system is veryquick and decisions on choise of vehicle androute of vehicle are made within few seconds.

Use of fuzzy logic and approximate reasoningalgorithms showed as very successful for solving

problems of design route in real time. Optimizedand heuristic methods are very hard or evenimpossible to apply in modeling of dispatcher's

behavior in real time and for solving problem ofbig dimensions (1000 travel requests during theday). Fuzzy logic provided modeling of

dispatcher's system of deciding and getting quickand qualitative decisions. Use of fuzzy logicshows many advantages over optimizing method:very quick solution getting, great dimension ofsolving problem, simple modeling of dispatcher'sreasoning, possibility of implementing a hugenumber of limitations in mathematic model.Approaches based on fuzzy logic provideapplying in solving problems with greatdimensions in real time, with fulfilling criteria ofquick work and quality of given solutions.

putnicima, preeni put bez putnika, vremeputovanja sa putnicima, vreme putovanja bezputnika, vreme stajanja, i dr. Na kraju radnogdana dobijaju se vrednosti skupa pokazatelja,na osnovu kojih je mogue oceniti efekte rada ikvaliteta pruenih prevoznih usluga.

6 ZAKLJUAK

U radu prikazan fazi sistem za projektovanje rutavozila u dynamic Dial-a-Ride sistemu. Fazisistem je testiran na velikom broju numerikih

primera, koji predstavljaju jedan radni danprevozioca. Testiranja su pokazala da se razvijenifazi sistem moe uspeno primeniti u konkretnimuslovima. Izvravanje fazi sistema je veoma brzo

i odluke o izboru vozila i rute vozila se dobijajuza nekoliko sekundi.

Primena fazi logike i algoritama aproksimativnogrezonovanja se pokazala kao veoma uspena zareavanje problema projektovanja ruta u realnomvremenu. Optimizacione ili heuristike metode jeveoma teko ili nemogue primeniti zamodeliranje ponaanja dispeera u realnomvremenu i za reavanje problema velikihdimenzija (1000 zahteva za prevozom u tokudana). Fazi logika je omoguila modeliranje

dispeerskog sistema odluivanja i dobijanjebrzih i kvalitetnih odluka. Primena fazi logikepokazuje niz prednosti u odnosu naoptimizacione metode: veoma brzo dobijanjereenja, velike dimenzije reavanih problema,

jednostavno modeliranje dispeerskograsuivanja, mogunost ugraivanja velikog

broja ogranienja u matematiki model. Pristupibazirani na fazi logici omoguavaju primenu ureavanju problema velikih dimenzija u realnomvremenu zadovoljavajui kriterijume brzine radai kvaliteta dobijenih reenja.


17/17


55

Reviewal / Recenzija: Ing. Michal Balog CSc

REFERENCES / LITERATURA

[1] Bodin, L., Golden, B.: Classification in vehicle routing and scheduling.Networks, 11, 97-108, 1981.[2] Desrosiers, J., Soumis, F., Desrochers, M., Sauve, M.:Methods for Routing with Time Windows.

European Journal of Operational Research, 23, 235-245, 1986.[3] Kaufmann, A., Gupta, M. M.:Introduction to Fuzzy Arithmetic. Van Nostrand Reinhold Company,New York, 1985.

[4] Kikuchi, S.: Scheduling of demand Responsive Transit Vehicles. Journal of TransportationEngineering, 110, 511-520, 1984.

[5] Kikuchi, S.: Vehicle Routing and Scheduling Development for Transportation of Elderly andHandicapped Persons. Transportation Quarterly, 41, 207-227, 1987.

[6] Kikuchi, S., Donnely, R.: Scheduling Demand-Responsive Transportation Vehicles using Fuzzy SetTheory. Journal of Transportation Engineering, 118, 430-440, 1992.

[7] Psaraftis, H.:A dynamic programming solution to the single vehicle many-to-many immediaterequest dial-a-ride problem. Transportation Science, 2, 130-154, 1980.

[8] Psaraftis, H.:An Exact Algorithm for the Single-Vehicle Many-to-many Dial-a-ride problem withTime Windows. Transportation Science, 17, 351-357, 1983.

[9] Radivojevi, G.:Multidisciplinary approach to optimization fleet management. MS Thesis, Centerfor Multidisciplinary Studies of the Belgrade University, Belgrade, 1992.

[10] Radivojevi, G.:Fuzzy systems for traffic route design. PhD Thesis, Faculty of Transport andTraffic Engineering, Belgrade, 2002.

[11] Sexton, T., Bodin, L.: Optimizing Single Vehicle Many-to-Many Operations with Desired DeliveryTimes: I. Scheduling. Transportation Science, 19, 378-410, 1985.

[12] Sexton, T., Bodin, L.: Optimizing Single Vehicle Many-to-Many Operations with Desired DeliveryTimes: II. Routing. Transportation Science, 19, 411-435, 1985.

[13] Solomon, M., Desrosiers, J.: Time Window Constrained Routing and Scheduling Problems.Transportation Science, 22, 1-13, 1988.

[14] Stein, D.: Scheduling dial-a-ride transportation systems. Transportation Science, 12, 232-249,1978.

[15] Teodorovi, D.: Transportation Networks Analysis. University of Belgrade, Belgrade, 1996.[16] Teodorovi, D., Kikuchi, S.:Application of fuzzy sets theory to the saving based vehicle routingalgorithm. Civil Engineering Systems, 8, 87-93, 1991.

[17] Teodorovi, D., Kikuchi, S.:Elements of Fuzzy Set Theory with Applications in TransportationEngineering. University of Belgrade, Belgrade, 1991, 1994.

[18] Teodorovi, D., Pavkovi, G.: The fuzzy set theory approach to the vehicle routing problem whendemand at nodes is uncertain. Fuzzy Sets and Systems, 82, 307-317, 1996.

[19] Teodorovi, D., Radivojevi, G.:Fuzzy Logic Approach to the Dynamic Dial-a-Ride Problem. 9thMini EURO Conference: Fuzzy Sets in Traffic and Transport Systems, Budva, Yugoslavia, 1997.

[20] Vukadinovi, K., Teodorovi, D.:A Fuzzy Approach to the Vessel Dispatching problem. EuropeanJournal of Operational Research, 76, 155-164, 1994.

[21] Zadeh, L.A.:Fuzzy Sets. Information and Control, 8, 338-353, 1965.[22] Zimmermann, H.J.:Fuzzy Sets. Decision Making, and Expert Systems, Kluwer Academic

Publishers, Boston, 1987.

Documents

04 Radivojevic