Public transport crowdshipping: moving shipments among parcel lockers located at public transport stations

Wy owski, Alexande ; Boysen, Nils; B isko n, Di k; Schwe d ege , S e an
A icle — Published Ve sion
Public anspo c owdshipping: mo ing shipmen s among
pa cel locke s loca ed a public anspo s a ions
OR Spec um
P o ided in Coope a ion wi h:
Sp inge Na u e
Sugges ed Ci a ion: Wy owski, Alexande ; Boysen, Nils; B isko n, Di k; Schwe d ege , S e an
(2024) : Public anspo c owdshipping: mo ing shipmen s among pa cel locke s loca ed a public
anspo s a ions, OR Spec um, ISSN 1436-6304, Sp inge , Be lin, Heidelbe g, Vol. 46, Iss. 3, pp.
873-907,
h ps://doi.o g/10.1007/s00291-024-00748-0
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/313827
S anda d-Nu zungsbedingungen:
Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen
Zwecken und zum P i a geb auch gespeiche und kopie we den.
Sie dü en die Dokumen e nich ü ö en liche ode komme zielle
Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich
machen, e eiben ode ande wei ig nu zen.
So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen
(insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en,
gel en abweichend on diesen Nu zungsbedingungen die in de do
genann en Lizenz gewäh en Nu zungs ech e.
Te ms o use:
Documen s in EconS o may be sa ed and copied o you pe sonal
and schola ly pu poses.
You a e no o copy documen s o public o comme cial pu poses, o
exhibi he documen s publicly, o make hem publicly a ailable on he
in e ne , o o dis ibu e o o he wise use he documen s in public.
I he documen s ha e been made a ailable unde an Open Con en
Licence (especially C ea i e Commons Licences), you may exe cise
u he usage igh s as speci ied in he indica ed licence.
h p://c ea i ecommons.o g/licenses/by/4.0/
Vol.:(0123456789)
OR Spec um (2024) 46:873–907
h ps://doi.o g/10.1007/s00291-024-00748-0
1 3
ORIGINAL ARTICLE
Public anspo c owdshipping: mo ing shipmen s
amongpa cel locke s loca ed a public anspo s a ions
Alexande Wy owski1· NilsBoysen1 · Di kB isko n2· S e anSchwe d ege 3
Recei ed: 2 Janua y 2023 / Accep ed: 12 Janua y 2024 / Published online: 25 Feb ua y 2024
© The Au ho (s) 2024
Abs ac
In iew o success s o ies o unico n s a ups om he sha ing and gig economy
such as Ai bnb, DiDi, o Ube , i is no su p ising ha pos al se ice p o ide s y
o ans e he sha ing idea owa d hei las -mile deli e y se ices: owne s o unde -
used asse s (he e p i a e c owdshippe s a eling anyway) a e connec ed wi h use s
willing o pay o he use o hese asse s (he e pos al se ice p o ide s ha ing o
deli e pa cels). In his pape , we conside a special o m o c owdshipping whe e
public anspo use s, s ee ed by a sma phone app, pick up pa cels om pa cel
locke s, ake hese shipmen s wi h hem on hei subway ides, and deposi hese
pa cels in o o he locke s. Finally, he ac ual ecipien s can pick up hei shipmen s
om hei mos con enien pa cel locke s, e.g., on hei own way back home om
wo k. We o mula e he op imiza ion p oblem ha ma ches c owdshipping demand
and supply and de e mines he ou es along locke s and c owdshippe s each pa -
cel akes. Speci ically, we allow ha each pa cel is mo ed by mul iple coope a ing
c owdshippe s and sol e his p oblem wi h di e en objec i e unc ions cap u ing
he indi idual aims o he main s akeholde s: shippe s, c owdshippe s, ecipien s,
and he pla o m p o ide . We e alua e he ela ionship o hese objec i es and quan-
i y he e iciency loss o a mo e es ic ed ma ching policy, whe e only a single
c owdshippe can be assigned o each pa cel’s comple e pa h be ween o igin and
des ina ion. Finally, we also explo e he impac o delays and in es iga e whe he
speci ic objec i es p o ec agains un o eseen e en s.
Keywo ds T anspo a ion· U ban logis ics· C owdshipping· Public anspo
1 In oduc ion
C owdshipping, de ined as he applica ion o indi iduals o deli e y o o he peo-
ples’ shipmen s on ips hey would make anyway (Beh end and Meisel 2018), has
ecei ed much a en ion in he ecen yea s. This is mainly igge ed by he ollow-
ing gene al ends:
Ex ended au ho in o ma ion a ailable on he las page o he a icle
874
A.Wy owski e al.
1 3
(i) Inc easing pa cel olumes: In Ge many, o ins ance, a s udy p edic s ha by
2024 5.1 bn shipmen s will need o be p ocessed pe yea compa ed o 2.47
bn in 2011 (S a is a 2022). Managing his sha p inc ease wi h he adi ional
cou ie se ice in as uc u e seems ba ely possible, especially in he aging
socie ies o many de eloped coun ies. The e o e, many pos al se ice p o id-
e s a e on he lookou o no el o ms o las -mile deli e y.
(ii) Gig economy: La ge sha ing pla o ms like Ube , Ly , and Ai BnB enjoy
inc easing popula i y. In Eu ope, he sha ing economy is es ima ed o ha e
gene a ed a o al sales olume o €28 bn in 2015 (Vaughan and Da e io 2016).
A sha ing pla o m connec s owne s o unde -used asse s, such as ca s, spa e
oom, o pa king spaces, wi h use s willing o pay o he use o hese asse s.
Na u ally, unused anspo capaci y is also a po en ial asse o be sha ed.
(iii) Ecological awa eness: Road anspo is among he mos se ious emis-
sion sou ces. I is es ima ed o con ibu e a 20% sha e o all CO
2
-emissions
(Sch o en e al. 2012). Ob iously, u ilizing unused anspo capaci y on ips
made anyway is a simple means o educe a ic olume and hus emissions.
Gi en hese ends, c owdshipping is he a emp o e aile s (e.g., Amazon Flex o
Walma ), logis ics companies (e.g., DHL), and specialized online pla o ms o e -
ing a ma ching o supply and demand as a se ice (e.g., Ube F eigh o pos ma es.
com) o ans e he basic idea o he sha ing economy o anspo se ices, espe-
cially on he las mile. In his con ex , his pape ea s a speci ic o m o c owdship-
ping, which we call public anspo c owdshipping.
On he demand side o public anspo c owdshipping, we ha e shipmen s, e.g.,
pa cels wi h goods o de ed online, which ha e o be anspo ed owa d sui able pa -
cel locke s. We assume ha hese locke s a e loca ed di ec ly in he access pa hs o
public anspo , so ha ecipien s can con enien ly ecei e hei shipmen s, e.g., on
hei way back home a e wo k. Ini ially, he shipmen s o be anspo ed a e placed
in o he pa cel locke s close o hei o igins. Fo ins ance, a small b ick-and-mo -
a s o e also unning an online sales channel can place an online o de in a pa cel
locke close o he s o e and can announce hei anspo demand on he c owdship-
ping pla o m. Al e na i ely, he pla o m o ganize could also o e he se ice o
pick up la ge shipmen olumes, e.g., a a dis ibu ion cen e o a e ail chain, and
place he pa cels in o well- equen ed locke s whe e many po en ial c owdshippe s
pass by. On he supply side, public anspo use s can egis e on he cen al c owd-
shipping pla o m and announce hei a el beha io , e.g., hei daily commu e o
and om wo k ia he me o sys em, in a sma phone app.
Once a su icien numbe o po en ial c owdshippe s is collec ed, he pla o m
ma ches supply and demand, e.g., wi h he help o he solu ion p ocedu es p o ided
in his pape , and announces anspo eques s on o he sma phones o selec ed
c owdshippe s. Such a eques ad ises a c owdshippe ia he sma phone o pick up
a shipmen a a speci ic pa cel locke and also con ains he access code o open he
espec i e locke compa men . The c owdshippe can acc edi he pickup by scan-
ning a ba code on he pa cel ia he sma phone app, which is also he signal ha
he espec i e locke compa men is a ailable again. Then, he c owdshippe s ake
he pa cels wi h hem on hei public anspo ides. Once a i ed, hey place he
875
1 3
Public anspo c owdshipping: mo ing shipmen s amongpa cel…
pa cels in o o he pa cel locke s ad ised by he app and acc edi he deposi by scan-
ning he ba codes o pa cels and locke compa men s. These locke s can ei he be
he pa cels’ inal des ina ions whe e hey a e picked up by he pa cels’ ac ual ecipi-
en s, o hey a e jus in e media e locke s whe e he pa cels wai o o he c owd-
shippe s o be mo ed onwa d.
The big ad an age o public anspo c owdshipping is i s sus ainabili y. Com-
pa ed o oad anspo a ion, ains a e eco- iendly means o anspo a ion
(Sch o en e al. 2012) and, since public anspo use s make hei ips anyway,
his o m o pa cel deli e y does no p oduce any addi ional a ic. Thus, especially
en i onmen ally awa e a ele s ge in insically mo i a ed and may eques no high
mone a y compensa ion o hei c owdshipping se ices, so ha public anspo
c owdshipping can also become a low-cos pa cel deli e y mode. Long- e m in es
is only equi ed o he de elopmen o he sma phone app, he se up o he IT
in as uc u e, and he pa cel locke s o be posi ioned in s a ions o public anspo .
On he nega i e side, many c owdshipping pla o ms s uggle wi h p o iding secu e,
scalable, and eliable anspo se ices (Le e al. 2019). They depend on he ola ile
pa icipa ion o c owdshippe s, which a ies om day o day and is ha d o o ecas .
Ways o ake on his challenge a e, o ins ance, discussed by Sa elsbe gh and Ulme
(2022).
The basic idea o public anspo c owdshipping is o mula ed in di e en publi-
ca ions, e.g., (Ga a e al. 2019a, b; Zhang e al. 2017), and companies such as Ama-
zon (Pa celHe o 2016) and His Sys em Co. (2019) ha e announced hei in en ions
o es ablish a ne wo k o pa cel locke s in public anspo s a ions. Howe e , he ( o
he bes o he au ho s’ knowledge) only company ha es ablished pa s o he pub-
lic anspo c owdshipping concep is he F ench pla o m Ch onobee. Public ans-
po use s can egis e on he Ch onobee pla o m (h ps:// app. ch on obee. com/) wi h
hei daily commu e and a e ma ched o anspo eques s also announced on he
pla o m. Howe e , pa cel pickup and deli e y a e no o ganized ia pa cel locke s
(bu ia di ec in e ac ion) and he e is no op ion o mul iple c owdshippe s sha ing
he anspo o a single pa cel.
In his pape , we in es iga e he basic op imiza ion p oblem o public anspo
c owdshipping and p o ide sui able solu ion me hods o ma ch c owdshipping sup-
ply and demand. The ma ching ask also includes he planning o each pa cel’s ou e
h ough he public anspo a ion ne wo k and i s u iliza ion o di e en pa cel lock-
e s as well as c owdshippe s un il inally eaching he des ina ion locke in ime.
Speci ically, we o mula e six al e na i e objec i e unc ions ha conside he aims
o di e en s akeholde s. While he c owdshipping pla o m aims o maximize hei
p o i consis ing o pos al cha ges o each deli e ed pa cel minus c owdshipping
ees, c owdshippe s a he ocus on hei own c owdshipping ees. The cus ome s
o pa cel deli e y se ices, ins ead, p e e eliable se ices and wan o a oid ha
pa cel hando e s be ween c owdshippe s a e missed in case o ain delays. We
o mula e ou public anspo c owdshipping p oblem and p o ide compu a ional
complexi y esul s o all p oblem e sions. Fu he mo e, we p o ide a heu is ic
decomposi ion app oach ha is easily adap able o sol e all p oblem e sions. This
allows us o in es iga e he ela ionship o he s akeholde s’ objec i es. Fu he mo e,
we compa e ou coope a i e c owdshipping policy ha allows mul iple subsequen
876
A.Wy owski e al.
1 3
c owdshippe s o join ly anspo a pa cel om o igin o des ina ion wi h a mo e
es ic i e policy ha excludes c owdshippe coope a ion. Finally, we also in es i-
ga e he impac o ain delays and explo e which o ou objec i es p oduces obus
plans whe e only a ew pa cels miss hei ecipien s.
Thus, ou pape makes he ollowing con ibu ions o he li e a u e: (a) We de ail
he ope a ional p ocesses and he basic ma ching ask o a no el o m o c owdship-
ping: public anspo c owdshipping. (b) We p o ide sui able solu ion me hods o
he basic ma ching ask wi h six di e en objec i es o co e he aims o all main
s akeholde s. (c) We apply ou solu ion me hods in a comp ehensi e compu a ional
s udy in o de o iden i y c i ical success ac o s. He e, we show ha a la ge c owd-
shippe base o olun ee ing public anspo use s mus be ec ui ed, explo e he
di e en aims o he main s akeholde s, in es iga e how o p o ec agains s anded
pa cels due o un o eseen ain delays, and e alua e he gains o coope a i e ans-
po whe e pa cels ake mul iple legs wi h di e en c owdshippe s owa d hei des-
ina ion locke s.
The emainde o he pape is s uc u ed as ollows. Sec ion2 e iews he ela ed
li e a u e. Sec ion3 de ines ou public anspo c owdshipping p oblem wi h i s six
al e na i e objec i es and explo es compu a ional complexi y. In Sec .4, we p o-
ide he basic model o mula ion and epo on necessa y adap ions when dealing
wi h he di e en objec i es. Ou heu is ic decomposi ion app oach is in oduced in
Sec .5. Insigh s in o he compu a ional pe o mance and manage ial issues a e p o-
ided in Sec .6 and7, espec i ely. Finally, Sec .8 concludes he pape .
2 Li e a u e e iew
The sha ing and gig economy in gene al and c owdshipping in pa icula ha e
a ac ed a lo o esea ch in he ecen yea s. Thus, we e e he eade o he ollow-
ing in-dep h su ey pape s: Dablanc e al. (2017) (on-demand deli e ies), Le e al.
(2019) as well as Sa elsbe gh and Ulme (2022) (c owdshipping), Boysen e  al.
(2019) (ma ching o supply and demand in he sha ing indus y), and Boysen e al.
(2021) (las -mile deli e y). Fo an o e iew on di e en c owdshipping applica-
ions, ou own li e a u e e iew, i s , elabo a es on he di e en use g oups ha a e
a ge ed as po en ial c owdshippe s:
(i) Hi ed d i e s: Some c owdshipping pla o ms hi e independen d i e s,
who a e hou ly paid, con ibu e hei own ehicle, and sign up in ad ance o p e-
ixed ime-slo s. These pla o ms a e ei he di ec ly ope a ed by la ge e aile s like
Amazon (wi h hei Amazon Flex se ice) o by hi d-pa y companies o e ing a
ma ching o supply and demand as a se ice (e.g., Ube F eigh o pos ma es.com).
Op imiza ion app oaches ma ching c owdshipping supply and demand as well as
planning deli e y ou es a e, o ins ance, p o ided by A che i e al. (2016) and
A slan e al. (2018). The main disad an age o his o m o c owdshipping is ha
pa cel deli e y is no p ocessed on ips made anyway. Ins ead, ex a a ic is gene -
a ed and, om an en i onmen al pe spec i e, no hing is gained compa ed o adi-
ional deli e y modes.

877
1 3
Public anspo c owdshipping: mo ing shipmen s amongpa cel…
(ii) Occasional d i e s: This disad an age is a oided, i pickup and deli e y
eques s o cus ome s a e p ope ly in eg a ed in o exis ing ips, e.g., o p i a e d i -
e s wi h hei own ca s ha ing some lexibili y ega ding he iming o hei egula
(independen ly planned) jou neys (Zeh abian e al. 2022) o axis o e ing addi ional
eigh se ices (Li e al. 2014).
(iii) In-s o e cus ome s: A ac ing a su icien ly la ge ex e nal d i e base can
p oduce a lo o e o (Le e al. 2019). Hence, i can be ad an ageous i speci ic
g oups o people, e.g., cus ome s o la ge e ail ou le s, can di ec ly be o e ed
c owdshipping pa icipa ion, e.g., o he pu chases o hei neighbo s. Applica ions
a e epo ed o e ail chain Walma (Daya ian and Sa elsbe gh 2020), and op imi-
za ion app oaches a e, o ins ance, p o ided by Gdowska e al. (2018).
(i ) Employees: La ge b ick-and-mo a e ail ou le s o dis ibu ion cen e s o
online e aile s employ hund eds o wo ke s, who can inc ease hei ea nings by
c owdshipping online o de s o neighbo s on hei way back home om wo k. Tes
uns a e epo ed o Walma , and decision suppo ma ching pa cels and employ-
ees is p o ided by Boysen e al. (2022).
( ) Ai passenge s: To exploi p ice di e ences be ween di e en coun ies and
sa e on ai mail eigh a i s, c owdshipping pla o ms such as piggybee.com
b oke c owdshipping ai passenge s wi h ee luggage space.
( i) Public anspo use s: In his pape , we conside public anspo use s as
po en ial c owdshippe s. The li e a u e in his speci ic a ea o c owdshipping is sum-
ma ized in mo e de ail in he ollowing.
The main ac o s in luencing he willingness o pa icipa e in public anspo
c owdshipping a e in es iga ed in (Ga a e al. 2019a, b). They epo on a su ey
om Rome (I aly) and s a e ha abou 50% o he ques ioned me o use s a e willing
o pa icipa e. A b ie e iew on u he empi ical s udies on c owdshipping pa ici-
pa ion is p o ided by Punel e al. (2019). In he ollowing, we only ocus on ope a-
ions esea ch con ibu ions.
A combina ion o deli e y by adi ional deli e y ans and public anspo is
conside ed by (Ghilas e al. 2016b, a, c, 2018). He e, company-owned deli e y ans
coope a e wi h public anspo ope a ing on ixed ime ables. Shipmen s can be
handed o e and, a e anspo , ecei ed om public anspo , which ac s as an
addi ional in e media e anspo op ion. A p oblem de ini ion and a i s MIP is p e-
sen ed by Ghilas e al. (2016b). The same p oblem is ackled by Ghilas e al. (2016a)
and Ghilas e al. (2018) wi h adap i e la ge neighbo hood sea ch and b anch-and-
p ice, espec i ely. A s ochas ic p oblem e sion is ea ed by Ghilas e al. (2016c).
A simila p oblem se ing o al e na i e ehicles, i.e., ca go bikes and buses, is
in es iga ed by Masson e al. (2017); Azcuy e al. (2021) as well as Schmid e al.
(2022). Kou e al. (2022) in es iga e he peculia i ies o combining deli e y ans
and public anspo in a u al se ing. In ou p oblem se ing, we ha e no deli e y
ans (o ca go bikes), and we decouple he hando e p ocess by pa cel locke s. Two
c owdshippe s coope a ing in he anspo o a speci ic pa cel need o subsequen ly
access he locke , bu no a he same ime. This leads o a comple ely di e en p ob-
lem s uc u e.
C owdshipping be ween di e en pa cel locke s is also conside ed by Chen
e al. (2017) and Chen e al. (2016). They, howe e , conside axis and no public
878
A.Wy owski e al.
1 3
anspo use s as po en ial c owdshippe s. This equi es an addi ional coo dina ion
o pa cel deli e y wi h people anspo and lea es mo e lexibili y, because axis a e
no bound o ixed ime ables. Fu he mo e, c owdshipping be ween pa cel locke s
wi hou any ime cons ain s is conside ed by Wang e al. (2016) and Zhang e al.
(2017). Finally, Kızıl and Yıldız (2022) conside he p oblem o decide he loca-
ion o pa cel locke s, ha is o choose he s a ions whe e pa cel locke s a e o be
ins alled, and e alua e solu ions, including backup se ices wi h ze o-emission ehi-
cles o pa cels ha a e no c owdshipped, using a scena io-based app oach. The
p oblem is o mula ed as a wo-s age s ochas ic p og am and sol ed by a b anch-
and-p ice app oach.
The exis ing c owdshipping li e a u e also includes ansshipmen nodes in o
ope a ional ou ing and assignmen p oblems (e.g., Mac ina e  al. 2020; Vincen
e al. 2022). These nodes add lexibili y whe e shipmen s, deli e ed by company
owned ehicles, a e inally picked up by he c owdshippe s. In ou p oblem se ing,
he o igin posi ion a he i s pa cel locke is ixed o each shipmen . Ins ead, we
allow ha mul iple c owdshippe s can pa icipa e in deli e ing shipmen s o hei
des ina ions by handing he pa cel o e a in e media e locke s. This ansshipmen
op ion a he ela es ou p oblem se ing o mul i-hop idesha ing (e.g., Masoud and
Jayak ishnan 2017; Wang e al. 2023), whe e passenge s can hi ch mul iple sub-
sequen ides o inally each hei des ina ions. In his domain, howe e , ehicles
(c owdshippe s) ypically do no ope a e on p ede ined ou es wi hou any ime lex-
ibili y and ha e a capaci y o mo e han one passenge (pa cel).
I can be concluded ha he c owdshipping li e a u e p o ides no sui able op i-
miza ion p ocedu es whe e public anspo use s wi h known a el beha io a e
coo dina ed o c owdship o he peoples’ pa cels be ween pa cel locke s.
Finally, he e a e o he op imiza ion p oblems om o he domains ha sha e
some impo an s uc u al simila i ies wi h ou op imiza ions p oblem o public
anspo c owdshipping. Howe e , we come back o hese simila i ies a e ha ing
de ined his p oblem in he ollowing sec ion.
3 P oblem de ini ion
The c i ical elemen o any c owdshipping solu ion is a cen al IT pla o m ha
ma ches supply and demand. This also holds ue o ou speci ic c owdshipping
applica ion, whe e public anspo use s pick up and deli e pa cels among pa cel
locke s loca ed in s a ions
s∈S
wi h gi en locke capaci y
Ls
o s o ing shipmen s
in locke compa men s.
(i) On he demand side, we ha e a se J o pa cels. Beginning om elease da e
j
, pa cel
j∈J
is a ailable a he pa cel locke a o igin s a ion
𝛼j
. To deli e
a pa cel success ully, i needs o a i e a he pa cel locke a des ina ion s a-
ion
𝜔j
no la e han deadline
dj
, which is he poin o ime when he pa cel’s
ac ual ecipien passes he locke s a s a ion
𝜔j
, e.g., on he way back home
om wo k. I pa cel
j∈J
is success ully deli e ed, he pla o m ecei es a
pos al cha ge
pj
. I a pa cel canno be o wa ded o i s des ina ion on ime, i
879
1 3
Public anspo c owdshipping: mo ing shipmen s amongpa cel…
canno be accep ed o c owdshipping se ices and he pla o m ecei es no
pos al cha ge.
(ii) On he supply side, we ha e a se I o public anspo use s who ha e egis-
e ed a he c owdshipping pla o m and a e willing o pa icipa e in pa cel
deli e y; we call hem c owdshippe s. Each c owdshippe
i∈I
is associa ed
wi h a ime-s amped pa h de ining i’s mo emen h ough he public anspo -
a ion ne wo k. Speci ically, he ime-s amped pa h is gi en as a sequence o
uples each e e ing o a depa u e ime a a speci ic s a ion. We p esuppose
ha only hose s a ion isi s a e added o he ime-s amped pa h, whe e he
espec i e c owdshippe has enough ime o pickup and/o deposi a pa cel
a a pa cel locke . Hence, we do no explici ly conside a speci ic pickup
and deposi du a ion. Fu he mo e, we only conside hose s a ions whe e a
pa cel locke is loca ed and whe e a pa cel is o be picked up o deli e ed o
(o a leas one o he c owdshippe can access he locke ). When a e sing a
a el leg be ween wo subsequen s a ions acco ding o a ime-s amped pa h,
a c owdshippe has a capaci y o ca y a mos one pa cel.
We e e o he join a el o a c owdshippe i and a pa cel j s a ing wi h i pick-
ing j up a s a ion
s∈S
, mo ing om s o ano he s a ion
s�∈S
, and inally
deposi ing j a s a ion
s′
as an en ainmen . Fo each en ainmen , an en ainmen
ee is paid o he c owdshippe by he pla o m. Fo a s a ion s and a poin in
ime a c owdshippe passes h ough s, we say ha
ns,
is he numbe o pa cels
s o ed in he locke s a s immedia ely a e . This numbe
ns,
is composed o (i)
pa cels ha o igina e om s a ion s and ha e no been picked up ye a , o (ii)
pa cels ha ha e been in e media ely deposi ed in s un il , bu ha e no been
picked ye , and o (iii) pa cels wi h deli e y s a ion s ha ha e al eady eached
hei des ina ion un il and ha e no been picked up by he ecipien ye since
ds>
.
A pa cel is mo ed om i s o igin o i s des ina ion s a ion no necessa ily by a
single en ainmen . Ins ead, a solu ion o ou c owdshipping p oblem is a sequence
𝜎j
o en ainmen s assigned o each pa cel
j∈J
. An emp y sequence
𝜎j
e lec s ha
pa cel j is no deli e ed a all. We say a solu ion is deli e y- easible, i o each pa -
cel
j∈J
wi h non-emp y sequence (a) he i s en ainmen s a s a s a ion
𝛼j
and
does no s a be o e elease da e
j
, (b) each o he en ainmen s a s a he s a ion
whe e he p e ious en ainmen ended and does so no be o e he end ime o he
p e ious en ainmen , and (c) he las en ainmen ends a s a ion
𝜔j
and does no
end a e deadline
dj
.
Fu he mo e, we say a solu ion is capaci y- easible, i (i) he c owdshippe s’
capaci y is no exceeded. This means ha o each c owdshippe i and each s a ion s
on he pa h he e is a mos one en ainmen in ol ing i ha s a s a s o a p e ious
s a ion on he pa h and ends a a s a ion ha is eached a e s. Fu he mo e (ii), he
pa cel locke s’ capaci ies a e no exceeded. Tha is o each s a ion s and each poin
in ime whe e a c owdshippe passes h ough s, he e a e a mos
Ls
pa cels in he
locke and we ha e
ns, ≤Ls
.
Finally, we say a solu ion is easible, i i is bo h deli e y- easible and capac-
i y- easible. Since we ha e di e en in ol ed s akeholde s, i.e., c owdshippe s,
880
A.Wy owski e al.
1 3
ecipien s, and he pla o m p o ide , he e may be di e en iews on wha is a good
solu ion among he easible ones. We conside six p oblem e sions in he ollowing:
(1) MAX-PROFIT: The p oblem is o ind a easible solu ion maximizing p o i . The
p o i associa ed wi h a easible solu ion is he o al pos al cha ge o success ully
deli e ed pa cels (i.e., hose wi h non-emp y sequences o en ainmen s) minus
he en ainmen ees o he c owdshippe s (i.e., he o al numbe o en ainmen s
mul iplied by ee ). This objec i e mi o s he aim o a c owdshipping pla o m
maximizing i s own p o i .
(2) MAX-PARCELS: The p oblem is o ind a easible solu ion wi h a p o i o a
leas a gi en h eshold P ha maximizes he numbe o deli e ed pa cels. This
objec i e aims o maximize he numbe o sa is ied cus ome s while g an ing
he pla o m a minimum p o i .
(3) MAX-INVOLVEMENT: The p oblem is o ind a easible solu ion wi h a p o i
o a leas a gi en h eshold P ha maximizes he numbe o c owdshippe s wi h
a leas one en ainmen . This objec i e aims o engage a maximum numbe o
c owdshippe s, while g an ing he pla o m a minimum p o i P.
(4) MIN-TOTAL-ENTRAINMENTS: The p oblem is o ind a easible solu ion wi h a
p o i o a leas a gi en h eshold P ha minimizes he o al numbe o en ain-
men s o e all pa cels. Since each en ainmen in ol es a ailu e isk, e.g., a
pa cel missing i s subsequen en ainmen due o a delayed ain, his objec i e
educes he isk o s anded pa cels. This is some hing bo h he pla o m and he
ecipien s p e e o a oid.
(5) MIN-MAX-ENTRAINMENTS: The p oblem is o ind a easible solu ion wi h
a p o i o a leas a gi en h eshold P ha minimizes he maximum leng h o
en ainmen sequences among all pa cels. A pa cel is only success ully deli e ed
owa d i s des ina ion, i all i s en ainmen s a e success ully comple ed. Thus,
educing he numbe o en ainmen s pe pa cel should p omo e he numbe o
success ul deli e ies by p o ec ing agains unce ain y. An ob ious disad an age
o his objec i e is ha in he wo s case a single shipmen wi h a la ge numbe
o ine i able en ainmen s emo es he op imiza ion p essu e om all o he
shipmen s. I will be pa o ou compu a ional s udy in Sec .7.3 o explo e how
se e ely his de e io a ing e ec impac s a e age esul s.
(6) MAX-MIN-SLACK: Fo each success ully deli e ed pa cel
j∈J
, we conside
he minimum slack ime a
𝜔j
and a each s a ion j whe e i is picked up by a
c owdshippe (including
𝛼j
). The slack ime o pa cel j a each such s a ion s is
he ime i spends he e in he locke be ween deli e y and pickup. Fo he sake
o con enience, we say ha o each o he pai o pa cel j and hose s a ions
whe e j is no handled he slack ime is in ini e, so ha hey do no in luence he
minimum slack ime. The p oblem is o ind a easible solu ion, which maximizes
he minimum slack ime among all pai s o pa cels and s a ions while g an ing a
leas a minimum p o i o P o he pla o m. Slack ime p o ec s agains delays o
ans and c owdshippe s, and he la ge he slack, he mo e delay o en ainmen s
is accep able wi hou leading o s anded pa cels. No e ha in he ield o obus
op imiza ion adding slack (bu e ) ime is one p ominen app oach o achie e
solu ion- obus ness (e.g., see B isko n e al. 2011; Kou elis and Yu 1996). Fu -
887
1 3
Public anspo c owdshipping: mo ing shipmen s amongpa cel…
Objec i e unc ion (1) de ines he aim o he pla o m p o ide , which is he maxi-
miza ion o he o al p o i consis ing o he sum o pos al cha ges o all success-
ully deli e ed pa cels minus he o al en ainmen ees o be paid o he c owdship-
pe s. No e ha o gi en x- a iables
yi,s
ge s assigned he smalles easible alue in
op imum solu ions due o (1). Cons ain s (2) en o ce he capaci y o (a mos ) a
single pa cel pe a el leg o each c owdshippe . Only a single c owdshippe can
mo e a pa cel j om a speci ic s a ion s due o (3). Na u ally, his can be c owd-
shippe
i∈I
, i and only i pa cel j is an elemen o
Ji,s
, which con ains all pa cels
ha can be mo ed om s a ion s by i. Cons ain s (4) gua an ee ha each pa cel j
mo ed o a s a ion s will be ca ied u he unless
𝜔j=s
, ha is i s is i s des ina-
ion. No e ha
i
∈I
+
i,s
and, hence, (4) co e s he case whe e a pa cel a els h ough
s wi hou being pu in a locke . No e, u he mo e, ha (4) implies ha a sequence
o en ainmen s can only end a a pa cel’s des ina ion. No e, inally, ha (4) oge he
wi h (3) implies ha pa cels canno a el in ci cles and, hence, each pa cel ha
is picked up a all ge s assigned a sequence o en ainmen s ending a he pa cel’s
des ina ion. Cons ain s (5), hen, ensu es ha such a pa cel is anspo ed om i s
o igin. Viola ions o locke s’ capaci ies a e p e en ed by cons ain s (6). The le
side e lec s
n
s,
i,s
, ha is he numbe o pa cels in he locke s a s immedia ely a e
c owdshippe i has le s. The i s sum coun s he pa cels which s a a s (
𝛼j=s
)
and ha e been pu in o a locke un il
i,s
(
i,s≥ j
). The second sum coun s he pa cels
which do nei he s a no end a s (
𝜔j≠s
) and ha e been anspo ed o s un il
i,s
(
i�∈I−
i,s∩I�
s
). The hi d sum coun s he pa cels which end a s (
𝜔j=s
), a i ed a
s un il
i,s
(
i�∈I−
i,s∩I�
s
), and ha e no been aken ou o he locke by he ecipien s
un il
i,s
(
dj≥ i,s
). Finally, he ou h sum coun s he pa cels ha ha e been ans-
po ed om s un il immedia ely a e
i,s
. No e ha a pa cel which a els h ough s
wi hou e e being pu in o a locke a s ne e con ibu es o he capaci y load. Con-
s ain s (7) and (8) en o ce ha
yi,s≥1
i j is picked up by i a s and s is no i’s i s
s a ion and s is i’s i s s a ion, espec i ely. No e ha in his case we ob ain
yi,s=1
in op imum solu ions, since
yi,s
will ge assigned a alue as small as easibly possi-
ble due o he objec i e unc ion. Finally, (9) and (10) de ine he a iables’ domains.
I nei he (7) no (8) en o ce
yi,s≥1
, hen we ob ain
yi,s=0
in op imum solu ions,
again, due o he objec i e unc ion.
No e ha i is no en o ced ha he sequence o en ainmen s ac ually s a s a he
pa cel’s o igin. We can, howe e , cu all en ainmen s leading o he pa cel’s o igin
wi hou dec easing he objec i e alue o losing easibili y. We sugges o add Con-
s ain s (11) and (12) o MAX-PROFIT-MIP o es ic he solu ion space.
(10)
y
i,s
≥0∀i∈I;s∈S
�
i
(11)
∑
i
∈I�
𝛼j
∶j∈Ji,s−
i,𝛼
j
xi,s−
i,𝛼j,j≤0∀j∈J

888
A.Wy owski e al.
1 3
Cons ain s (11) cu solu ions whe e he sequence o en ainmen s does no s a a
he pa cel’s o igin. Cons ain s (12) do no cu any solu ions bu make i explici
ha a sequence o en ainmen s mus end a a pa cel’s des ina ion. P elimina y
compu a ional es ha e shown ha hese ex ensions lead o a speed up o s anda d
sol e Gu obi, so ha all compu a ional es s epo ed in Sec .6 include hese alid
inequali ies.
Gi en ou basic model MAX-PROFIT-MIP, he adap ions in o de o co e ou
i e al e na i e objec i es a e uly s aigh o wa d. While MAX-PROFIT di ec ly
aims o maximize he p o i , he o he p oblems a he ha e a minimum pla o m
p o i P ha mus be ensu ed by addi ional cons ain
(12)
∑
i
∈I�
𝜔
j
∶j∈Ji,𝜔j
xi,𝜔j,j≤0∀j∈
J
Table 2 Addi ional no a ion o o he objec i es
Mla ge alue (BigM)
Pminimum pla o m p o i
Fi
bina y a iables: 1, i c owdshippe
i∈I
mo es any pa cel
j∈J
; 0, o he wise
Fe
con inuous a iable: maximum numbe o en ainmen s among all c owdshippe s
Fs
con inuous a iable: minimum slack among all c owdshippe s
zi,j
bina y a iables: 1, i c owdshippe
i∈I
mo es pa cel
j∈J
; 0, o he wise
Table 3 Ex ended MIP o mula ions o he emaining objec i es
P oblem Objec i e and new cons ain s in addi ion o (2)-(13)
MAX-PARCELS Maximize
∑
j∈J
∑
i∈I1
j
xi,𝛼j,
j
MAX-INVOLVE-
MENT
Maximize
∑i∈I
F
i
∑
s∈S�
i∑
j∈J
i
,
s
xi,s,j≥F
i
∀i∈I
Fi∈[0, 1]
∀i∈I
MIN-TOTAL-
ENTRAINMENTS
Minimize
∑
i
∈
I
∑
s
∈
S�
i
yi,
s
MIN-MAX-
ENTRAINMENTS
Minimize
Fe
∑s∈S
z
s,j
≤F
e
∀j∈J
x
i,s,j
−x
i,s
−
i,s
,j
≤z
s,
j
∀
i∈I,s∈S
�
i
zs
,
j≥0
∀j∈J;s∈S
MAX-MIN-SLACK Maximize
Fs
(2−x
i,s,j
−x
i�,s+
i,s
,j
)
⋅
M+(
i�,s+
i,s
−
i,s+
i,s
)≥Fs
∀i≠i�∈I;s∈S�
i
;
s
+
i,s
∈S�
i�
;j∈J
i,s
∩J
i�,s+
i
,
s
(1−x
i,𝛼
j
,j
)
⋅
M+(
i,𝛼
j−
j
)≥Fs
∀i∈I;s∈S�
i;j∈Ji
,
s;s=
𝛼
j
(1−x
i,s,j
)
⋅
M+(d
j
−
i,𝜔
j)≥Fs
∀i∈I;s∈S�
i;j∈J
i,s
,
s
+
i,s=
𝜔
j
889
1 3
Public anspo c owdshipping: mo ing shipmen s amongpa cel…
Gi en cons ain s (2)-(13) and he no a ion epo ed in Table2, he modi ied objec-
i e unc ions and he necessa y addi ional cons ain s o ou i e al e na i e objec-
i es a e summa ized in Table3.
Due o he complexi y s a us o ou p oblem e sions, we canno expec ha ou
MIPs a e sol able o an o - he-shel sol e i he numbe s o pa cels and c owd-
shippe s each dimensions ele an o eal-wo ld c owdshipping pla o ms. The e-
o e, he ollowing sec ion p o ides an addi ional heu is ic solu ion p ocedu e.
5 A heu is ic decomposi ion amewo k o all objec i es
A sui able solu ion p ocedu e should co e all o ou six p oblem e sions wi h only
mino adap ions, and i should deli e close o op imal solu ions in accep able ime
e en o conside able numbe s o pa cels and c owdshippe s. Ou sugges ion o
mee hese equi emen s is a heu is ic decomposi ion amewo k ha consis s o wo
s ages. On he i s s age, which we desc ibe in mo e de ail in Sec .5.1, we in o-
duce a modi ica ion o Dijks a’s algo i hm o gene a e a pool o single-pa cel ou s
h ough a gi en public anspo a ion ne wo k. On he second s age (see Sec .5.2),
we apply a s anda d sol e o selec pa cel ou s om he pool by sol ing a MIP
simila o he well-known se packing p oblem.
5.1 Gene a ing apool o single‑pa cel ou s
In he i s s age, we gene a e a pool o single pa cel ou s o all pa cels. I each
pa cel ou was op imized indi idually, hen mos o hem would u ilize he cen al
esou ces whe e mos a ic passes. The e o e, we apply a special mechanism whe e
also ou s ia less cen al esou ces a e gene a ed o ensu e di e si y wi hin he pool.
Speci ically, we conside a sequence
𝜋
o all pa cels in J and gene a e a ou o pa -
cels one by one in he o de indica ed by
𝜋
. When gene a ing a ou o he k- h pa -
cel in
𝜋
, we accoun o capaci ies o c owdshippe s occupied by ou s o he i s
k−1
pa cels. Vi ually, whene e a pa o a c owdshippe ’s pa h is occupied by he
k- h pa cel, we conside each emaining pa o his pa h as a dis inc c owdshippe
(who is a ailable h oughou his pa h) o he
(k+1)
- h pa cel.
Fo a speci ic pa cel
j∈J
, we hen gene a e a pa h om
𝛼j
o
𝜔j
espec ing
elease da e
j
, deadline
dj
, and he c owdshippe s’ ime-s amped pa hs as ollows.
The scheme loosely ollows Dijks a’s algo i hm and he A
∗
-algo i hm (Ikeda e al.
1994) wi h s a ions co esponding o nodes in a g aph and pa hs o c owdshippe s
co esponding o pa hs in ha g aph. Ra he han es ic ing ou sel es o a pu ely
ime-d i en e alua ion o pa hs o j, we conside
𝜙s=w𝜇
⋅
𝜇s+wd
⋅
qs+w
⋅
s
o
each s a ion
s∈S
, whe e
𝜇s
is he numbe o en ainmen s on he pa h o j om
𝛼j
o
s,
qs
ep esen s he Manha an dis ance be ween s a ions s and
𝜔j
,
s
is ime pa cel j
eaches s on he pa h, and
w𝜇
,
wd
, and
w
a e weigh s.
(13)
∑
j∈J
∑
i∈I1
j
pj⋅xi,𝛼j,j−
∑
i∈I
∑
s∈S�
i
⋅yi,s≥P
.
890
A.Wy owski e al.
1 3
We designed
𝜙s
o e lec a ious aspec s ele an o he di e en objec i es.
Fu he mo e, we main ain o each s a ion
s∈S
he c owdshippe
is
, which b ough
j o s. Ini ially, we se
𝜙
𝛼
j
=w
𝜇⋅
0+w
d⋅
q
𝛼
j
+w
⋅
j
and
𝜙s=∞
o each
s≠𝛼j
and
ini ialize
is=⋅
o each
s∈S
wi h a dummy. In each i e a ion, he p ocedu e hen
de e mines a s a ion
s∗
o which he bes pa h is hen ixa ed. Fu he mo e, we upda e
he bes ound pa hs o s a ions which can be eached be a eling one s a ion wi h a
c owdshippe om
s∗
, gi en ha
s∗
is eached a ime
s∗
. In he cou se o he p oce-
du e,
S
ep esen s he se o s a ions wi h ixa ed pa hs owa d hem. Ini ially, we
ha e
S=�
.
In each i e a ion,
s∗
is de e mined as
s
∗=a g min
{
𝜙s∣s∈S⧵S
}
. I
s∗=𝜔j
and
s
∗
≤dj
, we ha e ound he ( easible) pa h om
𝛼j
o
𝜔j
. I
s∗=𝜔j
and
s
∗
>dj
, he
p ocedu e ailed o ind a easible pa h. Finally, i
s∗≠𝜔j
, we de e mine he se
Is∗
o
c owdshippe s s a ing om
s∗
no be o e
s∗
. Fo each
i∈Is∗
and he co esponding
s a ion
s+
i,s∗
o which i a els om
s∗
, we de e mine he implied alue
𝜙
s+
i,s
∗,
i
o
𝜙
s+
i,s∗
as
In bo h cases,
q
s+
i,s∗
e lec s he dis ance be ween he nex s a ion
s+
i,s∗
and
𝜔j
, and
i,s+
i,s∗
ep esen s he ime pa cel j would each he nex s a ion
s+
i,s∗
i i is ca ied om
s∗
by
c owdshippe i. In he uppe case, his c owdshippe i is he same as he one ha
b ough j o
s∗
( ha is, j a els h ough
s∗
wi h i) and, hence,
𝜇
s
+
i,s
∗
=𝜇
s
∗
. In he lowe
case, c owdshippe i picks up j a
s∗
and, hence,
𝜇
s+
i,s
∗
=𝜇
s∗
+1
. No e ha he same
s a ion s migh be he nex s a ion o mul iple c owdshippe s in
Is∗
and he implied
alues migh di e among hem. We upda e all pa h in o ma ion o s a ion
s+
i,s∗
o
each
i∈Is∗
, i
ha is i he bes implied pa h by any c owdshippe a eling om
s∗
o
s+
i,s∗
yields a
lowe alue o
s+
i,s∗
.
To gene a e a pool wi h mul iple ou candida es o each pa cel, we epea edly
d aw a andom sequence
𝜋
and employ he p ocedu e de ailed abo e o ou di e en
weigh se s
(w𝜇,wd,w )=(1∕3, 1∕3, 1∕3),(1∕3, 2∕3, 0),(0, 1∕2, 1∕2),(0, 2∕3, 1∕3)
.
These weigh se s ha en p o en mos e ec i e in p elimina y es s, which ( o a ma -
e o conciseness a e no epo ed in his pape ). A ou is admi ed o he pool, i i
gene a es a p o i , ha is i he pos al cha ge exceeds he o al en ainmen ees. The
pool is comple e once we ga he ed 10 ou s pe pa cel on a e age. The la e choice,
oo, has p o en as a easonable comp omise be ween un ime and solu ion quali y in
p elimina y es s no epo ed in his pape .
𝜙
s+
i,s∗,i=
{
w𝜇⋅𝜇s∗+wd⋅qs+
i,s∗+w ⋅ i,s+
i,s∗i=is∗
w𝜇⋅(𝜇s∗+1)+wd⋅qs+
i,s∗+w ⋅ i,s+
i,s∗i≠is∗
.
𝜙
s+
i,s
∗>min
{
𝜙s+
i
�
,s
∗,i�∣i�∈Is∗,s+
i,s∗=s+
i�,s∗
},
891
1 3
Public anspo c owdshipping: mo ing shipmen s amongpa cel…
5.2 Combining single‑pa cel ou s
A e gene a ing a se
Tj
o single-pa cel ou s o each pa cel
j∈J
as de ailed in
Sec .5.1, we use an o - he-shel sol e and a MIP model o mula ion in o de o
combine single-pa cel ou s o a easible solu ion. We p esen he MIP model o mu-
la ion in he ollowing, while using he addi ional no a ion summa ized in Table4.
Again, we desc ibe ou basic MIP o objec i e MAX-PROFIT i s and epo on
necessa y adap ions o ou al e na i e objec i es a e wa d.
Ou MAX-PROFIT-SELECT model uses bina y a iable
𝜖𝜓
o each
𝜓∈Tj
,
j∈J
,
which akes alue 1 i ou
𝜓
is selec ed and alue 0 o he wise. A mos one ou can
be selec ed pe pa cel
j∈J
, see (15), ha is each pa cel is deli e ed a mos once.
Two ou s conce ning di e en pa cels canno be selec ed simul aneously, i hey
occupy he same c owdshippe on he same a el leg, see (16). Simila ly, a each
ele an poin o ime no mo e han
Ls
pa cels can be s o ed in a locke a s a ion s,
(14)
MAX-PROFIT-SELECT: Maximize
F(𝜖)=
∑
j∈J
∑
𝜓∈T
j
c𝜓
⋅𝜖𝜓
(15)
s. . ∑
𝜓∈T
j
𝜖𝜓≤1∀j∈
J
(16)
∑
j
∈J
∑
𝜓∈T
j
Ξi,s,𝜓
⋅𝜖𝜓≤1∀i∈I;s∈S
�
i
(17)
∑
j∈J
∑
𝜓∈T
j
Δi,s,𝜓
⋅𝜖𝜓≤Ls∀i∈I;s∈S
�
i
(18)
𝜖
𝜓
∈{
0, 1
}∀
𝜓
∈
T
j
,j
∈T
Table 4 Addi ional no a ion o s age 2
Tj
se o single-pa cel ou s o each pa cel
j
∈
J
c𝜓
p o i o ou
𝜓∈Tj
,
j∈J
Ξi,s,𝜓
bina y pa ame e s: 1, i c owdshippe
i∈I
mo es pa cel
j∈J
om s a ion
s
∈S
�
i
owa d
s+
i,s
acco ding o ou
𝜓∈Tj
; 0,
o he wise
Δi,s,𝜓
bina y pa ame e s: 1, i pa cel
j∈J
is s o ed in a locke a
s∈S
when
i∈I
lea es s acco ding o ou
𝜓∈Tj
; 0, o he wise
Γ𝜓
minimum slack in ou
𝜓∈Tj
,
j∈J
Y𝜓
numbe o en ainmen s in ou
𝜓∈Tj
,
j∈J
𝜖𝜓
bina y a iables: 1, i ou
𝜓∈Tj
,
j∈J
, is selec ed; 0, o he wise
892
A.Wy owski e al.
1 3
see (17). Finally, objec i e unc ion (14) ep esen s he goal o maximize he o al
p o i achie ed.
To ep esen ou i e al e na i e objec i es, addi ionally a minimum o al p o i
P is ensu ed by cons ain
Gi en cons ain s (15) o (19) and he no a ion lis ed in Table4, ou modi ied objec-
i e unc ions as well as he addi ional cons ain s a e speci ied in Table5.
Ou MIP o mula ions ex end he amous se packing p oblem (see Ga ey and
Johnson 1979). Today’s de aul sol e s a e gene ally known o be qui e capable in
sol ing his kind o model. The compu a ional pe o mance analysis epo ed on in
he ollowing sec ion explo es whe he his claim can be con i med in ou case.
6 Pe o mance o algo i hms
In his sec ion, we es he pe o mance o ou solu ion app oaches. Since no es ab-
lished es bed is a ailable o ou public anspo c owdshipping p oblem, we
i s elabo a e how ou ins ances ha e been gene a ed in Sec .6.1. A e wa d, in
Sec .6.2, we benchma k he pe o mance o ou heu is ic decomposi ion p ocedu e
wi h a s anda d sol e sol ing ou MIP models.
All compu a ions ha e been execu ed on a 64-bi PC wi h an 7-3770 3.40 GHz
CPU and 16.0 GB o RAM. All solu ion me hods ha e been implemen ed using Vis-
ualBasic (Visual S udio 2019), and o - he-shel sol e Gu obi ( e sion 9.1.2) has
been applied o sol ing he MIP models wi h a gene al ime limi o 300s, i no
explici ly s a ed o he wise.
(19)
∑
j∈J
∑
𝜓∈T
j
c𝜓
⋅𝜖𝜓≥P
.
Table 5 Ex ended se packing o mula ions o he di e en objec i es
P oblem Objec i e and new cons ain s in addi ion o (15)-(19)
MAX-PARCELS Maximize
∑
j∈J
∑
𝜓∈T
j
𝜖
𝜓
MAX-INVOLVEMENT Maximize
∑i∈IFi
∑
j∈J
∑
𝜓∈T
j∑
s∈S�
i
Ξ
i,s,𝜓
⋅𝜖𝜓≥F
i
∀i∈I
Fi∈[0, 1]
∀i∈I
MIN-TOTAL-ENTRAINMENTS Minimize
∑
j∈J
∑
𝜓∈T
j(
pj
−
c𝜓
)∕
⋅𝜖
𝜓
MIN-MAX-ENTRAINMENTS Minimize
Fe
(pj−c𝜓)∕
⋅𝜖
𝜓≤Fe
∀
𝜓
∈Tj,j∈J
MAX-MIN-SLACK Maximize
Fs
Γ𝜓
⋅𝜖
𝜓+(1−
𝜖
𝜓)
⋅
M≥Fs
∀
𝜓
∈Tj
,j
∈J

893
1 3
Public anspo c owdshipping: mo ing shipmen s amongpa cel…
6.1 Da a gene a o
This sec ion epo s on ou da a gene a o , which is based on he public anspo
sys em o Hambu g (Ge many). Ou da a gene a o ecei es he numbe o pa cels
|J| and he numbe o c owdshippe s |I| as i s own inpu da a. Gi en his inpu , each
single ins ance is ob ained as ollows.
• Public anspo ne wo k: Gi en he ailway sys em o Hambu g, we u ilize sub-
way lines U1, U2, U3, and U4 as well as u ban ailway lines S1, S21, S3, and
S31 (see Fig.2). Each line
l∈L
is de ined by a sequence o s a ions
Sl⊆S
, so
ha ou es bed consis s o
|S|=147
s a ions in o al. These s a ions o se S
a e pa i ioned in o wo subse s
S=SC∪SS
. S a ions o se s
SC
and
SS
ep esen
inne ci y and subu ban s a ions and hey a e ma ked in g ay and pink, espec-
i ely. Fo each line
l∈L
, we use equency
l
gi en by he o iginal schedule o
he HVV du ing he wo king hou s (i.e.,
U1= U2= U3=5
), and
l=10
o
he es o he ime. The a el imes be ween any wo consecu i e s a ions o
a line a e d awn om
U{1, 2, 3}
, which is in line wi h he as majo i y o eal-
wo ld s a ions. Finally, ou planning ho izon is se o 10 hou s, i.e.,
T=600
min-
u es.
• Locke s: Fo each s a ion
s∈S
, we d aw a locke capaci y
Ls
p opo ional o
he c owdshippe a ic. Pa ame e
Ls
is ini ially de e mined by no malized a io
no m
s
, de ined as he ’numbe o lines’ di ided by he ’sum o co esponding e-
quencies’. Subsequen ly,
Ls
is inally es ablished h ough
L
s=
1
8|
J
|
+
1
4|
J
|
⋅ no m
s.
Fig. 2 Public anspo sys em o Hambu g [Sou ce: HVV]
894
A.Wy owski e al.
1 3
This ensu es ha he minimum capaci y is
1
8|
J
|
, while he maximum capaci y is
3
8|
J
|
.
• Pa cels: Fo each pa cel
j∈J
, we d aw a elease da e
j∼U{1, …,|T|∕10}
and
a deadline
dj∼U{9
⋅
|T|∕10, …,|T|}
. We assume ha wi h a p obabili y o 50%
a pa cel has o be anspo ed om a ci y cen e o a subu ban s a ion, whe e
o igin and des ina ion s a ions a e andomly chosen om se s
SC
and
SS
, espec-
i ely, and wi h 50% ice e sa. Fo each success ully deli e ed pa cel, he pla -
o m ecei es a cons an pos al cha ge o
pj=p=5
.
• C owdshippe s: We assume ha 40% o he c owdshippe s mo e du ing he
mo ning hou s, i.e., we de e mine hei depa u e ime
i
by d awing om a
uni o m dis ibu ion:
i∼U{1, …,3
⋅
|T|∕10}
. Ano he 40% o c owdship-
pe s mo e du ing he la e hou s (
i∼U{6
⋅
|T|∕10 +1, …,9
⋅
|T|∕10}
),
and he emaining 20% o c owdshippe s mo e du ing main wo king hou s
(
i∼U{3
⋅
|T|∕10 +1, …,6
⋅
|T|∕10}
).
C owdshippe s o he mo ning hou s needs o a el om a subu ban a ea o a
ci y cen e s a ion (wi h a p obabili y o 60%), while 30% mo e in he opposi e
di ec ion, and 10% a el en i ely wi hin he ci y cen e . The o igin and des ina-
ion s a ions a e andomly selec ed om se s
SC
and
SS
.
Du ing he la e hou s, he selec ion o o igin and des ina ion s a ion is
e e sed, so ha 60% mo e om he ci y cen e o he subu ban a ea, while 30%
mo e in he opposi e di ec ion, and again 10% s ay in he ci y cen e .
Fo c owdshippe s ha a el du ing he main wo king hou s, we assume ha
hey a el wi h equal p obabili y om a subu ban a ea o he ci y cen e , he
o he way ound, o wi hin he ci y cen e .
Gi en he o igin s a ion, depa u e ime, and des ina ion o c owdshippe
i∈I
,
we de e mine he sho es pa h by he s anda d Dijks a algo i hm h ough ou
ne wo k in o de o de e mine hei ime-s amped pa hs
i,s
. The ixed en ainmen
ee is
=1
.
Finally, we se he epe i ion coun e o en o each da a se ing de ined by he num-
be o pa cels |J| and he numbe o c owdshippe s |I|. Hence, en ins ances, each
de i ed as de ined abo e, a e e u ned by ou da a gene a o .
6.2 Compu a ional esul s
Ou pe o mance es s benchma k ou heu is ic decomposi ion p ocedu e (see
Sec .5) wi h o - he-shel sol e Gu obi when ed wi h he MIPs o Sec .4. Ou
comple e es s ha e shown ha he e a e no signi ican pe o mance di e ences o
bo h compe i o s o he di e en objec i es. To no o e load his pape , we he e-
o e decided o only epo he pe o mance esul s o objec i e MAX-PROFIT.
When compa ing he pe o mance o hese solu ion app oaches in Table6, we epo
on he a e age op imali y gap in pe cen de e mined by Gu obi (column ’gap’), he
a e age gap in pe cen o he bes solu ion ound among bo h compe i o s (column
’gap
b
’), he numbe o ins ances whe e he app oach ound he bes solu ion among
895
1 3
Public anspo c owdshipping: mo ing shipmen s amongpa cel…
bo h compe i o s (column ’bes ’), he numbe o solu ions p o en o be op imal
(column ’op ’), he numbe o ins ances whe e a leas one easible solu ion wi h
an objec i e alue
≥0
was ob ained (column ’ eas’), and he a e age CPU-seconds
(column ’sec’). No e ha ime limi o he de aul sol e was se o 15min and he
CPU-seconds o he heu is ic include he p ep ocessing ime o pool gene a ion. In
ou s udy, we a y he numbe o pa cels |J| and he numbe o c owdshippe s |I|. Fo
each combina ion o hese pa ame e s, en ins ances as desc ibed in Sec .6.1 ha e
been ob ained, so ha in o al 270 ins ances cons i u e his es bed. The esul s sum-
ma ized in Table6 sugges he ollowing indings:
Table 6 Pe o mance es o Gu obi and he heu is ic decomposi ion p ocedu e o objec i e MAX-
PROFIT
Gu obi Decomposi ion heu is ic
|J| |I|gap gap
b
bes op eas sec gap
b
bes op eas sec
20 20 0.00 0.00 10 10 10 0.72 2.33 8 8 10 3.56
20 40 0.00 0.00 10 10 10 1.51 14.19 2 2 10 2.42
20 60 0.00 0.00 10 10 10 3.52 7.03 1 1 10 1.85
30 30 0.00 0.00 10 10 10 1.58 7.90 3 3 10 3.85
30 60 0.00 0.00 10 10 10 5.82 5.82 4 3 10 3.31
30 90 0.00 0.00 10 10 10 26.82 3.55 2 1 10 3.49
40 40 0.00 0.00 10 10 10 3.40 2.40 5 5 10 5.50
40 80 0.29 0.00 10 9 10 115.57 7.54 1 0 10 4.92
40 120 1.61 0.10 9 7 10 377.50 5.42 3 1 10 5.61
50 50 0.00 0.00 10 10 10 14.12 6.96 2 2 10 7.80
50 100 2.52 2.55 6 6 10 457.02 4.65 4 0 10 7.68
50 150 7.60 0.85 8 0 10 920.24 4.60 3 0 10 9.00
60 60 0.00 0.00 10 10 10 18.64 5.21 1 1 10 9.25
60 120 4.52 0.00 10 0 10 918.19 8.00 0 0 10 11.12
60 180 17.71 5.13 4 0 10 935.84 1.91 7 0 10 13.98
70 70 0.38 0.00 10 8 10 315.41 7.31 1 1 10 11.69
70 140 8.43 0.00 10 0 10 925.98 6.36 0 0 10 16.25
70 210 31.33 12.20 1 0 10 952.31 0.29 9 0 10 20.48
80 80 0.41 0.00 10 7 10 387.24 6.50 0 0 10 16.20
80 160 21.74 2.65 4 0 10 935.14 1.27 7 0 10 22.00
80 240 91.68 69.93 0 0 10 977.49 0.00 10 0 10 27.83
90 90 1.62 0.00 10 5 10 672.58 6.47 0 0 10 19.79
90 180 49.20 18.87 2 0 10 952.45 0.00 10 0 10 29.19
90 270 55.77 27.59 0 0 9 1015.92 0.00 10 0 10 41.56
100 100 4.40 0.00 10 0 10 921.50 4.55 0 0 10 25.54
100 200 55.38 24.13 0 0 9 968.71 0.00 10 0 10 37.91
100 300 79404.22 3027.54 0 0 8 1743.52 0.00 10 0 10 54.09
896
A.Wy owski e al.
1 3
• Gu obi: De aul sol e Gu obi pe o ms e y well when handling smalle
ins ance sizes o
|J|≤30
pa cels. He e, i is able o e i y all op imal solu-
ions wi hin sho compu a ional imes. Howe e , Gu obi s uggles wi h la ge
ins ance sizes o
|J|≥70
pa cels, especially wi h a la ge c owdshippe base.
He e, gaps as well as un imes inc ease and less bes solu ions a e ob ained. Fo
la ge ins ances wi h ewe c owdshippe s, howe e , Gu obi s ill ou pe o ms ou
heu is ic. Un o una ely, ou compu a ional e alua ion in Sec .7.1 will show ha
a la ge c owdshippe base is equi ed o mo e a subs an ial numbe o pa cels. In
hese cases, ou heu is ic seems he be e op ion. No e ha hese esul s did no
imp o e signi ican ly in u he es s, whe e we allowed he de aul sol e longe
unning imes up o one hou .
• Decomposi ion heu is ic: Ou heu is ic, ins ead, p oduces a good comp omise
be ween solu ion quali y and ime, especially o la ge ins ances wi h many pa -
cels and c owdshippe s. I de e mines easible solu ions o all ins ances and
equi es less han one minu e e en o he la ges ins ance sizes. The (op imali y)
gaps a e easonably small.
We conclude ha bo h solu ion app oaches seem an app op ia e choice o ou
c owdshipping p oblem. Especially, o la ge ins ances wi h many shipmen s and
po en ial c owdshippe s, ou heu is ic seems he be e choice, especially when as
decisions a e equi ed.
7 Manage ial issues
This sec ion is dedica ed o manage ial issues. We wan o iden i y c i ical ac o s o
he success ul di usion o public anspo c owdshipping. Speci ically, we explo e
how many olun ee ing c owdshippe s mus be ec ui ed in o de o success ully
deli e a gi en amoun o pa cels in Sec .7.1, we p o ide a ela ionship analysis
be ween he di e en objec i es in Sec .7.2, and we add ess obus ness issues o
a oid s anded pa cels in case o un o eseen ain delays in Sec .7.3. Finally in
Sec .7.4, we compa e a spli ing o a shipmen ’s a el om o igin o des ina ion
among mul iple c owdshippe s wi h di ec single-c owdshippe anspo s. The la -
e p omise a be e p o ec ion agains un o eseen ain delays bu o e less planning
lexibili y.
I no explici ly s a ed o he wise, we gene a e ou ins ances as desc ibed in
Sec .6.1 o a a ying numbe o pa cels |J| and a ailable c owdshippe s |I|. To no
spoil ou in es iga ions by heu is ic gaps, we decided o apply Gu obi (wi h a ime
limi o one hou ) on smalle ins ances wi h up o
|J|≤60
pa cels only.
7.1 How many c owdshippe s need obe ec ui ed?
Among he ou s anding challenges o success ully es ablish c owdshipping as a eli-
able e e y-day deli e y op ion is ce ainly he ola ile pa icipa ion o olun ee ing
903
1 3
Public anspo c owdshipping: mo ing shipmen s amongpa cel…
Howe e , he e may be e en be e objec i es and he bes choice among hem
is ce ainly only one le e . Fu u e esea ch should hus e alua e he impac o
o he objec i es and u he coun e measu es, such as a dynamic eplanning once
delays ha e occu ed wi h al e ed en ainmen missions o c owdshippe s al eady
unde way. The igh compensa ion scheme, which p ope ly ades o he impac o
s anded pa cels on cus ome sa is ac ion wi h losses o pla o m p o i , is ce ainly
an impo an choice.
7.4 Compa ison wi h hesingle‑c owdshippe ‑pe ‑pa cel policy
F ench public anspo c owdshipping pla o m Ch onobee (see Sec .1) applies
he single-c owdshippe -pe -pa cel (SCPP) policy. This means ha an accep ed
pa cel is b ough om o igin o des ina ion exclusi ely by a single c owdship-
pe . On he posi i e side, SCPP o e s mo e p o ec ion agains un o eseen delays.
T ain delays can s ill lead o pa cels missing he deadlines a hei des ina ions,
bu a leas he hando e isk o c owdshippe s missing each o he is elimina ed.
Ou esea ch p o ides op imiza ion app oaches unde he mul i-c owdshippe -
pe -pa cel (MCPP) policy, whe e asynch onous pa cel hando e s ia locke s
be ween mul iple c owdshippe s a e allowed. The asse o he MCPP policy is
ce ainly he la ge lexibili y o mo e pa cels wi h mul iple c owdshippe s. This
p omises highe deli e y a es bu inc eases he isk o s anded pa cels. This
sec ion benchma ks bo h policies ega ding hei p o i s wi h and wi hou ain
delays.
Speci ically, ou expe imen is se up as ollows. Using ou ins ance gene a-
o o Sec .6.1, we gene a e 10 ins ances wi h
|J|=30
egis e ed pa cels and
|I|=2|J|
olun ee ing c owdshippe s. To ob ain he p o i s o bo h policies in a
de e minis ic wo ld whe e no un o eseen delays occu , hese ins ances a e sol ed
wi h wo app oaches. Fo MCPP, we apply he app oach ha p o ed bes in he
p e ious sec ion. This means, we u ilize he MIN-MAX-ENTRAINMENTS
objec i e wi h a minimum pla o m p o i equal o he maximum p o i ob ained
by MAX-PROFIT o sol e he ins ances and eco d he esul ing p o i . Ano he
ad an age o he SCPP policy is a much easie ma ching ask, which cons i u es
a linea assignmen p oblem ha can e icien ly be sol ed, e.g., by he amous
Hunga ian me hod (Kuhn 1955). He e, we assign c owdshippe s o pa cels, whe e
he assignmen p o i is ei he he pa cel cha ge minus a single en ainmen ee i
20 30 40 50 60 70
(a) P e-delay p o i o SCPP in %o MCPP
20 30 40 50 60 70 80
(b)Pos -delay p o i o SCPP in %o MCPP
Fig. 5 Benchma k o MCPP and SCPP be o e (le ) and a e ( igh ) delays: P o i o SCPP in % o
MCPP’s p o i (ob ained by he MIN-MAX-ENTRAINMENTS objec i e wi h a minimum pla o m
p o i equal o he maximum p o i ob ained by MAX-PROFIT) in %

904
A.Wy owski e al.
1 3
he c owdshippe imely a els along he pa cel’s o igin and des ina ion o ze o
i no easible anspo by a speci ic c owdshippe is possible. Sol ing he max-
p o i linea assignmen p oblem deli e s he op imal p o i o he SCPP policy.
To also compa e bo h policies i un o eseen ain delays occu and s anded pa -
cels may educe he p o i , we apply he high- isk-small-delay se ing (i.e., wi h a
delay isk o
Pd=15
% and
d=3
minu e delays) and de e mine he ac ual p o i
o bo h solu ions i he espec i e delays occu . In Fig.5, we depic he p e-delay
(i.e., de e minis ic wo ld wi hou delays) and he pos -delay (i.e., ac ual p o i
including compensa ion o s anded pa cels in case o delays) p o i s. The box
plo s show he dis ibu ion o he p o i o SCPP di ided by he p o i o MCPP
in % o e he sol ed ins ances. Hence, a alue below (abo e) 100% indica es ha
SCPP ealizes a lowe (highe ) p o i han MCPP.
The esul s o Fig.5 indica e ha MCPP clea ly ou pe o ms SCPP. The loss
in lexibili y i only a single c owdshippe may anspo each pa cel educes he
median p o i o SCPP o only 40% o MCPP’s p o i in a de e minis ic wo ld.
As expec ed, his disad an age educes i un o eseen delay occu , bu he median
p o i o SCPP s ill me ely eaches 47% o MCPP’s p o i . Howe e , he e a e
h ee ins ances wi h high isk and long delays whe e he highe obus ness o
SCPP leads o e en be e esul s han MCPP. On a e age, howe e , ou expe i-
men shows a clea ad an age o MCPP, which leads us o ou inal manage ial
ake-home message.
Ac ionable insigh s: The cu en business p ac ice o only apply he SCPP policy
should be econside ed. Ou compu a ional esul s show ha he inc ease o lexibil-
i y enabled by he pa cel hando e among mul iple c owdshippe s clea ly o e com-
pensa es he highe isk o s anded pa cels in case o un o eseen delays.
8 Conclusions
This pape in es iga es public anspo c owdshipping and p o ides ma ching me h-
ods o selec shipmen s and hei ways h ough a public anspo a ion ne wo k when
accompanying c owdshippe s on hei commu e. Based on a compu a ional s udy
applying hese me hods, we iden i y he ollowing c i ical success ac o s o his
inno a i e las -mile deli e y concep :
(a) A la ge c owdshippe base o olun ee ing public anspo use s mus be
ec ui ed ha is signi ican ly la ge han he numbe o pa cels o be anspo ed.
Howe e , e en i such a base can success ully be ga he ed, a pla o m canno
expec ha all pa cels can be anspo ed. Thus, a eliable and lexible all-back
op ion mus be a hand.
(b) Un o una ely, he e is no single objec i e ha can sa is y all in ol ed s ake-
holde s equally. When only ocusing on he pla o m p o i , his ends o also
maximize he numbe o success ully c owdshipped pa cels (and hus he posi-
i e en i onmen al impac ) bu educes he numbe o in ol ed c owdshippe s.
This can ge in he way o ou p e ious success ac o .
905
1 3
Public anspo c owdshipping: mo ing shipmen s amongpa cel…
(c) To accoun o un o eseen ain delays and o p o ec agains s anded pa cels, we
iden i y he MIN-MAX-INVOLVEMENT objec i e, which es ic s he maxi-
mum numbe o hando e s among c owdshippe s pe pa cel, as bes sui ed.
(d) Finally, we show ha allowing pa cels o ake mul iple a el legs wi h mo e
han a single c owdshippe g ea ly inc eased planning lexibili y and p omises
much mo e anspo ed pa cels as well as highe pla o m p o i s han he single-
c owdshippe -pe -pa cel policy o cu en business p ac ice.
Fu u e esea ch could ake up ou esea ch in mul iple ways: O he op imiza ion
objec i es and mo e complex me hods including mul iple objec i es and explici ly
in ol ing s ochas ic delay in o ma ion should be de eloped. In his way, ma chings
ha be e se e all in ol ed s akeholde s, e en i un o eseen delays occu , could be
ob ained. Fu he mo e, ou solu ion me hods should be challenged, such ha hey
a e sui able o la ge eal-wo ld c owdshipping pla o ms wi h housands o ship-
men s and e en mo e c owdshippe s.
Acknowledgemen s This esea ch has been suppo ed by he Ge man Science Founda ion (DFG) by he
g an “Coo dina ion o demand and supply in he Sha ing Economy” (BO 3148/8-1 and BR 3873/10-1).
Funding Open Access unding enabled and o ganized by P ojek DEAL.
Open Access This a icle is licensed unde a C ea i e Commons A ibu ion 4.0 In e na ional License,
which pe mi s use, sha ing, adap a ion, dis ibu ion and ep oduc ion in any medium o o ma , as long
as you gi e app op ia e c edi o he o iginal au ho (s) and he sou ce, p o ide a link o he C ea i e
Commons licence, and indica e i changes we e made. The images o o he hi d pa y ma e ial in
his a icle a e included in he a icle’s C ea i e Commons licence, unless indica ed o he wise in
a c edi line o he ma e ial. I ma e ial is no included in he a icle’s C ea i e Commons licence and
you in ended use is no pe mi ed by s a u o y egula ion o exceeds he pe mi ed use, you will need
o ob ain pe mission di ec ly om he copy igh holde . To iew a copy o his licence, isi h p://
c ea i ecommons.o g/licenses/by/4.0/.
Re e ences
A che i C, Sa elsbe gh M, Spe anza MG (2016) The ehicle ou ing p oblem wi h occasional d i e s.
Eu J Ope Res 254:472–480
A slan AM, Aga z N, K oon L, Zuidwijk R (2018) C owdsou ced deli e y-a dynamic pickup and
deli e y p oblem wi h ad hoc d i e s. T ansp Sci 53:222–235
Azcuy I, Aga z N, Giesen R (2021) Designing in eg a ed u ban deli e y sys ems using public ans-
po . T ans Res Pa E: Logis T ans Re 156:102525
Beh end M, Meisel F (2018) The in eg a ion o i em-sha ing and c owdshipping: Can collabo-
a i e consump ion be pushed by deli e ing h ough he c owd? T ans Res Pa B: Me hodol
111:227–243
Boysen N, B isko n D, Schwe d ege S (2019) Ma ching supply and demand in a sha ing economy: Clas-
si ica ion, compu a ional complexi y, and applica ion. Eu J Ope Res 278:578–595
Boysen N, Emde S, Schwe d ege S (2022) C owdshipping by employees o dis ibu ion cen e s: Op imi-
za ion app oaches o ma ching supply and demand. Eu J Ope Res 296:539–556
Boysen N, Fed ke S, Schwe d ege S (2021) Las -mile deli e y concep s: a su ey om an ope a ional
esea ch pe spec i e. OR Spec um 43:1–58
B isko n D, Leung J, Pinedo M (2011) Robus scheduling on a single machine using ime bu e s. IIE
T ans 43:383–398
Chen C, Pan S, Wang Z, Zhong RY (2017) Using axis o collec ci ywide e-comme ce e e se lows: a
c owdsou cing solu ion. In J P od Res 55:1833–1844
906
A.Wy owski e al.
1 3
Chen C, Zhang D, Ma X, Guo B, Wang L, Wang Y, Sha E (2016) C owddeli e : planning ci y-wide pack-
age deli e y pa hs le e aging he c owd o axis. IEEE T ans In ell T ansp Sys 18:1478–1496
Dablanc L, Mo gan i E, A idsson N, Woxenius J, B owne M, Saidi N (2017) The ise o on-demand
‘ins an deli e ies’ in Eu opean ci ies. Supply Chain Fo um: An In J 18:203–217
Daya ian I, Sa elsbe gh M (2020) C owdshipping and same-day deli e y: Employing in-s o e cus ome s
o deli e online o de s. P od Ope Manag 29:2153–2174
E en S, I ai A, Shami A (1976) On he complexi y o ime able and mul icommodi y low p oblems.
SIAM J Compu 5:691–703
Ga ey MR, Johnson DS (1979) Compu e s and in ac abili y. F eeman, San F ancisco
Ga a V, Ma cucci E, Nig o M, Pa ella SM, Se a ini S (2019) Public anspo -based c owdshipping o
sus ainable ci y logis ics: Assessing economic and en i onmen al impac s. Sus ainabili y 11:145
Ga a V, Ma cucci E, Nig o M, Se a ini S (2019) Sus ainable u ban eigh anspo adop ing public
anspo -based c owdshipping o B2C deli e ies. Eu T ansp Res Re 11:13
Gdowska K, Viana A, Ped oso JP (2018) S ochas ic las -mile deli e y wi h c owdshipping. T ans Res
P ocedia 30:90–100
Ghilas V, Co deau JF, Demi E, Van Woensel T (2018) B anch-and-p ice o he pickup and deli e y
p oblem wi h ime windows and scheduled lines. T ansp Sci 52:1191–1210
Ghilas V, Demi E, Van Woensel T (2016) An adap i e la ge neighbo hood sea ch heu is ic o he pickup
and deli e y p oblem wi h ime windows and scheduled lines. Compu Ope Res 72:12–30
Ghilas V, Demi E, VanWoensel T (2016b) The pickup and deli e y p oblem wi h ime windows and
scheduled lines. INFOR: In o ma ion Sys ems and Ope a ional Resea ch 54, 147–167
Ghilas V, Demi E, Van Woensel T (2016) A scena io-based planning o he pickup and deli e y p ob-
lem wi h ime windows, scheduled lines and s ochas ic demands. T ans Res Pa B: Me hodol
91:34–51
His Sys em Co. (2019) On Ko ean Bizwi e websi e: Seoul me o o begin pa cel deli e y se ice. h p://
ko ea bizwi e. com/ seoul- me o- o- begin- pa cel- deli e y- se i ce/ 148909 (las access: No embe
2023)
Ikeda T, Hsu MY, Imai H, Nishimu a S, Shimou a H, Hashimo o T, Tenmoku K, Mi oh K (1994) A as
algo i hm o inding be e ou es by AI sea ch echniques, in: P oceedings o Vehicle Na iga ion
and In o ma ion Sys ems Con e ence, pp. 291–296
Kızıl KU, Yıldız B (2022) Public anspo -based c owd-shipping wi h backup ans e s. T ansp Sci
57:174–196
Kou X, Zhang Y, Long D, Liu X, Qie L (2022) An in es iga ion o mul imodal anspo o las mile
deli e y in u al a eas. Sus ainabili y 14:1291
Kou elis P, Yu G (1996) Robus Disc e e Op imiza ion and I s Applica ions. Noncon ex Op imiza ion
and I s Applica ions, Sp inge , US
Kuhn HW (1955) The Hunga ian me hod o he assignmen p oblem. Na al Resea ch Logis ics Qua -
e ly 2:83–97
Le TV, S a hopoulos A, Van Woensel T, Ukkusu i SV (2019) Supply, demand, ope a ions, and manage-
men o c owd-shipping se ices: A e iew and empi ical e idence. T ans Res Pa C: Eme g Tech-
nol 103:83–103
Li B, K ushinsky D, Reije s HA, Van Woensel T (2014) The sha e-a- ide p oblem: People and pa cels
sha ing axis. Eu J Ope Res 238:31–40
Mac ina G, Pugliese LDP, Gue ie o F, Lapo e G (2020) C owd-shipping wi h ime windows and ans-
shipmen nodes. Compu Ope Res 113:104806
Masoud N, Jayak ishnan R (2017) A decomposi ion algo i hm o sol e he mul i-hop pee - o-pee ide-
ma ching p oblem. T ans Res Pa B: Me hodol 99:1–29
Masson R, T en ini A, Lehuédé F, Malhéné N, Pé on O, Tlahig H (2017) Op imiza ion o a ci y logis ics
anspo a ion sys em wi h mixed passenge s and goods. EURO J T ans Logis 6:81–109
Pa celHe o (2016) Amazon’s P ime Ambi ion. h ps:// www. pa ce lhe o. com/ con e n / downl oads/ pd s/
amazon/ amazo ns- p ime- ambi ion- pa ce lhe o- indus y- epo . pd (las access: No embe 2023)
Punel A, E magun A, S a hopoulos A (2019) Push and pull ac o s in adop ing a c owdsou ced deli e y
sys em. T ansp Res Rec 2673:529–540
Ro h AE, Sönmez T, Ün e MU (2004) Kidney exchange. Q J Econ 119:457–488
Sa elsbe gh MW, Ulme MW (2022) Challenges and oppo uni ies in c owdsou ced deli e y planning
and ope a ions. 4OR 20, 1–21
Schmid J, Tilk C, I nich S (2022) Using public anspo in a 2-echelon las -mile deli e y ne wo k. Eu o-
pean Jou nal o Ope a ional Resea ch , o appea
907
1 3
Public anspo c owdshipping: mo ing shipmen s amongpa cel…
Sch o en A, Wa inga G, Bles M (2012) Ma ginal aba emen cos cu es o hea y du y ehicles. Back-
g ound Repo , CE Del , Del
Sli kins A (2010) Pa ame e ized ac abili y o edge-disjoin pa hs on di ec ed acyclic g aphs. SIAM J
Disc e Ma h 24:146–157
S a is a (2022) Pake sendungen e eichen neuen Reko dwe . h ps:// de. s a i s a. com/ in og a ik/ 9992/
in- deu s chland- on- den- pake - und- ku ie dien s en- be oe de en- sendu ngen/ (Accessed: No embe
2023)
Vaughan R, Da e io R (2016) Assessing he size o he collabo a i e economy in Eu ope. h ps:// publi
ca io ns. eu opa. eu/ en/ publi ca ion- de ai l/-/ publi ca ion/ 2acb7 619- b544- 11e7- 837e- 01aa7 5ed71 a1
(Accessed: No embe 2023)
Vincen FY, Jodiawan P, Redi AP (2022) C owd-shipping p oblem wi h ime windows, ansshipmen
nodes, and deli e y op ions. T ans Res Pa E: Logis T ans Re 157:102545
Wang D, Wang Q, Yin Y, Cheng T (2023) Op imiza ion o ide-sha ing wi h passenge ans e ia deep
ein o cemen lea ning. T ans Res Pa E: Logis T ans Re 172:103080
Wang Y, Zhang D, Liu Q, Shen F, Lee LH (2016) Towa ds enhancing he las -mile deli e y: An e ec i e
c owd- asking model wi h scalable solu ions. T ans Res Pa E: Logis T ans Re 93:279–293
Zeh abian S, La sen C, Wøhlk S (2022) Es ima ion o he a i al ime o deli e ies by occasional d i e s
in a c owd-shipping se ing. Eu J Ope Res 303:616–632
Zhang C, Du Z, Pa ma MD, Bai Y (2017) Pocke -swi ch-ne wo k based se ices op imiza ion in c owd-
sou ced deli e y sys ems. Compu Elec Eng 62:53–63
Publishe ’s No e Sp inge Na u e emains neu al wi h ega d o ju isdic ional claims in published maps
and ins i u ional a ilia ions.
Au ho s and A ilia ions
Alexande Wy owski1· NilsBoysen1 · Di kB isko n2· S e anSchwe d ege 3
* Nils Boysen
nils.bo[email p o ec ed]
h ps://www.om.uni-jena.de/en/NilsBoysen.h ml
Alexande Wy owski
alexande .wy ow[email p o ec ed]
h ps://www.om.uni-jena.de/en/alexande wy owski
Di k B isko n
b isko n@uni-wuppe al.de
h p://www.p odlog.uni-wuppe al.de
S e an Schwe d ege
s e an.schwe d [email p o ec ed]
h ps://www.om.uni-jena.de/en/S e anSchwe d ege
1 F ied ich-Schille -Uni e si ä Jena, Leh s uhl ü Ope a ions Managemen , Ca l-Zeiß-S aße 3,
07743Jena, Ge many
2 Be gische Uni e si ä Wuppe al, P o essu ü BWL, insbesonde e P oduk ion und Logis ik,
Raine -G uen e -S . 21, 42119Wuppe al, Ge many
3 F ied ich-Schille -Uni e si ä Jena, Leh s uhl ü Ope a ions Managemen andLeh s uhl ü
Managemen Science, Ca l-Zeiß-S aße 3, 07743Jena, Ge many