B azilian Jou nal o Ope a ions & P oduc ion Managemen 13 (2016), pp 400-407
PLANNING ROUTES AND SHIFTS DRIVING FOR A SMALL BUSINESS OF ROAD
PASSENGER TRANSPORT
Pablo Apa icio Ruiza; Jesús Muñuzu i Sanza; Alejand o Escude o San anaa; Ra ael G osso de la Vegaa
a Se illa Uni e si y (US) - Se illa, Spain
The p esen ed wo k is done o a company ha cu en ly ope a es wen y lines o passenge anspo in he me opoli an
a ea o Se ille. The planning o hese was o iginally ca ied ou manually, building ou es and shi s in an Excel sp eadshee .
In o de o au oma e he p ocess as much as possible. I was designed and implemen ed by a scheduling algo i hm ha
would be much simple han o he algo i hms in he li e a u e and ha , in addi ion, would make i possible o allow mixing
ehicles and d i e s be ween he lines. The objec i e was, i s ly, o employ he minimum numbe o d i e s; hen, i was
o y o use he leas possible numbe o ehicles; inally, he s udy ied o educe as much as possible he amoun o spli
shi s. In addi ion, es ic ions on he design o ou es and shi s we e added. A all imes he se ice equencies emained
abo e he se limi . To allow he possibili y o unexpec ed demand peaks, was es ablished in he capaci y o each ou e
some slack.
Keywo ds: planning ou es; shi s d i ing; bus; passenge anspo ; algo i hm
ABSTRACT
ABEPRO
DOI: 10.14488/BJOPM.2016. 13.n3.a16
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Volume 13, Núme o 3, 2016, pp. 400-407
DOI: 10.14488/BJOPM.2016. 13.n3.a16
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1. INTRODUCTION
Planning passenge s’ bus se ices is a complex op imiza ion
p oblem, because he condi ions and es ic ions ha o en
occu ing in hem a e usually speci ic o each case. This
necessi a es he use o simpli ied o pa ial app oaches o
each good enough designs. Thus, he global p oblem o
planning a bus se ice is b oken down in o basic modules, in
a o al o i e, acco ding o he o iginal desc ip ion o (Cede
e Wilson, 1986), shown in Table 1. Many scien i ic pape s
ocus on each o he s eps shown in Table 1, some imes
conside ing se e al s ages a once. Cede e Wilson p opose
a wo-s ep algo i hmic p ocedu e o es ablish he ne wo k
design and se ice equencies, whe eas (Guihai e e Hao,
2008) ca ied ou an ex ensi e collec ion o a icles ocusing
on he planning o schedules in he ne wo k. Finally,
ega ding planning on d i ing schedules, (E ns , 2004)
collec ed s udies abou heu is ic app oaches (e.g., Ma ello
e To h, 1986), column gene a ion me hods (Des oche s e
Soumis, 1989) me aheu is ics (W en e W en, 1995), o e en
mul i-objec i e app oaches (Lou enço e al., 2001).
This pape ocuses on he las h ee s ages o he planning
p ocess associa ed wi h he es ablishmen o schedules o
buses and shi s d i ing. These p oblems, which a e based
on p io knowledge o he ne wo k and he minimum
equency s ep and he demand di ided ime slo s and all
da a cos and ime cons ain s can be add essed in mul iple
ways. The mos ad anced app oach is o sol e he h ee
p oblems oge he (Ball e al., 1983; Rod igues e al., 2006;
Mesqui a e Paias, 2008). Howe e , his app oach has he
disad an age ha i equi es sol ing a linea op imiza ion
p oblem a some poin in he execu ion o he algo i hm.
An app oach is aken in his case because i is a small
company wi h ew lines, is a heu is ic app oach ha seeks
a easonably good solu ion in a ime in e al educed o
p o ide guidance o he company in planning schedules and
shi s d i ing. Thus, we decouple bo h p oblems, using he
esul o he i s as inpu o sol ing he second. The goal o
he algo i hm is: i s , i expec s o employ as ew conduc o s
as possible; hen, will seek o use he leas possible numbe
o ehicles; e en ually pu sue educe as much as possible
he amoun o spli shi s ha a e equi ed.
Table 1 Bus se ices planning p ocess.
Inpu s equi ed Planning ac i i y Ou pu s
Demand da a
Ne wo k Design
Rou e changes
Supply da a New ou es
Rou e pe o mance
indices Ope a ing s a egies
Budge o subsidy
a ailable Es ablishmen
equency Se ice equencies
Buses a ailable
Se ice policies
Demand o ime
slo s
Time able
de elopmen
T ip depa u e ime
T ip a i al ime
S a and end ime
o se ice
T a el ime
Deadhead imes
Bus schedules Bus schedules
B eak o es pe iods
Time es ic ions
S uc u e o ope a -
ing cos s
D i e wo k ules D i e s schedul-
ing
D i e shi s sched-
ules
S a cos s o s uc-
u e cos
Sou ce: Cede e Wilson (1986).
2. PROBLEM DEFINITION
F om he iles o he company, i was known he ollowing
in o ma ion o each o he lines: he ound ip ime ( ),
he numbe o daily se ices (ns), he s a and end o he
jou ney, he i s hou (h ) and las hou (hl) o depa u e,
he demand o each slo in each line (D). I a line has se e al
a ian s (i), he numbe o daily se ices (nsi) and he ound
ip ime ( i). As is e lec ed in Table 1, he comple e planning,
scheduling and shi s d i ing also equi ed in o ma ion on
he cos s in ol ed and he ime cons ain s applicable o
each line. This in o ma ion is de ailed below:
• S uc u e cos . The cos applicable o he se ice
depends on he ype o ac i i y, basically, d i e s
can pe o m h ee ypes o unc ions:
- Time o p esence (TP): I is he ime spend nex o
he ehicle wi hou d i ing. The e is an obliga o y
ime o p esence o 10 minu es a he beginning o
each day o p epa e he ehicle, and a simila end
o he liquida ion o he cash box.
- Time d i e -no- ecei e (TDNR): The d i e is
d i ing he ehicle wi hou ca ying passenge s.
Such imes a e o he ou es om he ga age o
he heade line and ice e sa, o ic i ious ou es
which a e placed on se ice planning.
- Time d i e - ecei e (TDR): The d i e is d i ing
he ehicle ca ying passenge s. I co esponds o
he egula bus se ices.
The ime cos s associa ed wi h hese h ee ypes o
unc ions ha e he nex ela ion: cos pe hou (TDR) > cos
pe hou (TDNR) > cos pe hou (TP)
• Tempo al es ic ions. The e is a es ic ion on
d i ing imes and es pe iods o d i e s. This
es ic ion is desc ibed by he ollowing ou
p inciples:
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- D i ing shi : The e a e wo ypes o shi s: ull and
spli shi s (mo ning, e ening).
- Leng h shi : no mal shi s a e 8 hou s, and
maximum an ex a addi ional hou a day.
- S a and end o shi s: mo ning shi s o en end
be o e 15h, and o en s a la e han 12h.
- Res pe iods: Maximum pe iod o con inuous
d i ing is 6h. I he shi is longe , i is obliga o y
o in oduce a b eak pe iod o a leas 15 minu es
(OBP, Obliga o y B eak Pe iod), i i is highe , is
eco ded a he p esen ime. Howe e , in spli
shi s ha b eak is a leas 1 hou , bu ime will no
be conside ed p esence i he b eak is longe .
In Figu e 2, di e en shi con igu a ion s uc u es a e
p esen ed.
Figu e 2. Tempo al Res ic ion.
In blue colou , i is shown he d i ing ime o he Time
D i e -Recei e , in o ange he Obliga o y B eak Pe iod,
his pe iod is always 15 minu es in he middle o he shi s.
Finally, in yellow is shown he Time o P esence (TP), i is he
ime spen nex o he ehicle wi hou d i ing, and when i
is mo e han an hou , he sys em builds a spli shi . In his
igu e is no shown he obliga o y ime p esence (OTP) o 10
minu es a he beginning o each day o p epa e he ehicle,
and a simila end o he liquida ion o he cash box.
3. THE PROPOSED SOLUTION
The p oposed solu ion is p esen ed in Figu e 3. The
solu ion consis s o an ini ial analysis and a heu is ic
calcula ion. Fi s is de ined inpu s (numbe o buses, hou s,
e c.). Then we wo k in an ini ial analysis, and a e ob ained
he ini ial ou pu s, he necessa y da a o his heu is ic,
ha de ine he bus schedule planning and he d i e s’
shi s planning. Finally, i is ob ained he ehicle, shi s and
schedules.
3.1. Ini ialanalysis
The ini ial calcula ion, which is ini ially de e mined,
he numbe o buses o be used in each line and a i s
app oxima ion o he schedules o hem, he lines o he
company a e classi ied in o di e en g oups, and his
consis s o se e al s eps:
• The calcula ion o he numbe o buses needed o
each line, es ima ed om:
(4.1)
Also, is calcula ed: he a el ime in one di ec ion ( d =
/ 2), hou s o se ice (hs = hl – h + d) o he numbe o
buses needed (nb = ns · / hs).
• G ouping and closing o he lines. I he decimal
pa o he nb is g ea e han 0.85 (modi iable
pa ame e ) will be conside ed closed lines. Fo
he emaining lines, o iden i y hose lines ha a e
coinciden , ha is, hey sha e he same e minal
poin in Se ille. Then:
- All possible g oups o ma ched lines a e es ed, in
o de o maximize he numbe o closed g oups.
Figu e 3. The planning algo i hm.
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- A e wa ds, g oups o lines ha a e misma ched
and no closed a e es ed, o building all possible
closed g oups.
Acco dingly, ou cases a e de ined:
- Type A: Indi idual lines closed wi h one ehicle
- Type B: Lines indi idual closed wi h wo o mo e
ehicles
- Type C: G oups wi h wo o mo e ehicles
- Type D: Lines wi h a ious ou es wi h di e en
imes. These lines a e ea ed as belonging o ype
C.
Thus, he o al numbe o buses is ob ained, ounded
o he nex whole numbe needed o each line and closed
g oup buses.
3.2 Heu is ic
A e p elimina y analysis, he heu is ic calcula ion
pe o ms he inal planning, he heu is ic is di ided in o wo
modules: he bus schedules and he d i e shi s planning.
3.2.1 Bus schedules
The planning module o bus schedules, is based on a
his o ical demand o each line and a el imes acco ding o
he ime o day. Rou e designs a e done by de e mining he
numbe o ehicles equi ed and depa u e imes.
To unde s and he heu is ic, an ope a ion o a bus, wi h
ou se ices ( wo depa u es and wo a i als, be ween
wo e minals) is shown in Figu e 4. Fo each se ice, i has
shown ime in each e minal, depa u e ime in one e minal
and a i al ime in he o he , in he line, he slope de ines
speed and dis ance be ween bo h e minals.
Figu e 4. Desc ip ion o he ope a ion o a bus line wi h wo se ices.
The ope a ion o he heu is ic o de e mining bus
schedules depend on he ype o line, acco ding o he
de ini ion in he p elimina y analysis. The p ocedu e o
each ype o possible lines a e desc ibed:
• Type A: lines ha only need a single ehicle o all
se ices, he p ocess is as ollows:
- The only ehicle de ines hei se ices beginning
a he s a ime o se ice (h ). As in Figu e 2,
ou wa d jou neys a e de ined a (h + , h + 2 , h
+ 3 ,...) and e u n jou neys a (h + s, h + + s,
h + 2 + s,…) o mee he demand o minimum
se ice associa ed wi h each slo ime. When all
se ices in he ime slo ha e been pe o med,
he bus is wai ing o he nex se ice. The p ocess
con inues in his way un il he end o he day (hl).
• Type B: lines wi h wo o mo e ehicles o all
se ices, he p ocess is as ollows:
- Times a e de e mined o he i s ehicle in he
same way as in he ype A (Bus 1 in Figu e 5).
- Fo he second ehicle, he backwa d p ocess is
pe o med. De ined he ou es backwa ds om he
ime o he las a i al (hl - , hl - 2 , hl - 3 ,…) and
om he opposi e e minal (hl - s, hl - - s, hl - 2
- s,…), un il he s a o he day. (Bus 2 in Figu e 5).
Figu e 5. Type B.
- I i is necessa y a hi d ehicle, he e is
ein oduced o wa d, like he i s . (Bus 3 in Figu e
5). The depa u e ime o he i s se ice will be he
midpoin be ween he i s and he second ehicle
depa u e ime (hm). F om he e, we p oceed
iden i ying se ices un il he end o he day.
- The p ocess con inues in his way un il he
numbe o ehicles needed is comple ed.
• Type C: The si ua ion is mo e complex when a e
line g oups wi h wo o mo e ehicles, in which
is known amoun o ehicles, and a e sha ed he
se ices assigned o hem all. In such lines, he
heu is ic ope a es in a g eedy way, ollowing a
simila p ocedu e o he p e ious cases. This
p elimina y es ima ion abou ime schedules is
buil on he classi ica ion o lines made abo e.
Thus:
- Alloca e o each g oup enough buses as indica ed
by he in ege pa o bn.
- Alloca e hese bus schedules ollowing he same
pa e n han in ype A and B.
- Fo o he buses: i i is only a single, is conside ed
sha ed be ween all lines o he g oup. I hey a e m
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buses o be dis ibu ed in n lines o he g oup (wi h
m<n), ake he m lines wi h decimal pa uppe o
bn, and combine wi h emaining nm lines ying
han he sum o lines in all combina ions is as small
as possible.
- I he bus has o se e p lines, in each line is
p oceeded wi h he calcula ion
D/bn, o he mo ning and a e noon. These bus a el is
sequen ially alloca ed o bus lines based on ha calcula ion.
3.2.2. The d i e shi s planning
D i ing shi s a e cons uc ed aking in o accoun he b eak
imes, lunch imes i he e a e spli shi s, ime cons ain s
d i ing and he associa ed cos s. I allows mul i-shi wo ke
alloca ion along he lines, ha allowing a single wo ke is
alloca ed o di e en lines on he same day, depending on
he needs o he se ice and ying o op imize b eak imes.
Fo a line o g oup o lines wi h bn necessa y ehicles and
dn d i e s needed. Two possible cases may occu : Fi s , i n =
1, all he ime will be assigned o a single conduc o . Second,
i n>1, u he ul illing ha n = 2 · bn, we will ocus on his
case. Finally, i n> 1 and n> 2 · bn.
In he second case, each ehicle was ini ially alloca ed
wo d i e s, one a he opening and one a he end o he
day. The numbe o se ices n ha a e assigned a he
beginning (end) o he jou ney. Tha numbe can only be
such ha n · is be ween 35% and 65% o he numbe o
daily d i ing hou s. This will gi e x o al possible alues o .
A e (be o e) o make ha numbe o ips, he d i e can
enjoy a sho b eak (less han 1 hou ) o long b eak (no less
han 1 hou ), and a e (be o e) his b eak, he d i e may
ejoin o ei he bn ehicles o he line, pe o ming all ips
ha s ill ha e o do he bus.
To show he complexi y o he p oblem, o example,
a line o g oup o lines wi h 4 buses and 8 d i e s who
could make 2 o 3 ips ( wo possibili ies) be o e b eak, he
numbe o possibili ies be o e he b eak will be: VR (2,8) =
28 = 256, and he b eaks can be sho and long we will ha e
65,536 possibili ies (256 · 256). A e he b eak, we should
combine each d i e wi h each o he possibili ies o each
bus. Thus, he ou d i e s who s a ed he day could end
hei u n in each o he ou buses, esul ing V (4,4) = 24
a ian s. Likewise, each conduc o used o close he bus line,
can s a you day in each o he ou buses, aking ano he
24 possibili ies, and gi ing a o al o 37,748,736 a ian s
(65,536 · 24 · 24). This numbe would be inc eased by a
ac o ha depends on he numbe o possible a ia ions
caused by he long o sho b eak in each case.
In he e alua ion o each al e na i e, should be penalized
wi h plb hou s long b eak o e an hou , wi h px hou s ex a,
and wi h psb hou s o sho b eak o e 15 minu es, whe e: plb
< px < psb. The goal is o minimize he o al cos .
The p ocedu e o alloca ing d i e s o he se ices is
ca ied ou by g eedy heu is ic. Fo each g oup, he jou ney
o one o he nc d i e s needed is alloca ed o one o he
ini ial se ices in a line. A he end o ha se ice, is assigned
he new se ice ha is close o s a o he whole g oup
(which will usually be in he same line, howe e , his is no
necessa ily he case).
This is he p ocess un il you ha e co e ed 50% o hei
wo kday. I he e is a su icien gap be ween se ices o a
sho b eak, is assigned and he d i e con inues o alloca e
se ices o he end o hei jou ney. I he e is no space, he
alloca ion o he bus d i e s s op.
The ollowing d i e s a e also assigned o se ices, bu
his ime om back o on , assigning he las line se ices,
un il he momen o b eak. We p oceed in he same way
wi h all nc d i e s un il some o hem a e comple ed, and
o he s ha e co e ed only up o hei b eak, backwa ds o
o wa ds.
Then a e alloca ed he b eaks o d i e s, ini ially all sho ,
o y o maximize he numbe o consecu i e shi s and
assigning se ices con inues un il comple ely co e ed. I
he se ice ea lie han can be assigned o a d i e has an
excessi ely la ge slack a e he sho b eak, his is eplaced
by a long b eak and he alloca ion is con inued.
4. CASE STUDY
The p oblem consis s in he planning o a company ha
ope a es wen y lines in he me opoli an a ea o Se ille.
The lines ha e adial cha ac e , ope a ing om a e minal in
he ci y o Se ille and ano he loca ed in he me opoli an
a ea. Th ee di e en e minals in Se ille, wi h app oxima ely
equal numbe s in each line. The lines need wo planning
p ocesses pe yea (win e and summe ). A he beginning
o ou wo k, his p ocess was done manually o each o
he lines sepa a ely, using a sp eadshee . Au oma ing
he p ocess, a ached o he possibili y o combining lines
be ween ehicles and d i e s ha ha e he same e minal.
Thus, his wo k p esen s g ea oppo uni ies o inc eased
e iciency.
To conside opening up a desc ip ion o scena ios, when
his p ojec was applied in a eal company, his should
be done in a way o allow anonymi y, o his eason i is
applied only in a small a ic i ious example ha is shown in
his sec ion.
A case s udy desc ibes ypical adminis a i e issues o
p oblems con on ing a manage in an o ganiza ion. I is
usually p esen ed om he s andpoin o he decision make
in ol ed.

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Figu e 1. Me opoli an a ea o Se ille
Table 2. Minimum se ices and demand o a bus line.
Range S a
ime
End
ime
Demand
Te minal 1
(T1)
Demand
Te minal 2
(T2)
Min.
Se ice
T1
A e age
Time
T1→T2
A e age
Time
T2→T1
Min.
Se ice
T2
1 06:00 08:00 25 0 0 00:30 00:30 1
2 08:00 10:00 0 1 1 00:30 00:30 1
3 10:00 12:00 45 34 0 00:30 00:30 0
4 12:00 14:00 65 35 0 00:30 00:30 0
5 14:00 16:00 45 76 0 00:30 00:30 0
6 16:00 18:00 0 1 1 00:30 00:30 0
718:00 20:00 0 0 1 00:30 00:30 0
Table 3. Bus schedules (wi h only one bus).
S a End F om Fic i ious Range ansshipmen
e minal
1 06:00 06:30 T1 no 1 T1
2 06:30 07:00 T2 no 1 T1
3 08:00 08:30 T1 no 2 T1
4 08:30 09:00 T2 no 2 T1
5 10:00 10:30 T1 no 3 T1
6 10:30 11:00 T2 no 3 T1
712:00 12:30 T1 no 4 T1
8 12:30 13:00 T2 no 4 T1
9 13:00 13:30 T1 no 4 T1
10 14:00 14:30 T2 no 5 T1
11 14:30 15:00 T1 no 5 T1
12 15:00 15:30 T2 no 5 T1
13 16:00 16:30 T1 no 6 T1
14 16:30 17:00 T2 no 6 T1
15 18:00 18:30 T1 no 7T1
16 18:30 19:00 T2 yes 7T1
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In his case he se ice is planned o an example o bus
line. The de ini ion is pe o med in a heo e ically de ined
si ua ion wi h condi ions ha depend on he cha ac e is ics
o he day o he yea (weekday, weekend, holiday, aca ion,
e c.). The able 2 show he numbe o minimum se ice
gua an eed and he demand, when he i s ou pu is a 6.00
and he las a i al is a 19.00.
Wi h his demand and minimum se ices, ollowing he
me hodology desc ibed abo e, he depa u e imes o buses
ha a e needed a e cons uc ed, see Table 3.
The shi in a company depends on he condi ions:
• In he example 1, i he adminis a i e ime is 15
minu es, he b eak pe iod should be be ween he
hi d and he i h hou , he longi ude o his b eak
is 15 minu es, and he limi in he shi pe iod is
nine hou s and he maximum ime o build in a
spli shi is 45 minu es, he sys em builds his wo
shi ha appea s in Table 4, whe e one is a b oken
shi wi h 8.75 hou s, six as a d i e , 2.5 hou s as
a p esence, and 0.25 hou s as an adminis a i e
ime. And he sys em builds a sho shi (because
is a small example) wi h 3.25 hou s: 1.5 as a d i e ,
0.5 hou s o p ecep o d i e , 1 hou o p esence
ime and 15 minu es o adminis a i e ime.
• In he example 2, i he adminis a i e ime is 24
minu es, he b eak pe iod should be be ween he
second and he ou h hou , he longi ude o his
b eak is 27 minu es, and he limi in he shi pe iod
is eigh hou s and he maximum ime o build in a
spli shi is 78 minu es, he sys em builds his wo
shi ha appea in Table 4, whe e one is a comple e
shi wi h 7.4 hou s, 4 hou s o d i ing, 2.55 hou s
o p esence ime, and 0.4 hou s o adminis a i e
ime. And he sys em builds a second comple e
shi wi h 6.4 hou s: 3.5 as a d i e , 0.5 hou s o
Table 4. The d i e shi s planning.
Example 1 Example 2
Shi S a End Type F om Shi S a End Type F om
0 05:45:00 06:00:00 OTP - 0 05:36:00 06:00:00 OTP -
0 06:00:00 06:30:00 TDR T1 0 06:00:00 06:30:00 TDR T1
0 06:30:00 07:00:00 TDR T2 0 06:30:00 07:00:00 TDR T2
007:00:00 08:00:01 TP T1 0 07:00:00 08:00:01 TP -
0 08:00:01 08:30:01 TDR T1 0 08:00:01 08:30:01 TDR T1
0 08:30:01 09:00:01 TDR T2 0 08:30:01 09:00:01 TDR T2
0 09:00:01 10:00:01 SPLIT - 0 09:00:01 09:27:01 OBP -
0 10:00:01 10:30:01 TDR T1 0 09:27:01 10:00:01 TP -
0 10:30:01 11:00:01 TDR T2 0 10:00:01 10:30:01 TDR T1
0 11:00:01 12:00:01 TP - 0 10:30:01 11:00:01 TDR T2
0 12:00:01 12:30:01 TDR T1 0 11:00:01 12:00:01 TP -
0 12:30:01 13:00:01 TDR T2 0 12:00:01 12:30:01 TDR T1
0 13:00:01 13:30:01 TDR T1 0 12:30:01 13:00:01 TDR T2
0 13:30:01 14:00:01 TP - 1 13:00:01 13:30:01 TDR T1
0 14:00:01 14:30:01 TDR T2 1 13:30:01 14:00:01 TP -
0 14:30:01 15:00:01 TDR T1 1 14:00:01 14:30:01 TDR T2
0 15:00:01 15:30:01 TDR T2 1 14:30:01 15:00:01 TDR T1
1 16:00:01 16:30:01 TDR T1 1 15:00:01 15:30:01 TDR T2
1 16:30:01 17:00:01 TDR T2 1 15:30:01 15:57:01 OBP -
117:00:01 18:00:01 TP - 1 15:57:01 16:00:01 TP -
1 18:00:01 18:30:01 TDR T1 1 16:00:01 16:30:01 TDR T1
1 18:30:01 19:00:01 TDNR T2 1 16:30:01 17:00:01 TDR T2
1 19:00:01 19:15:01 OTP - 1 17:00:01 18:00:01 TP -
1 18:00:01 18:30:01 TDR T1
1 18:30:01 19:00:01 TDNR T2
1 19:00:01 19:24:01 OTP -
B azilian Jou nal o Ope a ions & P oduc ion Managemen
Volume 13, Núme o 3, 2016, pp. 400-407
DOI: 10.14488/BJOPM.2016. 13.n3.a16
407
p ecep o d i e , 1.55 hou s o p esence ime and
0.4 hou s o adminis a i e ime.
In p e ious esul s is shown as he ool you can each
di e en ypes o shi wo ke s: comple e shi , spli shi
o pa ial shi , depending on he cha ac e is ics o he
p oblem.
This is a small example, bu in he eal example he
sys em ope a es wen y lines o passenge anspo in he
me opoli an a ea o Se ille. The line has a adial cha ac e
wi h 3 e minals wi h equal numbe o lines in he ci y. In
gene al, i uses 2 planning p ocess pe yea , one in he win e
and one in he summe , his planning ha e di e en ype o
days, weekend, weekdays, holidays and o he special days.
The planning o hese was o iginally ca ied ou manually,
building ou es and shi s in an Excel sp eadshee , he mixing
ehicles and d i e s be ween di e en lines is allowed. The
nex sec ion explains he esul and conclusions.
5. RESULTS AND CONCLUSIONS
In his pape , we ha e p esen ed a simple algo i hm
o schedule wo k shi s om d i ing in a me opoli an
company wi h a small size o passenge anspo and bus
se ices. While i does no gua an ee he op imal solu ion,
i does allow he company o achie e a good solu ion in a
small space o ime, a oiding ha ing o eso o comme cial
op imiza ion so wa e packages o modelled complexes.
The applica ion o his me hodology o he Se ille
Company unde s udy allowed o achie e a educ ion o
12.5% in he numbe o buses equi ed o mee all he daily
se ices, 8% in he numbe o d i e s and 7.5% in he o al
cos o ope a ion. I is he e o e a ool e ec i ely, suscep ible
as well as being applicable in any company wi h simila
cha ac e is ics, in which he manual planning and lack o
alida ion o p ocedu es end o hide g ea oppo uni ies o
imp o ing e iciency and educing cos s.
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