Roelink, Daniël; Campuzano, Gio anni; Mes, Ma ijn; Lalla-Ruiz, Edua do Anibal
A icle
The selec i e mul iple depo pickup and deli e y p oblem
wi h mul iple ime windows and pai ed demand
Ope a ions Resea ch Pe spec i es
P o ided in Coope a ion wi h:
Else ie
Sugges ed Ci a ion: Roelink, Daniël; Campuzano, Gio anni; Mes, Ma ijn; Lalla-Ruiz, Edua do Anibal
(2025) : The selec i e mul iple depo pickup and deli e y p oblem wi h mul iple ime windows and
pai ed demand, Ope a ions Resea ch Pe spec i es, ISSN 2214-7160, Else ie , Ams e dam, Vol. 14,
pp. 1-24,
h ps://doi.o g/10.1016/j.o p.2025.100342
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The selec i e mul iple depo pickup and deli e y p oblem wi h mul iple ime
windows and pai ed demand
Daniël Roelink a, Gio anni Campuzano b,c, Ma ijn Mes a, Edua do Lalla-Ruiz a,∗
aDepa men o High-Tech Business and En ep eneu ship, Uni e si y o Twen e, D iene lolaan 5, Enschede, 7522 NB, The Ne he lands
bFacul ad de Ingenie ía, A qui ec u a y Diseño, Uni e sidad San Sebas ian, Lago Panguipulli 1390, Pue o Mon , 5501842, Chile
cDepa men o Ma i ime and T anspo Technology, Del Uni e si y o Technology, Mekelweg 2, Del , 2628 CD, The Ne he lands
A R T I C L E I N F O
Keywo ds:
Vehicle Rou ing P oblem
Adap i e La ge Neighbo hood Sea ch
Simula ed Annealing
Backhauling
F eigh selec ion
F eigh exchange
A B S T R A C T
A ecu ing challenge o anspo a ion companies is he ine iciency o e u ning (pa ially) emp y ehicles,
o backhauling, a e deli e ing o de s. To add ess his issue, companies sea ch on eigh exchange pla o ms
o p o i able pickup and deli e y o de s, aiming o educe he cos s associa ed wi h emp y e u n ips.
The inc easing eliance on eigh exchange pla o ms p esen s bo h an oppo uni y and a challenge: while
hey o e access o p o i able loads, e ec i ely selec ing he igh combina ion o o de s o maximize e u ns
is challenging. This pape add esses his challenge by in oducing he Selec i e Mul iple Depo Pickup and
Deli e y P oblem wi h Mul iple Time Windows and Pai ed Demand (SMDPDPMTWPD). We o mula e he
SMDPDPMTWP as a Mixed-In ege Linea P og am (MILP) o maximize p o i and op imize eigh selec ion
o e u n ips. In addi ion o he main model, h ee p oblem ex ensions a e p oposed: (i) p o i maximiza ion
including CO2 cos s, (ii) so ime windows, and (iii) so ime windows including CO2 cos s. Gi en he
complexi y o he p oblem, we de elop an Adap i e La ge Neighbo hood Sea ch (ALNS) me aheu is ic o sol e
la ge ins ances wi hin easonable compu ing imes and compa e i wi h a Simula ed Annealing (SA) heu is ic.
Resul s show ha ALNS ou pe o ms SA and inds he same op imal solu ions as he MILP o mula ion o
small ins ances. Fu he mo e, ALNS achie es an a e age imp o emen o 308.17% o e he ini ial solu ions
o he p o i maximiza ion a ian . The model a ian wi h CO2 cos s shows a sligh sensi i i y o he ou ing
schedules o he CO2 emissions cos s, whe eas we obse e a signi ican change when allowing so ime
windows. Finally, so ime windows signi ican ly inc ease he p o i s ea ned compa ed o he ha d ime
windows (179.54% on a e age), due o he addi ional lexibili y c ea ed when la e a i als a e possible.
1. In oduc ion
Road anspo con inues o play a c ucial ole in global logis ics.
Acco ding o he Ne he lands S a is ics Bu eau, he sha e o oad ans-
po in o al eigh anspo in he Ne he lands inc eased om 40.65%
in 2016 o 43.26% in 2022 [1]. Howe e , in he same pe iod, bo h
anspo p ices and he numbe o emp y kilome e s ha e inc eased,
speci ically, he la e inc eased om 25.60% o 26.14% ([2,3]). Be-
cause emp y kilome e s a e ine icien , unp o i able and con ibu e o
inc easing anspo a ion cos s, anspo a ion companies a e exe ing
s ong e o s o minimize hei occu ence. Besides he economic im-
pac o emp y kilome e s, he e is also an en i onmen al impac in he
o m o CO2 pollu an s and o he emissions [4]. Due o he heigh ened
global awa eness o educing CO2 emissions and he Eu opean Union’s
adop ion o he Co po a e Sus ainabili y Repo ing Di ec i e (CSRD) in
2021, which manda es ha companies should ack and mi iga e hei
∗Co esponding au ho .
E-mail add esses: [email p o ec ed] (D. Roelink), [email p o ec ed] (G. Campuzano), [email p o ec ed] (M. Mes), [email p o ec ed]
(E. Lalla-Ruiz).
en i onmen al impac , educing he numbe o emp y kilome e s is a
necessi y o anspo a ion companies.
Emp y kilome e s may be ine i able, especially in ce ain sec o s,
as e idenced in cons uc ion. S ill, hey can be e ec i ely educed in
o he sec o s, such as in e na ional anspo , whe e emp y kilome e s
ypically occu on e u n ips. T anspo a ion companies y o educe
emp y kilome e s by enhancing planning e o s and op imizing he
ou es o be a eled by ucks. Howe e , a anspo a ion company
may lack a su icien o di e se o de se o c ea e e icien ou es
wi h a low numbe o emp y kilome e s. In hose cases, anspo a ion
companies can u ilize so-called eigh exchange pla o ms. These pla -
o ms acili a e he exchange o o de s among membe s and connec
anspo a ion companies wi h a ailable capaci y o eigh p o ide s
in need o anspo a ion se ices. In o he wo ds, eigh exchange
h ps://doi.o g/10.1016/j.o p.2025.100342
Recei ed 23 July 2024; Recei ed in e ised o m 9 Ma ch 2025; Accep ed 13 May 2025
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
A ailable online 31 May 2025
2214-7160/© 2025 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY license ( h p://c ea i ecommons.o g/licenses/by/4.0/ ).
D. Roelink e al.
pla o ms p o ide a ma ke place whe e anspo a ion companies wi h
excess o de s can o e hem o o he companies acing a sho age o
o de s, enabling hem o bid on hese oppo uni ies. Howe e , selec ing
eigh s on hese pla o ms is o en a manual and ime-consuming
p ocess ha elies on he skills, knowledge, and expe ience o human
planne s.
In his pape , we in oduce a no el a ian o he Vehicle Rou -
ing P oblem (VRP) called he Selec i e Mul iple Depo Pickup and
Deli e y P oblem wi h Mul iple Time Windows and Pai ed Demand
(SMDPDPMTWPD). This p oblem models a uck backhauling sys em
in which companies u ilize eigh exchange pla o ms o iden i y and
acqui e p o i able o de s selec i ely, le e aging emp y ucks o execu e
deli e ies. The main mo i a ion o s udying he SMDPDPMTWPD is
o op imize uck backhauling ope a ions h ough eigh exchange
pla o ms, educing emp y miles, lowe ing emissions, and alle ia ing
oad conges ion.
As an inhe en ly NP-ha d p oblem, he SMDPDPMTWPD p esen s
signi ican compu a ional challenges, especially o la ge-scale ins a-
nces. To e ec i ely add ess hese complexi ies, ad anced me aheu is ic
algo i hms a e essen ial. As no ed in [5], he exis ing li e a u e on
mul i-depo backhauling wi h selec i e o de s is limi ed, highligh ing
he impo ance o his esea ch. This pape add esses he iden i ied
esea ch gap (see Sec ion 2.4) by in eg a ing ea u es such as (i) uck
capaci y cons ain s, (ii) selec i e o de s, (iii) mul iple ime windows,
and (i ) mul iple depo s, ac oss ou dis inc objec i e unc ions. The
main con ibu ions o his pape a e as ollows.
•We in oduce a no el ex ension o he VRP ha add esses he
eme ging challenges aced by logis ics companies using eigh
exchange pla o ms. This p oblem is e e ed o as he Selec i e
Mul iple Depo Pickup and Deli e y P oblem wi h Mul iple Time
Windows and Pai ed Demand (SMDPDPMTWPD). We o mula e
he SMDPDPMTWPD as a MILP o op imize he non-compulso y
pickup o o de s o e u n ips. Addi ionally, We ex end he
SMDPDPMTWPD o p oposed h ee p oblem a ian s: (i) p o i
maximiza ion including CO2 cos s, (ii) so ime windows, and (iii)
so ime windows including CO2 cos s.
•We de elop an e ec i e Adap i e La ge Neighbo hood Sea ch
(ALNS) me aheu is ic wi h a Simula ed Annealing accep ance c i-
e ion o sol e he SMDPDPMTWPD. To enhance he pe o mance
o ALNS, se e al des oy and epai ope a o s a e adap ed and
ailo ed om he li e a u e. ALNS can be seamlessly connec ed o
eigh exchange pla o ms o educe cos s and inc ease e enues
o anspo a ion companies.
•To e alua e ou op imiza ion app oaches, we compa e he pe o -
mance agains ano he me aheu is ic conside ing bo h ins ances
adap ed om he li e a u e as well as new ins ances based on a
eal case. Expe imen s using hese ins ances ensu e he alidi y o
ou app oach and p o ide a eliable indica ion o he bene i o
using ou app oach in eal-wo ld condi ions.
•We p o ide decision-make s wi h insigh s in o he e ec i eness
o using eigh exchange pla o ms o educe emp y kilome e s
du ing e u n ips. Fu he mo e, we analyze he impac o a i-
ous SMDPDPMTWPD p oblem a ian s on he ou ing schedules
gene a ed by ou op imiza ion app oaches.
The emainde o his pape is o ganized as ollows. A li e a u e
e iew is p esen ed in Sec ion 2. Then, Sec ion 3 ma hema ically o mu-
la es he SMDPDPMTWPD. Sec ion 4 desc ibes ou ALNS me aheu is ic
algo i hm. Sec ion 5 p esen s he nume ical expe imen s, pa ame e
uning, and esul s. We end wi h conclusions and u u e esea ch
di ec ions in Sec ion 6.
2. Li e a u e e iew
Pickup and deli e y p oblems (PDPs) a e a special ca ego y o
ehicle ou ing p oblems (VRPs) whe e ehicles mus ul ill a se ies
o pickup and deli e y eques s [6]. The e a e se e al a ian s o he
PDP, such as he Vehicle Rou ing P oblem wi h Simul aneous Pickup
and Deli e y (VRPSPD), he Pickup and Deli e y Vehicle Rou ing P ob-
lem wi h Time Windows (PDVRPTW), and he Pickup and Deli e y
P oblem wi h Loading Cons ain s. This sec ion e iews he ele an
li e a u e on PDPs ha include key ea u es o he SMDPDPMTWPD,
such as mul iple depo s, cus ome selec ion, ime windows, and pai
demand. Sec ion 2.1 e iews he li e a u e on he Selec i e Full T uck-
load Mul iple Depo Vehicle Rou ing P oblem wi h Time Windows.
Then, Sec ion 2.2 e iews he li e a u e on he Mul iple Depo Pickup
and Deli e y P oblem wi h Time Windows. A e ha , Sec ion 2.3
e iews he li e a u e on he Selec i e Pickup and Deli e y P oblem
wi h Time Windows and Pai ed Demand. Finally, Sec ion 2.4 p esen s
he iden i ied esea ch gap ha we aim o b idge wi h his pape .
2.1. The selec i e ull uckload mul iple depo ehicle ou ing p oblem wi h
ime windows
The Selec i e Full T uckload Mul iple Depo Vehicle Rou ing P ob-
lem wi h Time Windows (SFTMDVRPTW) deals wi h emp y e u n
scena ios, whe e o de s a e selec ed and ucks a e ou ed ac oss mul-
iple depo s o deli e o pick up ull uckloads while espec ing
cus ome ime windows. The goal is o selec a subse o Full T uck-
load (FTL) o de s o cus ome s, assign cus ome s o ehicles, and ind
he op imal ou e o all ehicles ha maximizes p o i om se ing
cus ome s while espec ing ime-window cons ain s. Each o de has
an associa ed e enue, cos , pickup and deli e y loca ion, and pickup
and deli e y ime windows. In he SFTMDVRPTW, bo h he ea lies
depa u e and la es a i al ime o each ehicle o espec i ely begin
and comple e i s ou e a e known in ad ance. Fu he mo e, anspo a-
ion cos s o emp y kilome e s and penal y cos s o wai ing a e also
known in ad ance o he case when a uck a i es ea ly a a pickup
o deli e y loca ion [5,7–11].
In he li e a u e, we ha e iden i ied a small esea ch s eam ha
ocuses on he SFTMDVRPTW, which consis s o six pape s om he
same au ho s [5,7–11]. We summa ize he SFTMDVRPTW li e a u e in
Table 1. O e all, he au ho s ea he same ma hema ical model and
sol e ins ances o di e en sizes wi h hei op imiza ion app oaches.
Only one pape implemen s an exac app oach wi h CPLEX o sol e
ins ances o up o hi y cus ome s and h ee ucks [9]. El Bouyahyiouy
and Bellabdaoui [9] sol e o op imali y wen y- wo ou o wen y- h ee
ins ances wi hin h ee minu es o compu a ional ime, achie ing an op-
imali y gap o 5.58% o he emaining ins ance. Di e en app oxima e
app oaches a e implemen ed in he o he pape s: An Colony Op i-
miza ion algo i hm (ACO) [8], Gene ic Algo i hm (GA) [5,7,11], and a
ans o ma ion in combina ion wi h Reac i e Tabu Sea ch (RTS) [10].
2.2. The mul iple depo pickup and deli e y p oblem wi h ime windows
The Mul iple Depo Pickup and Deli e y P oblem wi h Time Win-
dows (MDPDPTW) deals wi h ou ing ehicles o se e cus ome o de s,
each consis ing o a pickup and deli e y eques . Each pickup eques
is di ec ly assigned o exac ly one deli e y eques . Thus, he demand
is pai ed, i.e., one- o-one [12]. Ex ensions o he MDPDPTW conside
o he ypes o assigna ions, whe e i is possible o ha e mul iple pickup
o deli e y eques s o a single commodi y, i.e., one- o-many o many-
o-many. The goal is o minimize he ou ing cos s o ehicles s a ing
om mul iple depo s such ha all cus ome s a e se ed, while consid-
e ing ime windows, capaci y, and p ecedence ela ions, i.e., a pickup
loca ion mus be i s isi ed be o e p oceeding o i s co esponding
deli e y loca ion. Acco ding o Ve donck [13], he MDPDPTW has no
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
2
D. Roelink e al.
Table 1
O e iew o he analyzed li e a u e on he SFTMDVRPTW, wi h MD = Mul iple Depo s, F = Flee (whe e HE = He e ogeneous and HO = Homogeneous), TW = Time Windows,
C = Capaci y, S = Selec ion, E = Exac , A = App oxima e, N = Cus ome s and K = Vehicles.
Re e ence P oblem ea u es Objec i e unc ion E/A Sol ing Ins ance size
MD F TW C S me hod (N, K)
El Bouyahyiouy and Bellabdaoui [7]✓HO ✓ ✓ Max o p o i , consis ing
o (1) e enue, (2) mo ing
cos s, (3) emp y cos s and
(4) wai ing cos
A GA (13, 3)
El Bouyahyiouy and Bellabdaoui [8]✓HO ✓ ✓ ‘‘’’ A ACO (12, 2)
El Bouyahyiouy and Bellabdaoui [9]✓HO ✓ ✓ ‘‘’’ E CPLEX Up o (30, 3)
El Bouyahyiouy and Bellabdaoui [10]✓HO ✓ ✓ ‘‘’’ A RTS Up o (75, 7)
El Bouyahyiouy and Bellabdaoui [5]✓HO ✓ ✓ ‘‘’’ A GA Up o (75, 7)
El Bouyahyiouy and Bellabdaoui [11]✓HO ✓ ✓ ‘‘’’ A GA + CPLEX Up o (75, 7)
This wo k ✓HE ✓ ✓ ✓ Max p o i , consis ing o
(1) e enue, (2) mo ing
cos s, (3) d i e cos s and
(4) se ing cos s
E & A Sol e & ALNS Up o (250, 7)
been esea ched in dep h. The ele an li e a u e on he MDPDPTW is
summa ized in Table 2.
Dumas e al. [14] analyze he MDPDPTW and p oposed an exac
algo i hm based on column gene a ion (CG) and cons ained sho es
pa h o sol e he pickup and deli e y p oblem. The p oposed algo i hm
can handle mul iple depo s and a he e ogeneous ehicle lee , showing
a be e pe o mance i each cus ome has a la ge demand and he ca-
paci y cons ain s a e es ic i e. Then, Jung and Haghani [15] add ess
he same p oblem bu conside only one depo and an adap ed objec i e
unc ion. Ins ead o only minimizing he ou ing cos s, hey also in-
clude he ixed cos s o using he ehicles and cus ome incon enience
(penal y) cos s due o he iola ion o he ime windows. They assess
hei op imiza ion app oaches, showing ha a Gene ic Algo i hm ound
he same op imal solu ions as he MILP and ou pe o ms he MILP o
la ge ins ances. Addi ionally, a GA is also used in [16] o sol e he
MDPDPTW, whe e o al ou e leng h is minimized.
Ropke and Pisinge [17] s udy an MDPDPTW a ian wi h an ob-
jec i e unc ion encompassing mul iple cos aspec s. In hei MILP
o mula ion, he objec i e unc ion consis s o a weigh ed sum o (1)
he dis ance a eled, (2) he ime spen by each ehicle, and (3) he
numbe o eques s no scheduled. This las elemen is pa icula ly
in e es ing, as [17] conside o de selec ion in hei model. Namely,
some o de s may be assigned o a i ual eques bank, whe e an
ope a o has o handle hem. Fo ins ance, do no hing o hi e ex a
ehicles. The model, howe e , does no dis inguish be ween di e en
o de s and only includes penal y cos s o he o al numbe o o de s
no se ed. Thus, he e is no p o i o cos associa ed wi h each in-
di idual o de . To sol e he MDPDPTW a ian , hey de eloped an
Adap i e La ge Neighbo hood Sea ch (ALNS) heu is ic, which was he
i s appea ance o his me hod. In [13,18], he au ho s implemen he
same me aheu is ic o s udy he collabo a ion be ween anspo a ion
companies. The au ho s o bo h pape s o mula e hese p oblems as an
MDPDPTW, whe e he ou ing cos s a e minimized and sha ed using
game heo e ic p inciples. The collabo a ion be ween anspo a ion
companies and he ans o ma ion o he p oblem o an MDPDPTW is
also s udied in [19], whe e he au ho s implemen a di e en sol ing
me hod, ha is, a modi ied e sion o he heu is ic-sol e ROUTER.
Baldacci e al. [20] p opose an exac algo i hm o sol e a sin-
gle depo a ian o he MDPDPTW. The algo i hm is based on a
se -pa i ioning-like in ege o mula ion. The au ho s desc ibe and im-
plemen bounding p ocedu es ha can ind nea -op imal dual solu ions
o he LP- elaxa ion. Heilig e al. [21] sol e he mul i-objec i e MD-
PDPTW implemen ing a Simula ed Annealing (SA) algo i hm. Al hough
he main ocus is on in e - e minal anspo and no on he MDPDPTW,
he au ho s a gue ha his p oblem can be modeled as an MDPDPTW,
whe e he objec i e unc ion consis s o ou ing cos s, delay penal ies,
and se ice imes. Adi e al. [22] also ocuses on in e - e minal ans-
po bu sol es he p oblem using a di e en op imiza ion app oach:
Rein o cemen Lea ning (RL). They compa e he pe o mance o his
app oach wi h wo o he me aheu is ic app oaches om li e a u e,
i.e., Simula ed Annealing and Tabu Sea ch. They conclude ha hei
RL algo i hm ou pe o ms he o he app oaches.
Finally, in [23,24], he au ho s conside he MDPDPTW o minimize
he o al ou e leng h and sol e i using a Pa icle Swa m Op imiza ion
(PSO) algo i hm. A e es ing he app oaches on a la ge da a se ,
bo h au ho s concluded ha PSO ou pe o ms o he me hods used in
li e a u e o sol e hese p oblem a ian s.
2.3. The selec i e pickup and deli e y p oblem wi h ime windows and
pai ed demand
In he Selec i e Pickup and Deli e y P oblem wi h Time Windows
and Pai ed Demands (SPDPTWPD) each cus ome o de is associa ed
wi h one pickup and deli e y loca ion. Thus, o de s a e pai ed one-
o-one, meaning ha each pickup eques is exac ly linked o one
deli e y eques , and a gi en good can only be deli e ed i i s pickup
has occu ed. The goal is o selec a subse o cus ome s and design
ou es o he ehicles o e icien ly se e he selec ed cus ome s while
adhe ing o ime windows, capaci y, and p ecedence cons ain s. Table
3 summa izes he ela ed li e a u e on he SPDPTWPD.
The selec i e pickup and deli e y p oblems a e ela i ely ecen ,
s a ing wi h Ting and Liao [25]. Al hough no ime windows and pai ed
o de s a e conside ed, he p oblem is s ill ele an o his e iew, as he
model is simila o a ian s inco po a ing ime windows and pai ed
o de s. Tha is, only ew adap ions a e necessa y o inco po a e he
abo e-men ioned ea u es. The p oblem is NP-ha d, acco ding o he
au ho s, and, as a esul , sol ed using a me aheu is ic called Meme ic
Algo i hm (MA). Ting e al. [26] p opose a mul i- ehicle e sion o
he ea lie model, wi h an addi ional es ic ion on he maximum
a el dis ance. The model is sol ed using h ee di e en me aheu is ics
app oaches, ha is, Tabu Sea ch (TS), Gene ic Algo i hm, and Sca e
Sea ch (SS). The esul s show ha he Tabu Sea ch ou pe o ms he
o he wo me aheu is ics in solu ion quali y and con e gence speed.
Fi e pape s om he same au ho s ha e appea ed on he
SPDPTWPD [27–31]. Howe e , he objec i es, sol ing me hods, and
ma hema ical o mula ions a e di e en ac oss he a icles. Mos o
he models in hese pape s a e sol ed u ilizing he op imiza ion sol e
Gu obi [27,28,31]. Fu he mo e, only wo scien i ic pape s a e sol ed
by implemen ing me aheu is ics app oaches, ha is, Hyb id GA [29]
and an ex ension o Tabu-embedded Simula ed Annealing [30]. Addi-
ionally, single- and mul i-objec i e unc ions a e s udied wi h p o i
maximiza ion and dis ance minimiza ion.
Besides ha , he au ho s ha e also s udied mul i-pe iod [32] and
obus [33,34] e sions o he p oblem, e.g., adding scena ios wi h
unce ain a eling imes, which a e sol ed wi h Hyb id GA, G eedy
Randomized Adap i e Sea ch P ocedu e (GRASP), and a combina ion
o GRASP wi h ALNS.
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
3
D. Roelink e al.
Table 2
O e iew o he analyzed li e a u e on he MDPDPTW, wi h MD = Mul iple Depo s, F = Flee (whe e HE = He e ogeneous and HO = Homogeneous), TW = Time Windows, C =
Capaci y, S = Selec ion, E = Exac , A = App oxima e, N = Cus ome s and K = Vehicles.
Re e ence P oblem ea u es Objec i e unc ion E/A Sol ing Ins ance size
MD F TW C S me hod (N, K)
Dumas e al. [14]✓HE ✓ ✓ Min ou e cos s E CG Up o (55, 22)
Jung and Haghani [15] HE ✓ ✓ Min sum o ou e, usage
and incon enience cos s
A GA Up o (30, 10)
Ropke and Pisinge [17]✓HE ✓ ✓ ✓ Min weigh ed sum o (1)
dis ance a eled, (2) ime
spen by each ehicle and
(3) eques s no scheduled
A ALNS Up o (1000, 2759)
K ajewska e al. [18]✓HO ✓ ✓ Min ou e cos s A ALNS Up o (250, 39)
Baldacci e al. [20] HO ✓ ✓ Min ou e cos s w/wo
ixed cos s
E Se pa i ioning
+ sol e o
algo i hm
Up o (1000,100)
Dahl and De igs [19]✓HE ✓ ✓ Unknown A Modi ied e sion
o ROUTER
Unknown
Alaïa e al. [16]✓HO ✓ ✓ Min o ou e leng h A GA Up o (52, 24)
Alaïa e al. [23]✓HO ✓ ✓ Min o ou e leng h A PSO Up o (53, 25)
Heilig e al. [21]✓HO ✓Min sum o ou e, penal y
and se ice imes cos s
A SA Up o (70, 17)
Ve donck [13]✓HO ✓ ✓ Min ou e cos s A ALNS Up o (120, 5)
Ha baoui D idi e al. [24]✓HO ✓ ✓ Min o al ou e leng h A PSO Up o (53, 25)
Adi e al. [22]✓HO ✓ ✓ Min usage, penal ies,
emp y- uck and wai ing
cos s
A RL Up o (285, 3)
This wo k ✓HE ✓ ✓ ✓ Max p o i , consis ing o
(1) e enue, (2) mo ing
cos s, (3) d i e cos s and
(4) se ing cos s
E & A Sol e & ALNS Up o (250, 7)
The au ho s o he p e ious pape s ha e also con ibu ed o o he
wo ks [37,38]. In [37], he au ho s implemen ed a hyb id Pa icle
Swa m Op imiza ion (PSO), whe e he PSO is combined wi h local
sea ch p ocedu es o sol e a mul iple objec i e model. The au ho s
analyze a Pa e o on o each ins ance, whe e p o i maximiza ion and
dis ance minimiza ion a e op imized as objec i e unc ions. In [38],
he au ho s ocus on an ex ension called he Selec i e Pickup and
Deli e y P oblem wi h T ans e s (SPDPT). In he SPDPT, T ans e s
mean ha goods can be ans e ed om one ehicle o ano he on
special consolida ion o ans e poin s. The model includes a max–min
objec i e unc ion, i.e., p o i maximiza ion and dis ance minimiza ion,
and is sol ed using a hyb id PSO.
Li e al. [35] s udy an ex ension o he SPDPTWPD, namely he
Pickup and Deli e y P oblem wi h Time Windows, P o i s, and Re-
se ed Reques s (PDPTWPR). This p oblem models ca ie collabo a-
ion ac ions, whe e one pa o he o de s is ese ed o each ca ie ,
i.e., manda o y o be se ed. Then, a second pa is selec i e, meaning
ha hey may be se ed by he co esponding ca ie o o he ca ie s
o comple ely ejec ed. To sol e he PDPTWPR, he au ho s de elop
an ALNS me aheu is ic wi h a me a-des oy mechanism and a dynamic
adjus men o ope a o beha io (DAOB). Resul s show ha ALNS
inds he same op imal solu ions as he MILP o mula ion o small
ins ances o up o 50 eques s, and ou pe o ms he MILP o mula ion
o la ge ins ances o up o 100 eques s. Gans e e e al. [36] s udy
ano he ex ension called he Mul i-Vehicle P o i able Pickup and Deli -
e y P oblem (MVPPDP). The au ho s o mula e he MVPPDP as a MILP
and de elop a me aheu is ic amewo k based on Gene al Va iable
Neighbo hood Sea ch (GVNS). They compa e he GVNS pe o mance
o a Guided Local Sea ch (GLS) based me aheu is ic. Resul s show ha
he GVNS ou pe o ms he GLS-based me aheu is ic in e ms o solu ion
quali y bu a he expense o highe compu a ional imes.
Sun e al. [39] p esen a p oblem a ian whe e a el imes a e
dependen on he ime o he day. This p oblem is called he Time-
Dependen P o i able Pickup and Deli e y P oblem wi h Time Windows
(TDPPDPTW). The au ho s a gue ha he wo k o [35,36] a e he only
pape s co e ing simila ma hema ical models. The au ho s implemen
an ALNS me aheu is ic o op imize p o i maximiza ion. The mos
ecen scien i ic pape s udying he TDPPDPTW is p esen ed in [40],
whe e bo h a PDPTWPR and a mul i-objec i e SPDPTWPD a e sol ed.
The au ho s a gue ha he ela ed li e a u e mainly add esses single ob-
jec i es and limi ed esea ch is ocused on sol ing bi-objec i e p oblem
a ian s. The au ho s de elop a wo-phase heu is ic amewo k (Pa e o
Local Sea ch), based on he decomposi ion o he sea ch space.
In addi ion o he p e iously discussed li e a u e, we highligh he
Team O ien ee ing Pickup and Deli e y P oblem wi h Time Windows
(TOPDPTW) in oduced in [41]. The TOPDPTW deploys a lee o ucks
o maximize he p o i om selec ing pickup and deli e y o de s, while
adhe ing o ha d ime windows and capaci y cons ain s. To sol e
his p oblem, he au ho s p oposed a b anch-and-p ice (BP) algo i hm
enhanced wi h a p uning echnique, which signi ican ly accele a es
he solu ion o he associa ed subp oblem, educing compu a ional
imes by 67%. Mos esea ch on he TOPDPTW ei he in oduces new
p oblem a ian s wi h simila cha ac e is ics o de elops al e na i e BP
algo i hms wi h compa able ea u es [42–44]. Fu he mo e, o he bes
o ou knowledge, no me aheu is ic algo i hm has been p oposed o
sol e la ge ins ances o he TOPDPTW han hose add essed in he
o iginal pape .
2.4. Resea ch gap
Se e al simila i ies and di e ences eme ge when compa ing he key
ea u es o he analyzed anspo a ion p oblems. Table 4 p o ides a
compa a i e o e iew o he ou p oblems mos closely ela ed and
hei ela ion o ou wo k. To he bes o ou knowledge, no exis ing
esea ch examines an op imiza ion p oblem ha e ec i ely add esses
he logis ics challenges ha anspo a ion companies ace when using
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
4
D. Roelink e al.
Table 3
O e iew o he analyzed li e a u e on he SPDPTWPD, wi h MD = Mul iple Depo s, F = Flee (whe e HE = He e ogeneous and HO = Homogeneous), TW = Time Windows, C =
Capaci y, S = Selec ion, E = Exac , A = App oxima e, N = Cus ome s and K = Vehicles.
Re e ence P oblem ea u es Objec i e unc ion E/A Sol ing Ins ance size
MD F TW C S me hod (N, K)
Ting and Liao [25] HO ✓ ✓ Min ou e cos s A MA based on GA Up o (500, 1)
Li e al. [35] HE ✓ ✓ ✓ Max p o i om selec ed
o de s
A ALNS Up o (100, ?)
Al Chami e al. [27]✓HE ✓ ✓ ✓ Max p o i om o min
dis ance o selec ed o de s
E Gu obi sol e Up o (100, 11)
Al Chami e al. [28]✓HE ✓ ✓ ✓ Max p o i om and/o
min dis ance o selec ed
o de s (bo h single and
mul i-obj)
E Gu obi sol e Up o (100, 13)
Al Chami e al. [29]✓HE ✓ ✓ ✓ Max p o i om and min
dis ance o selec ed o de s
(mul i-obj)
A Hyb id GA Up o (100, 11)
Ting e al. [26] HO ✓ ✓ Min ou e cos s A TS, GA and SS Up o (480, 22)
Gans e e e al. [36] HO ✓ ✓ Max p o i om selec ed
o de s
S GVNS Up o (1000, 8)
Al Chami e al. [33] HO ✓ ✓ ✓ Max p o i om selec ed
o de s
A GRASP Up o (100, 11)
Al Chami e al. [32] HE ✓ ✓ ✓ Min dis ance o selec ed
o de s
A Hyb id GA Up o 50 in 10 pe iods
Al Chami e al. [30]✓HE ✓ ✓ ✓ Max p o i om and min
he dis ance o selec ed
o de s (mul i-obj)
A Tabu SA Up o (100, 13)
Al Chami e al. [31]✓HO ✓ ✓ ✓ Max p o i om selec ed
o de s
E Gu obi sol e Up o (100, 11)
Peng e al. [37] HE ✓ ✓ ✓ Max p o i om and min
dis ance o selec ed o de s
(mul i-obj)
A Hyb id PSO Up o (100, 13)
Peng e al. [38] HE ✓ ✓ ✓ Max p o i om and min
dis ance o selec ed o de s
(mul i-obj)
A Hyb id PSO Up o (100, ?)
Sun e al. [39] HO ✓ ✓ ✓ Max p o i om selec ed
o de s minus a el
du a ion cos s minus se up
cos s
A ALNS Up o (75, 4)
Al Chami e al. [34] HO ✓ ✓ ✓ Max p o i om selec ed
o de s
A GRASP + ALNS Up o (100, 11)
Ben-Said e al. [40] HO ✓ ✓ ✓ Max p o i om selec ed
o de s and min a el cos s
(mul i-obj)
A Two phase
Pa e o LS
Up o (100, 13)
This wo k ✓HE ✓ ✓ ✓ Max p o i , consis ing o
(1) e enue, (2) mo ing
cos s, (3) d i e cos s and
(4) se ing cos s
E & A Sol e & ALNS Up o (250, 7)
eigh exchange pla o ms o e u n ips o emp y ucks. The com-
pa ison in Table 4 highligh s ha while he e iewed p oblems sha e
simila i ies wi h ou esea ch, none ully cap u e he p oblem add essed
in his pape . Speci ically, he SFTMDVRPTW conside s only ull uck-
loads, he MDPDPTW lacks o de selec ion, and he SPDPTWPD does
no accoun o mul iple depo s o di e en s a ing and ending de-
po s. Likewise, he TOPDPTW excludes ou ing cos s, p e en ing a
ealis ic e alua ion o he bene i s o eigh exchange pla o ms. Fu -
he mo e, none o hese models inco po a e mul iple ime windows
o (un)loading o he possibili y o mul iple ending depo s pe uck.
This esea ch gap p esen s signi ican missed oppo uni ies o eigh
exchange pla o m use s, leading o limi ed compe i i eness o small
anspo companies and ine icien eigh ma ching in he ma ke .
Hence, we b idge his esea ch gap by (i) de ining his anspo a ion
p oblem as he SMDPDPMTWPD and p oposing a ma hema ical o -
mula ion (see Sec ion 3), and (ii) de eloping an ALNS me aheu is ic
amewo k (see Sec ion 3) o e icien ly sol e la ge-scale ins ances
wi hin easonable compu a ional imes.
3. The selec i e mul iple depo pickup and deli e y p oblem wi h
mul iple ime windows and pai ed demand
This sec ion o mally in oduces he SMDPDPMTWPD. A de ailed
desc ip ion o he p oblem is p o ided in Sec ion 3.1. Then, Sec ion 3.2
enume a es he assump ions ha a solu ion mus sa is y. Finally, Sec-
ion 3.3 p esen s a ma hema ical o mula ion o he SMDPDPMTWPD.
3.1. P oblem desc ip ion
The SMDPDPMTWPD is de ined o e a di ec ed g aph = (,),
wi h node se and a c se . The node se is de ined as =
∪∪∪′ and he a c se as = {(𝑖, 𝑗)|𝑖∈, 𝑗 ∈} ∪ {(𝑖, 𝑗)|𝑖, 𝑗 ∈
∪∶𝑖≠𝑗} ∪ {(𝑖, 𝑗)|𝑖∈, 𝑗 ∈′}, whe e = {𝜏1,…, 𝜏𝐾} is
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
5
D. Roelink e al.
Table 4
Compa ison o he ea u es o he e iewed model and he model o his esea ch, wi h RC = Rou ing Cos s, P = P o i , CO2=CO2 emissions, C = Capaci y, S = Selec ion, PD =
Pai ed Demand, MLU = Mixed Loading/Unloading and Di = Di e en .
Ac onym Objec i e Depo Time window C S PD MLU
RC P CO2Mul i Di s a & end Mul i end Single Mul i
SFTMDVRPTW ✓ ✓ ✓ ✓ ✓ ✓ ✓
MDPDPTW ✓ ✓ ✓ ✓ ✓ ✓ ✓
SPDPTWPD ✓ ✓ ✓ ✓ ✓ ✓
TOPDPTW ✓ ✓ ✓ ✓ ✓ ✓ ✓
This wo k ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
he se o s a ing depo s, ′= {𝜏′
1,…, 𝜏′
𝐾} he se o ending depo s,
= {1,…, 𝑛} is he se o pickup loca ions, = {𝑛+1,…,2𝑛} is he
se o deli e y loca ions, and = {1,…, 𝐾} is he se o ucks. Fo
simplici y, we de ine =∪′ as he depo se and =∪ as
he se o o de s. He e, 𝜏′= {𝜏′
𝑘1,…, 𝜏′
𝑘𝑚𝑘} is he se o a ailable ending
depo s o uck 𝑘∈, whe e 𝑚𝑘 is he o al numbe o ending depo s
o uck 𝑘. Fu he mo e, se 𝑖= {1,…, 𝑀𝑖} g oups he a ailable ime
windows a loca ion 𝑖∈, whe e 𝑀𝑖 is he o al numbe o a ailable
ime windows a loca ion 𝑖.
The SMDPDPMTWPD consis s o selec ing o de s om a la ge se
o o de s, e.g., eigh exchange pla o ms, and de e mining op imal
ou es o a se o ucks o maximize p o i . Each uck 𝑘∈ has
a maximum capaci y 𝑄𝑘 and should execu e he pickup and deli e y
ope a ions a loca ion 𝑖∈, wi hin one o he 𝑡∈𝑖 he ime-window
in e als [𝑒𝑡
𝑖, 𝑙𝑡
𝑖] and wi h a du a ion o 𝑠𝑖. Ea ly a i als a he pickup
and deli e y loca ions a e allowed, bu ehicles should wai un il he
ime window becomes a ailable. La e a i al imes a e no allowed,
excep o he so ime-window a ian . Thus, in he SMDPDPMTWPD,
ucks should anspo 𝑞𝑖 goods om pickup loca ions 𝑖∈ o deli e y
loca ions 𝑗∈, whe e e enue 𝑝𝑖 is ea ned, se ice cos s 𝑐𝑖 a e
incu ed, and d i e s’ wages o 𝑓𝑡 should be paid pe uni o ime.
Addi ionally, o each a c (𝑖, 𝑗) ∈ 𝐴 he e is an associa ed a el cos
𝑐𝑖𝑗 , dis ance 𝑑𝑖𝑗 , and a el ime 𝑡𝑖𝑗 .
The objec i e unc ion op imizes he selec ion o o de s and uck
ou ing schedules o maximize p o i , while espec ing ime-window
cons ain s, maximum capaci y, maximum weigh , and p ecedence con-
s ain s, i.e., deli e ies can only be execu ed a e picking up he o de s.
The p o i is calcula ed as he summa ion o all e enues minus he
in ol ed cos s, consis ing o : (i) anspo a ion cos s, (ii) se ice cos s,
and (iii) d i e s’ wages. Hence, in he SMDPDPMTWPD, he ollowing
decisions need o be made: (i) i ehicle 𝑘∈ a els om loca ion
𝑖∈⧵′ o 𝑗∈⧵, (ii) i se ice a loca ion 𝑖∈ is execu ed
du ing ime window 𝑡∈𝑖, (iii) wai ing ime o uck 𝑘∈ due o
ea ly a i al ime a loca ion 𝑖∈⧵, (i ) load and weigh on uck
𝑘∈ when lea ing loca ion 𝑖∈, and ( ) a i al and depa u e ime
o uck 𝑘∈ a loca ion 𝑖∈. Fig. 1 illus a es an example easible
ou ing schedule o he SMDPDPMTWPD.
The example illus a es a solu ion wi h 𝐾=3 ehicles and 𝑛=5 o -
de s in he selec ion pool, e.g., o de s a ailable on he eigh exchange
pla o m, whe e depo s a e depic ed by squa es and he o de s a e
ep esen ed by ci cles o nodes. The g een and o ange squa es ep esen
he s a () and ending (′) depo s, espec i ely. Simila ly, he blue
and g ay nodes show he selec ed and unselec ed o de s. Addi ionally,
diamonds ep esen he co esponding ucks, indica ing he s a and
ending depo s o each ehicle. Wi hin he ci cles, he numbe s ep esen
he o de s, whe eas he plus (+) and minus (−) symbols show i hey
co espond o a pickup () o deli e y () loca ion. Fo cla i y, he
illus a ion does no display o de weigh s, ime windows, o ehicle
capaci y. Howe e , i is impo an o no e ha a easible solu ion
mus sa is y hese cons ain s. Fu he mo e, each pickup and deli e y
loca ion mus ha e a leas one ime window.
In he solu ion, each ehicle depa s om a di e en s a loca ion
and may ha e mul iple ending depo s. Fo example, uck 1 can a i e
a depo s 9 o 10, while ucks 2 and 3 each ha e a single designa ed
ending depo . Based on e enue and associa ed cos s ( a el, se ice,
and d i e wages), o de s 4, 5, and 7 a e selec ed o he e u n ips
o ucks 1 and 2. Con e sely, uck 3 a els di ec ly om depo 3 o
10, as he emaining o de s ei he ail o gene a e addi ional p o i o
canno be accommoda ed due o ime-window o capaci y cons ain s.
This shows he lexibili y o he SMDPDPMTWPD in modeling eal-
wo ld scena ios encoun e ed by companies using eigh exchange
pla o ms. Hence, i an o de is unp o i able o a uck canno mee
i s cons ain s, he sys em ensu es ha he ehicle p oceeds di ec ly o
i s assigned depo . Addi ionally, ucks can pick up and deli e o de s
simul aneously, as seen in he ou e o uck 1. Ins ead o a eling
di ec ly om depo 1 o depo 9 o 10, uck 1 de ou s o pick up o de s
4 and 7, maximizing he inal p o i .
3.2. P oblem assump ions
The SMDPDPMTWPD is a anspo a ion p oblem ha models he
challenge o using eigh exchange pla o ms o educe cos s o max-
imize p o i s o emp y ucks in hei e u n ips. Consequen ly, o
p ope ly model hese anspo a ion dynamics, he undamen al as-
sump ions o he SMDPDPMTWPD a e ou lined as ollows:
•An o de can only be selec ed i he ime window cons ain s a e
sa is ied o bo h pickups and deli e ies.
•Each o de has one pickup and one deli e y loca ion, which can
be se ed by a mos one ehicle.
•Di ec pai ed o de s a e conside ed. Each pickup loca ion is di-
ec ly pai ed wi h a speci ic deli e y loca ion. Thus, pai ed o de s
mus be handled by he same ehicle.
•Sequen ial pickup and deli e y ope a ions a e allowed. Hence,
in he same ip, ucks should i s pickup he goods be o e
deli e ing hem.
•Each ehicle depa s om one s a ing depo and may ha e one
o se e al possible ending depo s o a i e.
•Each ehicle can only s a om i s s a ing depo a e he
s a ing ime has passed. Simila ly, a ehicle mus a i e a one
o he ending depo s be o e i s co esponding closing ime.
•Vehicles can a i e ea lie han he opening ime o he ime
windows a he pickup and deli e y loca ions. Howe e , ehicles
ha e o wai un il he ime windows become a ailable o pe o m
he se ice.
•A ehicle 𝑘 canno load mo e han i s maximum capaci y 𝑄𝑘. The
capaci y 𝑄𝑘 is measu ed in Loading Me e s (LDM; see explana ion
below).
We exp ess he capaci y o ucks in loading me e s (LDM). LDMs
a e a common measu emen uni in oad anspo o a eigh ha is
no s ackable [45]. One LDM is equi alen o 1.00 m leng h om he
back o a aile . A s anda d aile has a wid h o 2.4 m and, hence, one
LDM is equi alen o 1.00 ×2.40 =2.40 m2 [46]. The LDM o eigh s
is calcula ed as shown in Eq. (1).
LDM =(leng h o eigh × wid h o eigh )
wid h o aile (1)
Measu ing he capaci y o ucks in LDM gene alizes he capaci y
ac oss di e en eigh s. Mos eigh s a e anspo ed on Eu opalle s,
wi h dimensions 1.20 by 0.80 m. A Eu opalle is, he e o e, equi alen
o (1.20 ×0.80)∕2.40 =0.40 LDMs. A s anda d uck wi h a capaci y o
13.60 LDM can, hus, ca y a o al o 13.60∕0.40 =34 Eu opalle s.
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
6
D. Roelink e al.
Fig. 1. Illus a ion o a easible solu ions o he SMDPDPMTWPD.
3.3. Ma hema ical model
The p o i maximiza ion SMDPDPMTWPD is o mula ed as a MILP
in Sec ion 3.3.1. Then, Sec ion 3.3.2 ex ends he SMDPDPMTWPD o
s udy he p o i maximiza ion including cos s o CO2 emissions. A e
ha , Sec ion 3.3.3 in oduces he so ime-window a ian . Finally,
Sec ion 3.3.4 p esen s an ex ension ha conside s so ime windows
and cos s o CO2 emissions.
3.3.1. The p o i maximiza ion SMDPDPMTWPD
Table 5 p esen s he se s and pa ame e s o he MILP o mula ion o
he p o i maximiza ion SMDPDPMTWPD, and he ex ensions p esen ed
in Sec ions 3.3.2, 3.3.3, and 3.3.4.
The ollowing decision a iables a e in ol ed:
𝑥𝑘
𝑖𝑗 =⎧
⎪
⎨
⎪
⎩
1,i ehicle 𝑘∈ a els om loca ion
𝑖∈∖′ o loca ion 𝑗∈∖
0,o he wise
𝑏𝑡
𝑖=⎧
⎪
⎨
⎪
⎩
1,i se ice akes place du ing ime window
𝑡∈𝑖 a loca ion 𝑖∈
0,o he wise
𝑤𝑖=wai ing ime (ea liness) be o e picking up o
deli e ing a loca ion 𝑖∈
𝑞𝑘
𝑖=load o ehicle 𝑘∈ when lea ing om loca ion 𝑖∈
ℎ𝑘
𝑖=weigh o ehicle 𝑘∈ when lea ing om loca ion 𝑖∈
𝑎𝑘
𝑖=a i al ime o ehicle 𝑘∈ a loca ion 𝑖∈
𝑑𝑘
𝑖=depa u e ime o ehicle 𝑘∈ a loca ion 𝑖∈
𝑦𝑘
𝑖=a i al ime o ehicle 𝑘∈ a loca ion 𝑖∈𝜏′
𝑘
The MILP o mula ion o he p o i maximiza ion SMDPDPMTWPD
is as ollows:
𝑀𝑎𝑥 𝑍 =∑
𝑘∈∑
𝑖∈∖′∑
𝑗∈∖∪{𝑖}(𝑝𝑗−𝑐𝑗−𝑐𝑖𝑗 )𝑥𝑘
𝑖𝑗 −∑
𝑘∈∑
𝑖∈𝜏′
𝑓𝑡𝑦𝑘
𝑖(2)
s. . ∑
𝑘∈∑
𝑗∈∖,
𝑗≠𝑖
𝑥𝑘
𝑖𝑗 ≤1𝑖∈(3)
∑
𝑗∈∖,
𝑗≠𝑖
𝑥𝑘
𝑖𝑗 =∑
𝑗∈∖,
𝑗≠𝑖
𝑥𝑘
(𝑛+𝑖)𝑗𝑖∈, 𝑘 ∈(4)
∑
𝑗∈∖′,
𝑗≠𝑖
𝑥𝑘
𝑗𝑖 =∑
𝑗∈∖,
𝑗≠𝑖
𝑥𝑘
𝑖𝑗 𝑖∈, 𝑘 ∈(5)
𝑥𝑘
𝑖𝑖 =0𝑖∈, 𝑘 ∈(6)
∑
𝑗∈∪𝜏′
𝑘
𝑥𝑘
𝜏𝑘𝑗=1𝑘∈(7)
∑
𝑖∈∑
𝑗∈∖
𝑥𝑘
𝑖𝑗 =1𝑘∈(8)
∑
𝑖∈∪𝜏𝑘∑
𝑧∈𝜏′
𝑘
𝑥𝑘
𝑖𝑧 =1𝑘∈(9)
∑
𝑖∈∖′∑
𝑗∈′
𝑥𝑘
𝑖𝑗 =1𝑘∈(10)
𝑑𝑘
𝑖≥𝑎𝑘
𝑖𝑖∈, 𝑘 ∈(11)
𝑎𝑘
(𝑛+𝑖)+𝑤(𝑛+𝑖)≥𝑎𝑘
𝑖+𝑤𝑖+𝑠𝑖+𝑡𝑖,(𝑛+𝑖)
−𝑀⎛⎜⎜⎝
1−∑
𝑗∈∖
𝑥𝑘
𝑖𝑗 ⎞⎟⎟⎠
𝑖∈, 𝑘 ∈(12)
𝑑𝑘
𝜏𝑘=∑
𝑡∈𝜏𝑘
𝑒𝑡
𝜏𝑘𝑏𝑡
𝜏𝑘𝑘∈(13)
𝑦𝑘
𝑗≥𝑎𝑘
𝑗−𝑎𝑘
𝜏𝑘
−𝑀⎛⎜⎜⎝
2−∑
𝑧∈𝑃∪𝜏′
𝑘
𝑥𝑘
𝜏𝑘𝑧−∑
𝑧∈𝐷∪𝜏𝑘
𝑥𝑘
𝑧𝑗 ⎞⎟⎟⎠
𝑗∈𝜏′
𝑘, 𝑘 ∈(14)
𝑎𝑘
𝑗≥𝑑𝑘
𝑖+𝑡𝑖𝑗 −𝑀(1−𝑥𝑘
𝑖𝑗 )𝑖∈∖′, 𝑗 ∈∖,
𝑘∈∶𝑖≠𝑗(15)
𝑎𝑘
𝑗≤𝑎𝑘
𝑖+𝑤𝑖+𝑠𝑖+𝑡𝑖𝑗 +𝑀(1−𝑥𝑘
𝑖𝑗 )𝑖∈∖′, 𝑗 ∈∖,
𝑘∈∶𝑖≠𝑗(16)
𝑑𝑘
𝑗≥𝑑𝑘
𝑖+𝑡𝑖𝑗 +𝑤𝑗+𝑠𝑗−𝑀(1−𝑥𝑘
𝑖𝑗 )𝑖∈∖′, 𝑗 ∈∖,
𝑘∈∶𝑖≠𝑗(17)
𝑤𝑗≥∑
𝑡∈𝑗
𝑒𝑡
𝑗𝑏𝑡
𝑗−(𝑑𝑘
𝑖+𝑡𝑖𝑗 +𝑀(1−𝑥𝑘
𝑖𝑗 )) 𝑖∈∖′, 𝑗 ∈∖,
𝑘∈∶𝑖≠𝑗(18)
𝑑𝑘
𝑖+𝑡𝑖𝑗 +𝑤𝑗+𝑠𝑗−𝑀(1−𝑥𝑘
𝑖𝑗 )≤∑
𝑡∈𝑗
𝑙𝑡
𝑗𝑏𝑡
𝑗𝑖∈∖′, 𝑗 ∈∖,
𝑘∈∶𝑖≠𝑗(19)
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
7
D. Roelink e al.
Table 5
Se s and pa ame e s o he MILP o mula ion o he p o i maximiza ion SMDPDPMTWPD and i s ex ensions.
Pa ame e s Se s
𝑛Numbe o o de s Di ec g aph, = {,}
𝐾Numbe o ehicles Node se , = {,}
𝑄𝑘Capaci y o ehicle 𝑘 (in LDMs) A c se , = {(𝑖, 𝑗)|𝑖∈, 𝑗 ∈} ∪
𝐻𝑘Maximum weigh allowed in ehicle 𝑘 (in kg’s) {(𝑖, 𝑗)|𝑖, 𝑗 ∈∪∶𝑖≠𝑗} ∪
ℎ𝑘
𝑠𝑡𝑎𝑟𝑡 S a weigh o ehicle 𝑘 (in kg’s) {(𝑖, 𝑗)|𝑖∈, 𝑗 ∈′}
[𝑒𝑡
𝑖, 𝑙𝑡
𝑖]Time window 𝑡 o loca ion 𝑖, whe e 𝑒𝑡
𝑖 and 𝑙𝑡
𝑖 a e he ime (in
minu es) on he cus om clock
O de se , =∪= {1,…,2𝑛}
𝑀Big numbe Pickup se , = {1,…, 𝑛}
𝑀𝑖Numbe s o ime windows du ing which (un)loading may
ake place a loca ion 𝑖
Deli e y se , = {𝑛+1,…,2𝑛}
𝑠𝑖Se ice ime o an o de o be (un)loaded a loca ion 𝑖,
whe e 𝑠𝑖=0 o a depo and 𝑠𝑖≥0 o any o he loca ion
Depo se , =∪′
𝑞𝑖Demand o an o de o be (un)loaded a loca ion 𝑖, whe e
𝑞𝑖≥0 o a pickup loca ion, 𝑞𝑖≤0 o a deli e y loca ion
and 𝑞𝑖=0 o a depo
S a loca ion se , = {𝜏1,…, 𝜏𝐾}
ℎ𝑖Weigh o an o de o be (un)loaded a loca ion 𝑖, whe e
ℎ𝑖≥0 o a pickup loca ion, ℎ𝑖≤0 o a deli e y loca ion
and ℎ𝑖=0 o a depo
′End loca ion se , ′= {𝜏′
1,…, 𝜏′
𝐾},
whe e 𝜏′
𝑘= {𝜏′
𝑘1,…, 𝜏′
𝑘𝑚𝑘}
𝑐𝑖Cos s o an o de o be (un)loaded associa ed wi h (se ice
on) loca ion 𝑖, whe e 𝑐𝑖≥0 o a pickup o deli e y loca ion
and 𝑐𝑖=0 o a depo
𝑖Index se o ime windows a
loca ion 𝑖, whe e 𝑖= {1,…, 𝑀𝑖}
𝑝𝑖Re enue o an o de o be (un)loaded loca ion 𝑖, whe e 𝑝𝑖≥0
o a pickup loca ion ( ep esen ing he e enue associa ed
wi h an o de ) and 𝑝𝑖=0 o a deli e y loca ion o a depo
Vehicle se , = {1,…, 𝐾}
𝑑𝑖𝑗 Dis ance be ween loca ion 𝑖 and 𝑗
𝑐𝑖𝑗 Cos o a eling be ween loca ion 𝑖 and 𝑗
𝑡𝑖𝑗 T a el ime be ween loca ion 𝑖 and 𝑗
𝑓𝑡Wage o a uck d i e pe minu e
𝑚𝑘Numbe o ending loca ions o ehicle 𝑘
∑
𝑡∈𝑖
𝑏𝑡
𝑖=1𝑖∈(20)
∑
𝑡∈𝑖
𝑏𝑡
𝑖=∑
𝑘∈∑
𝑗∈∖′
𝑥𝑘
𝑗𝑖 𝑖∈(21)
𝑞𝑘
𝑗≥𝑞𝑘
𝑖+𝑞𝑗−𝑀(1−𝑥𝑘
𝑖𝑗 )𝑖∈∖′, 𝑗 ∈∖,
𝑘∈∶𝑖≠𝑗(22)
𝑞𝑘
𝑖≤𝑄𝑘∑
𝑗∈∖,
𝑗≠𝑖
𝑥𝑘
𝑖𝑗 𝑖∈, 𝑘 ∈(23)
𝑞𝑘
𝑖≤(𝑄𝑘+𝑞𝑖)∑
𝑗∈∖,
𝑗≠𝑖
𝑥𝑘
𝑖𝑗 𝑖∈, 𝑘 ∈(24)
ℎ𝑘
𝑗≥ℎ𝑘
𝑖+ℎ𝑗−𝑀(1−𝑥𝑘
𝑖𝑗 )𝑖∈∖′, 𝑗 ∈∖,
𝑘∈∶𝑖≠𝑗(25)
ℎ𝑘
𝑖≤(𝐻𝑘−ℎ𝑘
𝑠𝑡𝑎𝑟𝑡)∑
𝑗∈∖,
𝑗≠𝑖
𝑥𝑘
𝑖𝑗 𝑖∈, 𝑘 ∈(26)
ℎ𝑘
𝑖≤(𝐻𝑘−ℎ𝑘
𝑠𝑡𝑎𝑟𝑡 +ℎ𝑖)∑
𝑗∈∖,
𝑗≠𝑖
𝑥𝑘
𝑖𝑗 𝑖∈, 𝑘 ∈(27)
𝑥𝑘
𝑖𝑗 ∈ {0,1}𝑖, 𝑗 ∈, 𝑘 ∈(28)
𝑏𝑡
𝑖∈ {0,1}𝑖∈, 𝑡 ∈𝑖(29)
𝑎𝑘
𝑖, 𝑑𝑘
𝑖, 𝑦𝑘, 𝑤𝑖, 𝑞𝑘
𝑖, ℎ𝑘
𝑖≥0𝑖∈, 𝑘 ∈(30)
The objec i e unc ion (2) maximizes he p o i ea ned om he
selec ed o de s. The i s summa ion ep esen s he e enue ob ained
om he selec ed o de s, whe eas he second summa ion ep esen s he
d i e wages associa ed wi h he o al anspo a ion imes. Cons ain s
(3) s a e ha e e y pickup loca ion can be isi ed a mos once. Con-
s ain s (4) ensu e ha he same uck pe o ms he pickup and deli e y
o a gi en o de . Cons ain s (5) s a e ha i a uck isi s a ce ain
loca ion, he same uck should lea e om i . Cons ain s (6) p e en
cycles in he uck ou es. Cons ain s (7) o ce he ucks o depa
om he s a ing depo s. Cons ain s (8) es ablish ha each uck is
u ilized only once. Cons ain s (9) ensu e ha each uck a i es a
only one o i s mul iple ending depo s. Cons ain s (10) in combina ion
wi h Cons ain s (9) o ce he ucks no o isi he a i ing depo s o
o he ucks. Cons ain s (11) s a e ha he depa u e ime o ucks
om a gi en node is g ea e o equal o he a i al ime o he ucks.
Cons ain s (12) ensu e ha , o a gi en uck, all he deli e ies a e
execu ed a e picking hem up. Cons ain s (13) impose ha he ucks’
depa u e imes a e equal o he opening imes o he ime windows
om whe e hey depa . Cons ain s (14) de ine he o al ou ing ime
o each uck. Cons ain s (15) es ablish ha , when a eling om
𝑖 o 𝑗, he uck a i al ime a 𝑗 is g ea e han o equal o he
depa u e ime om 𝑖 plus he anspo a ion imes be ween 𝑖 and 𝑗.
Cons ain s (16) link he a i al imes wi h he ucks’ wai ing imes
when a eling om 𝑖 o 𝑗. Cons ain s (17) link he depa u e imes
wi h he ucks’ wai ing imes when a eling om 𝑖 o 𝑗. Cons ain s
(18) de ine he ucks’ wai ing imes. Cons ain s (19) es ablish ha he
deli e y and pickups should be execu ed be o e he closing imes o
he ime windows. Cons ain s (20) ensu e ha only one o he ime
windows is chosen o e e y s a ing and ending depo . Cons ain s
(21) indica e ha only one o he mul iple ime windows mus be
chosen a each cus ome loca ion. Cons ain s (22)–(24) es ablish he
low balance o he loads on he uck ou es. Cons ain s (25)–(27)
ensu e he low balance o he weigh s on he uck ou es. Cons ain s
(28)–(30) p esen he a iable de ini ions.
3.3.2. The p o i maximiza ion including CO2 emissions SMDPDPMTWPD
This p oblem a ian includes CO2 emissions in he p o i maximiza-
ion objec i e unc ion. We ollow he app oach om [47] o ans o m
he CO2 emissions o going om loca ion 𝑖 o 𝑗 in o a cos ac o .
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
8
D. Roelink e al.
Table 10
Compa ison o he ALNS me aheu is ic wi h he MILP model on a small se o ins ances. No e ha he esul s o ALNS a e he maximum alues seen ac oss 10 eplica ions o
ai compa ison wi h he MILP.
𝑛 𝐾 =1𝐾=2
MILP ALNS MILP ALNS
𝑍 (e) Gap (%) Time (s) 𝑍 (e)𝛥𝑀𝐼𝐿𝑃 (%) Time (s) 𝑍 (e) Gap (%) Time (s) 𝑍 (e)𝛥𝑀𝐼𝐿𝑃 (%) Time (s)
5−617.75 0.00 0.24 −617.75 0.00 4.65 −1313.58 0.00 0.28 −1313.58 0.00 8.64
10 609.75 0.00 23.18 609.75 0.00 26.54 −86.08 0.00 33.57 −86.08 0.00 35.14
15 1155.25 0.00 65.14 1155.25 0.00 89.60 459.42 0.00 121.82 459.42 0.00 48.61
20 1155.25 0.00 879.16 1155.25 0.00 110.93 459.42 0.00 1219.96 459.42 0.00 73.31
A g 575.63 0.00 241.93 575.63 0.00 57.93 −120.21 0.00 343.91 −120.21 0.00 41.43
Table 11
Resul s o he ALNS me aheu is ic o he p o i maximiza ion SMDPDPMTWPD (HTW).
Exp. Da a ins ance 𝑍 (e)𝑍𝐼𝑛𝑖𝑡 (e)𝛥𝑍𝐼𝑛𝑖𝑡 (%) Time Wai ing La e Dis ance T a el ime N . o % FTL % T a el ime
(s) (min) (min) (km) (min) o de s o de s ≥80% loaded
P o i maximiza ion
D-1-25 979.05 −203.12 154.39 112.69 62.60 0.00 1635.93 1500.40 1.80 60.00 26.28
D-1-50 2830.15 316.01 423.41 69.68 17.00 0.00 1298.95 1184.80 1.00 100.00 49.74
D-1-100 4268.95 −504.78 850.03 507.58 17.00 0.00 1512.56 1428.40 2.00 100.00 63.11
D-1-250 2602.08 −634.74 427.68 637.18 109.10 0.00 1517.67 1369.60 1.40 85.00 40.97
D-2-25 256.82 −1185.07 149.82 71.35 62.60 0.00 2239.30 1988.40 1.80 60.00 19.69
D-2-50 2142.69 −1042.89 269.38 88.82 17.00 0.00 1873.37 1649.10 1.00 100.00 35.70
D-2-100 3573.12 −693.59 1993.35 280.68 17.00 0.00 2093.95 1898.40 2.00 100.00 47.48
D-2-250 5997.39 −1957.48 1478.04 1811.42 401.00 0.00 4226.05 3852.30 4.00 25.00 30.24
D-4-25 92.22 −1543.20 113.90 119.15 229.00 0.00 3395.23 2943.50 2.00 100.00 29.66
D-4-50 1302.13 −2899.57 147.52 210.53 163.00 0.00 3264.19 2824.20 2.00 100.00 28.97
D-4-100 2746.90 −2733.58 216.44 583.18 163.00 0.00 3472.79 3063.80 3.00 100.00 36.91
D-4-250 5643.23 −3389.09 284.89 1800.19 481.80 0.00 5603.60 5003.80 4.40 46.00 29.82
SFT1-C25-16-2 −156.88 −688.70 75.53 99.86 33.30 0.00 400.93 324.50 2.00 100.00 23.13
SFT2-C25-16-2 −470.83 −867.16 45.43 94.76 9.00 0.00 420.93 341.00 1.00 100.00 8.80
SFT1-C50-24-3 773.92 −848.97 206.96 391.45 8.00 0.00 975.58 789.00 6.00 100.00 42.59
SFT2-C50-24-3 127.62 −945.84 114.29 238.35 14.20 0.00 798.26 643.60 4.40 100.00 30.71
SFT1-R25-20-2 396.63 −673.83 171.91 234.08 29.00 0.00 816.51 657.80 4.00 100.00 35.61
SFT2-R25-20-2 −97.67 −722.59 86.00 281.90 31.00 0.00 650.00 525.00 4.00 100.00 36.19
SFT1-R50-30-3 342.75 −879.93 144.03 464.49 45.00 0.00 795.35 642.00 5.00 100.00 51.87
SFT2-R50-30-3 −407.92 −1216.03 66.26 189.05 42.00 0.00 461.63 373.00 2.00 100.00 30.03
SFT1-RC25-20-2 106.08 −759.72 114.43 250.82 93.50 0.00 923.02 746.80 4.00 75.00 45.66
SFT2-RC25-20-2 107.42 −654.57 118.49 93.45 38.00 0.00 486.05 393.00 2.00 50.00 18.07
SFT1-RC50-30-3 614.00 −958.58 165.88 575.42 0.00 0.00 1251.16 1008.00 6.00 100.00 56.35
SFT2-RC50-30-3 1286.50 −899.96 313.28 558.48 35.00 0.00 1094.19 883.00 6.00 83.33 67.61
SFT1-R100-50-5 50.98 −1757.43 102.98 935.13 111.40 0.00 1440.58 1164.00 7.90 74.64 42.05
SFT2-R100-50-5 206.72 −1843.42 111.31 862.80 71.00 0.00 1387.44 1122.00 6.00 100.00 33.69
SFT1-R100-75-7 910.60 −2223.03 142.27 1814.59 88.10 0.00 2183.60 1762.30 13.70 92.69 46.60
SFT2-R100-75-7 804.97 −1996.33 140.80 1816.05 37.50 0.00 2132.79 1720.10 12.70 92.09 47.29
A e age 1322.49 −1228.83 308.17 542.61 86.65 0.00 1726.84 1492.92 4.04 87.28 37.67
he solu ion space when op imizing he non-compulso y pickup o
o de s o e u n ips. Fu he mo e, he ou ing schedules show ha
he ehicles, on a e age, a el 1726.84 km, in 1492.92 min, and wai
86.65 min o se e 4.04 o de s. The e o e, we conclude ha he eigh
exchange pla o ms ep esen an e ec i e app oach o dealing wi h
emp y e u n ips. Thus, he ehicles only needed o se e 4.04 o de s,
on a e age, o gene a e p o i s. This highligh s he posi i e impac o
eigh exchange pla o ms and also ha a small numbe o o de s can
mi iga e he cos s o emp y e u n ips.
5.8. Analysis on he p o i maximiza ion including CO2 emissions SMD-
PDPMTWPD
Table 12 p esen s he esul s o he ALNS me aheu is ic o he
p o i maximiza ion SMDPDPMTWPD wi h CO2 emissions cos s, es ed
on a la ge se o ins ances. The columns lis he same in o ma ion as
he columns in Table 11. Fu he in o ma ion on hese compu a ional
expe imen s is p esen ed in Appendix D.
The esul s show ha he ALNS me aheu is ic a e ages objec i e
alues o e1267.03, whe eas he ini ial solu ions (𝑍𝐼𝑛𝑖𝑡) epo a e age
objec i e alues o e−1281.73. These esul s alida e he pe o mance
o he ALNS me aheu is ic, which ou pe o ms he a e age alues o
he ini ial solu ions by 641.39%, wi hin compu a ional imes o 559.41
s. O e all, we obse e a sligh dec ease in he a e age objec i e alues
o he SMDPDPMTWPD solu ions when inco po a ing CO2 emissions
cos s. Ne e heless, his dec ease does no a ec he pe o mance o he
ALNS me aheu is ic no signi ican ly impac he ou ing schedules. In
he esul s, he ehicles a el 1728.42 km, in 1494.98 min, and wai
87.74 min o se e 4.09 o de s. Thus, we conclude ha e en hough
inco po a ing CO2 emissions cos s in o he p o i maximiza ion can lead
o lowe incomes, hose new sus ainable solu ions do no signi ican ly
comp omise he business ope a ions and la ge changes o he ehicle
ou ing schedules. The e o e, he eigh exchange pla o ms also show
a s ong po en ial o deal wi h emp y kilome e s o e u n ips when
inco po a ing CO2 emissions cos s.
5.9. Analysis on he so ime windows SMDPDPMTWPD
Table 13 p esen s he esul s o he ALNS me aheu is ic o he
so ime windows SMDPDPMTWPD, es ed on a la ge se o ins ances.
The columns lis he same in o ma ion as he columns in Table 11.
Fu he in o ma ion on hese compu a ional expe imen s is p esen ed
in Appendix D.
The ALNS me aheu is ic shows a e age objec i e alues o
e3696.93, whe eas he ini ial solu ions (𝑍𝐼𝑛𝑖𝑡) epo a e age alues
o e−3284.26. Compa ed o he esul s o he ha d ime-window
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
15
D. Roelink e al.
Table 12
Resul s o he ALNS me aheu is ic o he p o i maximiza ion wi h CO2 emissions cos s SMDPDPMTWPD (HTW +CO2).
Exp. Da a ins ance 𝑍 (e)𝑍𝐼𝑛𝑖𝑡 (e)𝛥𝑍𝐼𝑛𝑖𝑡 (%) Time Wai ing La e Dis ance T a el ime N . o % FTL % T a el ime
(s) (min) (min) (km) (min) o de s o de s ≥80% loaded
P o i
maximiza ion
wi h CO2
emissions
D-1-25 912.26 −452.94 161.09 114.13 62.60 0.00 1650.58 1512.40 1.80 60.00 26.11
D-1-50 2763.26 −526.86 322.88 67.44 17.00 0.00 1309.07 1192.90 1.00 100.00 49.43
D-1-100 4188.22 300.87 552.67 478.79 17.00 0.00 1509.77 1426.20 2.00 100.00 63.22
D-1-250 2503.01 −255.89 326.01 663.44 103.70 0.00 1577.09 1419.10 1.40 80.00 41.57
D-2-25 282.47 −1194.69 159.56 79.28 44.30 0.00 2267.79 2018.70 1.90 55.00 18.36
D-2-50 2064.63 −1715.75 263.57 92.16 17.00 0.00 1892.79 1664.80 1.00 100.00 35.36
D-2-100 3497.12 −1362.26 445.19 300.11 17.00 0.00 2087.21 1893.00 2.00 100.00 47.62
D-2-250 5889.08 −2163.96 499.88 1576.42 401.00 0.00 4223.37 3850.20 4.00 25.00 30.26
D-4-25 27.80 −2240.50 101.71 128.54 229.00 0.00 3381.16 2932.00 2.00 100.00 29.76
D-4-50 1223.24 −2395.47 227.73 224.22 163.00 0.00 3266.40 2826.10 2.00 100.00 28.93
D-4-100 2567.32 −1965.62 227.92 608.01 154.20 0.00 3435.12 3029.00 2.90 95.00 36.66
D-4-250 5552.79 −2778.24 12 409.16 1815.13 513.60 0.00 5622.79 5038.10 4.80 44.00 29.49
SFT1-C25-16-2 −161.45 −718.15 76.23 108.57 33.10 0.00 397.21 321.50 2.00 100.00 23.34
SFT2-C25-16-2 −474.47 −855.62 44.31 101.37 9.00 0.00 420.93 341.00 1.00 100.00 8.80
SFT1-C50-24-3 733.43 −912.79 198.95 434.29 8.00 0.00 975.58 789.00 6.00 100.00 42.59
SFT2-C50-24-3 126.54 −922.62 114.26 270.91 25.70 0.00 788.14 635.20 4.80 100.00 32.92
SFT1-R25-20-2 372.00 −815.36 148.13 258.78 26.00 0.00 823.02 663.00 4.20 100.00 36.42
SFT2-R25-20-2 −120.53 −672.92 80.00 308.71 31.00 0.00 650.00 525.00 4.00 100.00 36.19
SFT1-R50-30-3 302.49 −1303.77 123.64 506.83 45.00 0.00 795.35 642.00 5.00 100.00 51.87
SFT2-R50-30-3 −421.56 −1180.52 63.74 218.05 42.00 0.00 461.63 373.00 2.00 100.00 30.03
SFT1-RC25-20-2 63.29 −755.18 108.85 276.48 97.00 0.00 923.49 747.20 4.00 75.00 45.64
SFT2-RC25-20-2 93.75 −819.18 112.94 103.54 38.00 0.00 486.05 393.00 2.00 50.00 18.07
SFT1-RC50-30-3 544.97 −1030.73 157.97 643.69 0.00 0.00 1251.16 1008.00 6.00 100.00 56.35
SFT2-RC50-30-3 1215.84 −790.52 553.75 624.38 35.00 0.00 1094.19 883.00 6.00 83.33 67.61
SFT1-R100-50-5 −6.65 −1672.12 99.58 1058.85 112.50 0.00 1383.72 1118.20 7.90 74.45 41.54
SFT2-R100-50-5 163.12 −2162.17 107.63 975.11 88.50 0.00 1379.88 1115.00 6.00 100.00 33.90
SFT1-R100-75-7 804.84 −2158.94 138.84 1813.81 86.10 0.00 2199.53 1775.10 14.00 92.86 46.68
SFT2-R100-75-7 769.91 −2366.58 132.75 1812.31 40.30 0.00 2142.67 1727.80 12.90 92.24 48.11
A e age 1267.03 −1281.73 641.39 559.41 87.74 0.00 1728.42 1494.98 4.09 86.67 37.74
SMDPDPMTWPD in Sec ion 5.7, we obse e a signi ican inc ease
in he a e age objec i e alues, when conside ing so ime win-
dows. As expec ed, so ime windows enla ge he solu ion space o
he SMDPDPMTWPD. Consequen ly, ALNS epo s an imp o emen o
430.37% o e he ini ial solu ion, wi h compu a ional imes a e aging
1048.92 s. In he ou ing schedules, he ehicles a el 2304.57 km in
2012.58 min, wai 180.72 min o se e 5.83 o de s, and expe ience
1140.45 min o delayed deli e ies. So ime windows signi ican ly
impac he ou ing schedules and he p o i abili y, as we obse e a e-
duc ion in a el and wai ing imes compa ed o he ha d ime window
scena ios. Mo eo e , o he so ime window SMDPDPMTWPD, ucks
inc ease he numbe o se ed o de s o 5.83. This indica es ha e en
hough he delayed imes a e age 1140.45 min, he ela ed cos s o
delayed deli e ies do no mi iga e he p o i s o se ing mo e o de s.
In e es ingly, he esul s show ha when allowing so ime windows,
he pe cen age o FTL o de s sligh ly dec eased o 80.11%, whe eas he
a el ime ≥80% loaded ma ginally inc eased o 39.73%, espec i ely.
These esul s highligh ha he e is no s ong ela ion be ween he
occupa ion a es o he ehicles and he gene a ed p o i s.
5.10. Analysis on he so ime windows including CO2 emissions SMD-
PDPMTWPD
Table 14 p esen s he esul s o he ALNS me aheu is ic o he
so ime windows wi h 𝐶𝑂2 emissions cos s SMDPDPMTWPD, es ed
on a la ge se o ins ances. The columns lis he same in o ma ion as
he columns in Table 11. Fu he in o ma ion on hese compu a ional
expe imen s is p esen ed in Appendix D.
The ALNS me aheu is ic shows a e age objec i e alues o
e3636.08, whe eas he ini ial solu ions (𝑍𝐼𝑛𝑖𝑡) epo a e age alues
o e−3140.79. Compa ed o he esul s in Sec ions 5.7 and 5.8, we
obse e a simila endency when inco po a ing CO2 emissions cos s in o
he so ime-window SMDPDPMTWPD: he e is a sligh dec ease in he
a e age objec i e alues. Ne e heless, his dec ease does no s ongly
a ec he ou ing schedules o he SMDPDPMTWPD. ALNS epo s
a e age imp o emen s o 2738.12% o e he ini ial solu ion, wi hin
compu a ional imes o 1046.00 s. In pa icula , hese esul s alida e
he impo ance o he so ime-window app oach o exploi he bene i s
o he eigh exchange pla o ms when sol ing SMDPDPMTWPD. E en
hough he e is a sligh dec ease in he a e age objec i e alues, he
anspo a ion me ics o he ou ing schedules ba ely change when
including CO2 emissions cos s. In he esul s, he ehicles a el on
a e age 2270.09 km in 1982 ˙
38 min, wai 179.45 min o se e 5.65
o de s, and expe ience 1088.23 min o delayed deli e ies. Thus, he
ehicle occupa ion me ics show simila a es wi h a e age alues o
79.14% and 39.01% o he % FTL o de s and % T a el ime ≥80%
loaded, espec i ely.
5.11. Manage ial insigh s and discussion
This sec ion summa izes he manage ial insigh s and p esen s a
discussion ac oss he conduc ed se s o expe imen s. Fig. 2 illus a es
he a e age alues o he ALNS algo i hm when sol ing he ollowing
SMDPDPMTWPD a ian s: (ha d ime windows) maximizing p o i s
(HTW), (ha d ime windows) maximizing p o i s wi h CO2 emissions
cos s (HTW + CO2), so ime windows maximizing p o i s (STW),
and so ime windows maximizing p o i s wi h CO2 emissions cos s
(STW + CO2) in o ma ion o he objec i e unc ion alues and numbe
o o de s o each p oblem a ian . The a e age alues co espond
o he objec i e unc ion alues (Z), and numbe o se ed o de s.
Simila ly, Table 15 summa izes he anspo a ion me ics o he same
SMDPDPMTWPD a ian . The columns epo he a e age alues o
uck wai ing ime (min), co e ed dis ance (km), and a el ime (min).
The esul s show a sligh dec ease in he a e age objec i e alues
when including he CO2 emissions cos s. As expec ed, he p o i is less
han excluding he CO2 emissions cos s. Ne e heless, hese addi ional
cos s sligh ly a ec he ou ing schedules. Hence, when compa ing he
anspo a ion me ics o HTW and HTW+CO2 in Tables 11 and 12,
espec i ely, he co e ed dis ances and a el imes show he same
esul s o he 28 s udied ins ances.
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
16
D. Roelink e al.
Table 13
Resul s o he ALNS me aheu is ic o he p o i maximiza ion SMDPDPMTWPD wi h so ime windows (STW).
Exp. Da a ins ance 𝑍 (e)𝑍𝐼𝑛𝑖𝑡 (e)𝛥𝑍𝐼𝑛𝑖𝑡 (%) Time Wai ing La e Dis ance T a el ime N . o % FTL % T a el ime
(s) (min) (min) (km) (min) o de s o de s ≥80% loaded
So ime
windows p o i
maximiza ion
D-1-25 2151.40 −472.93 734.96 288.01 209.00 267.10 1659.42 1540.10 2.00 100.00 56.70
D-1-50 4374.31 −456.82 477.09 553.65 35.20 855.00 2324.19 2064.30 2.00 65.00 28.42
D-1-100 5713.38 −111.47 2172.67 1580.92 17.60 1826.80 2242.33 2066.90 2.80 95.00 51.74
D-1-250 11400.91 432.88 1108.71 1830.02 0.40 1552.10 2082.79 1888.60 2.50 97.50 46.55
D-2-25 2332.36 −1985.37 365.11 766.82 819.00 1772.70 3586.05 3266.70 6.00 33.33 26.70
D-2-50 4377.11 −2324.73 508.76 756.82 290.80 960.40 3564.77 3176.60 3.00 40.00 17.64
D-2-100 5916.66 −2251.47 496.84 1785.17 238.00 2024.90 3444.88 3146.60 3.90 74.17 35.68
D-2-250 15056.69 −1937.93 1686.16 1850.71 331.00 2537.70 4173.60 3679.50 6.30 36.19 44.08
D-4-25 11697.05 −3574.20 615.42 497.03 1394.10 2791.10 5645.58 5038.00 6.90 43.57 27.12
D-4-50 5848.25 −3618.41 371.90 559.77 339.70 2104.00 5785.23 5135.30 4.30 58.00 24.85
D-4-100 8322.08 −5778.85 256.43 1383.13 238.00 3698.00 5803.95 5209.80 5.40 81.33 34.75
D-4-250 21007.81 −3681.07 1514.70 1847.80 373.40 6604.10 6902.09 6158.40 10.10 43.62 39.76
SFT1-C25-16-2 −163.68 −2059.42 92.02 93.22 33.60 0.00 406.51 329.00 2.00 100.00 22.81
SFT2-C25-16-2 −470.83 −2432.27 80.55 71.96 9.00 0.00 420.93 341.00 1.00 100.00 8.80
SFT1-C50-24-3 823.10 −2411.45 134.52 1257.33 76.00 109.00 1047.67 848.00 8.00 100.00 49.41
SFT2-C50-24-3 137.72 −2775.67 105.03 341.04 23.00 67.50 803.37 647.40 4.90 100.00 32.62
SFT1-R25-20-2 496.36 −2181.32 123.23 733.93 41.00 379.20 696.63 562.90 4.00 100.00 41.65
SFT2-R25-20-2 −97.67 −3058.59 96.80 467.15 31.00 0.00 650.00 525.00 4.00 100.00 36.19
SFT1-R50-30-3 348.32 −4039.08 108.68 998.98 28.00 21.00 884.88 715.00 6.00 100.00 52.31
SFT2-R50-30-3 −407.92 −4641.04 91.16 281.96 42.00 0.00 461.63 373.00 2.00 100.00 30.03
SFT1-RC25-20-2 218.73 −2331.43 109.52 700.81 28.00 786.00 786.05 636.00 4.00 75.00 53.62
SFT2-RC25-20-2 115.42 −2560.61 104.58 124.39 38.00 2.00 489.30 395.40 2.40 56.67 19.67
SFT1-RC50-30-3 760.70 −3301.58 123.30 1811.56 20.00 654.30 1452.09 1170.10 9.80 100.00 70.50
SFT2-RC50-30-3 1 321.22 −2917.40 145.89 1629.35 35.00 499.70 1381.51 1116.30 7.90 87.32 71.37
SFT1-R100-50-5 124.27 −6647.26 101.87 1821.86 139.50 429.80 1624.19 1311.90 11.00 81.76 49.75
SFT2-R100-50-5 205.19 −7117.25 102.91 1624.80 69.40 245.90 1427.56 1154.40 7.00 100.00 36.56
SFT1-R100-75-7 930.67 −9428.40 109.89 1854.96 100.60 657.60 2237.21 1804.20 16.80 85.15 48.43
SFT2-R100-75-7 974.40 −8296.17 111.78 1856.67 59.90 1086.70 2543.49 2051.70 17.20 89.57 54.61
A e age 3696.93 −3284.26 430.37 1048.92 180.72 1140.45 2304.57 2012.58 5.83 80.11 39.73
Table 14
Resul s o he ALNS me aheu is ic o he p o i maximiza ion wi h CO2 emissions cos s and so ime windows SMDPDPMTWPD (STW +CO2).
Exp. Da a ins ance 𝑍 (e)𝑍𝐼𝑛𝑖𝑡 (e)𝛥𝑍𝐼𝑛𝑖𝑡 (%) Time Wai ing La e Dis ance T a el ime N . o % FTL % T a el ime
(s) (min) (min) (km) (min) o de s o de s ≥80% loaded
So ime
windows
p o i
maximiza ion
wi h CO2
emissions
D-1-25 2103.84 44.18 216.29 290.89 209.00 245.70 1633.02 1518.70 2.00 100.00 57.46
D-1-50 4365.57 −713.81 630.03 579.93 0.00 942.20 2390.93 2112.70 2.00 65.00 26.76
D-1-100 5293.50 −69.07 839.20 1382.85 35.20 1345.80 2129.30 1945.80 2.40 90.00 46.63
D-1-250 10866.02 −190.35 1002.91 1822.73 0.10 1573.70 2137.56 1938.10 2.40 93.33 45.07
D-2-25 2170.93 −732.08 872.63 783.08 819.00 1794.10 3612.44 3288.10 6.00 33.33 26.53
D-2-50 4122.57 −1364.37 371.30 769.88 255.60 943.80 3494.07 3108.20 3.00 46.67 18.93
D-2-100 5894.24 −1258.48 1335.15 1817.71 238.00 2075.60 3448.60 3159.60 4.00 75.00 36.99
D-2-250 15068.48 −1934.77 1579.17 1876.24 331.00 2628.80 4212.33 3715.20 6.40 37.14 44.14
D-4-25 11522.68 −3087.20 506.83 498.75 1393.60 2720.30 5611.28 5044.40 6.80 44.57 27.12
D-4-50 6032.62 −3775.13 65031.87 565.61 271.90 2144.50 5893.60 5200.30 4.10 53.50 21.88
D-4-100 7853.49 −3498.85 1912.80 1473.26 294.10 3358.90 5790.47 5194.80 5.40 73.33 32.44
D-4-250 22099.22 −4451.25 660.93 1855.18 445.30 5768.30 6334.42 5654.20 8.80 48.11 36.96
SFT1-C25-16-2 −310.32 −1936.79 83.77 149.62 30.30 392.80 470.12 379.90 3.30 98.67 24.70
SFT2-C25-16-2 −474.47 −2482.22 80.80 80.50 9.00 0.00 420.93 341.00 1.00 100.00 8.80
SFT1-C50-24-3 759.64 −2493.37 130.54 1095.36 43.20 102.60 989.77 801.00 7.00 100.00 46.85
SFT2-C50-24-3 115.81 −2850.50 104.11 336.25 20.80 61.30 801.51 645.80 4.90 100.00 32.70
SFT1-R25-20-2 480.37 −2288.60 121.20 698.73 41.00 492.00 676.74 547.00 4.00 100.00 42.78
SFT2-R25-20-2 −120.53 −3015.63 95.98 483.35 31.00 0.00 650.00 525.00 4.00 100.00 36.19
SFT1-R50-30-3 303.17 −4124.09 107.40 1113.40 28.00 21.00 884.88 715.00 6.00 100.00 52.31
SFT2-R50-30-3 −421.56 −4770.52 91.14 274.57 42.00 0.00 461.63 373.00 2.00 100.00 30.03
SFT1-RC25-20-2 175.54 −2491.29 107.14 680.87 33.60 676.60 802.56 649.40 4.20 72.00 52.97
SFT2-RC25-20-2 97.34 −2827.46 103.49 139.72 38.00 1.00 487.67 394.20 2.20 53.33 18.87
SFT1-RC50-30-3 648.31 −3376.66 119.40 1809.07 15.10 704.90 1463.95 1179.70 9.70 100.00 69.51
SFT2-RC50-30-3 1 220.40 −3177.33 140.00 1562.95 35.00 125.10 1134.30 914.60 6.80 76.61 68.67
SFT1-R100-50-5 64.21 −6490.16 101.00 1822.23 149.80 428.50 1570.58 1268.80 10.50 80.58 50.23
SFT2-R100-50-5 168.30 −7295.54 102.31 1581.87 61.10 274.80 1394.30 1127.70 6.60 100.00 35.73
SFT1-R100-75-7 846.64 −9158.63 109.26 1852.04 106.30 534.60 2157.44 1740.90 15.30 87.80 47.09
SFT2-R100-75-7 864.31 −8132.07 110.66 1891.32 47.50 1113.50 2508.02 2023.50 17.50 86.93 54.00
A e age 3636.08 −3140.79 2 738.12 1046.00 179.45 1088.23 2270.09 1982.38 5.65 79.14 39.01
Table 15
Compa ison o anspo a ion me ics o he a e age alues o he di e en SMDPDPMTWPD a ian s.
P oblem a ian Wai ing (min) La e (min) Dis ance (km) T a el ime (min)
HTW 86.65 0.00 1726.84 1492.92
HTW + CO287.74 0.00 1728.42 1494.98
STW 180.72 1140.45 2304.57 2012.58
STW + CO2179.45 1088.23 2270.09 1982.38
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
17
D. Roelink e al.
Fig. 2. Compa ison o objec i e unc ion alues and numbe o o de s o he di e en SMDPDPMTWPD a ian s.
A simila endency is obse ed in he anspo a ion me ics o
Tables 13 and 14, when compa ing he esul s o STW and STW +
CO2, espec i ely. The e o e, inco po a ing CO2 emissions cos s in o
he objec i e unc ions leads o sligh ly lowe objec i e alues while
no hea ily a ec ing he ou ing schedules. This can be explained
by he ela i ely low CO2 emissions cos s es ablished by he a e age
alues o he Eu opean Union’s Emissions T ading Scheme, i.e., 𝑐𝑒=
e 0.08421. We conclude ha he solu ions o he ALNS algo i hm
a e bene icial o he eigh -exchange-pla o ms p o i abili y and align
wi h he Eu opean Union’s goal o educing emissions.
On he o he hand, when compa ing he HTW o he STW and
he HTW + CO2 o he STW + CO2, we obse e a subs an ial change
in he ou ing schedules. On a e age, wi h an addi ional 1.68 o de s
o he STW p oblem a ian s, he objec i e unc ion alues o he
STWs inc ease mo e han 2.5 imes he inal p o i compa ed o he
HTW p oblem a ian s. This p o ides in e es ing insigh s. Fi s , a sligh
inc ease in he numbe o o de s leads o subs an ial addi ional income,
demons a ing ha he eigh exchange pla o ms a e a success ul
app oach o dealing wi h he emp y kilome e s o e u n ips. Fu -
he mo e, he esul s indica e ha a la ge p o i does no equi e a high
numbe o o de s. Second, al hough companies incu penaliza ion cos s
o la e deli e ies, he bene i s o ul illing la e o de s compensa e o
hese cos s, esul ing in highe incomes. This is ad an ageous om an
economic pe spec i e. Howe e , he impac o la e deli e ies should
also be assessed ega ding se ice quali y. Thus, while he penaliza ion
cos s o la e deli e ies may be low, o he unmeasu ed cos s (such as
diminished cus ome sa is ac ion) could signi ican ly a ec he business
case in he long e m. Thi d, allowing ucks o ul ill la e o de s esul s
in signi ican ly highe incomes, showing he ad an ages o lexible
deli e y schedules o he p o i abili y o he selec ion. Mo eo e , by
inco po a ing so ime windows, companies can e ec i ely add ess he
issue o emp y e u n ips and inc ease p o i s.
6. Conclusions and u u e wo k
This pape in oduces he Selec i e Mul iple Depo Pickup and
Deli e y P oblem wi h Mul iple Time Windows and Pai ed Demand
(SMDPDPMTWPD). The SMDPDPMTWPD is a ich VRP a ian ha
add esses he challenge o selec ing p o i able o de s om a eigh
exchange pla o m o educe backhauling cos s associa ed wi h emp y
ehicle e u ns. The SMDPDPMTWPD holds signi ican po en ial o
in eg a ing anspo managemen sys ems in o eigh exchange pla -
o ms, enabling anspo a ion companies o educe cos s and inc ease
e enues.
To s udy he SMDPDPMTWPD, we in oduced ou p oblem a i-
an s: (𝑖) p o i maximiza ion, (𝑖𝑖) p o i maximiza ion inco po a ing
CO2 emissions cos s, (𝑖𝑖𝑖) p o i maximiza ion wi h so ime windows,
and (𝑖𝑣) p o i maximiza ion inco po a ing CO2 emissions cos s and
so ime windows. These a ian s a e o mula ed as MILPs and sol ed
wi h op imiza ion so wa e. Gi en he compu a ional complexi y o
he MILPs, we de eloped an ALNS me aheu is ic o sol e la ge in-
s ances. We conduc ed six se s o expe imen s o es ou op imiza ion
app oaches and p oblem a ian s. The esul s indica ed ha ALNS
ou pe o med a Simula ed Annealing (SA) me aheu is ic in 25 ou o
he 28 es ed ins ances, wi h a e age objec i e alues ha a e wice
as la ge as hose o SA. Fu he mo e, o a small ins ance se , he
ALNS me aheu is ic ound he same solu ions as he MILP o mula ion
bu in sho e compu a ional imes. This alida es he pe o mance
o he ALNS algo i hm, showing ha ou app oxima e algo i hm is
well-sui ed o sol e he s udied p oblems. Addi ionally, we obse ed
ha inc easing he numbe o a ailable o de s leads o highe inal
p o i s in he op imal solu ions compa ed o he smalle ins ances.
This imp o emen is no due o ehicles ca ying mo e o de s, bu
because he addi ional o de s a e be e sui ed in e ms o loca ion, ime
windows, and anspo a ion cos s.
Rega ding he SMDPDPMTWPD a ian s, we obse ed a sligh de-
c ease in he objec i e unc ion alues when inco po a ing he CO2
emissions cos s. This endency is obse ed in he esul s o he ha d and
so ime-window SMDPDPMTWPD. The esul s show ha he SMD-
PDPMTWPD a ian s a e no signi ican ly a ec ed by hese addi ional
cos s. Mo eo e , we obse ed a signi ican inc ease in he inal objec-
i e alues when allowing so ime windows. Inco po a ing so ime
windows inc eased he a e age numbe o o de s om 4.09 o 5.65,
esul ing in incomes abo e 2.5 imes la ge han hose o scena ios
wi h ha d ime windows. These indings indica e ha allowing so ime
windows is c ucial o imp o ing he p o i abili y o a selec ion. Despi e
sol ing ins ances wi h up o 100 o de s, he ehicles se ed 4.90 o de s
on a e age, showing ha execu ing a small numbe o s a egically
chosen o de s is su icien o gene a e subs an ial p o i s and mi iga e
he cos s associa ed wi h emp y e u n ips.
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
18
D. Roelink e al.
This wo k p o ides a ounda ion o se e al esea ch di ec ions.
On he one hand, we belie e ha his ailo ed ALNS, along wi h i s
des oy and epai ope a o s, can se e as a baseline o u he esea ch
on algo i hms o in e ac ing wi h eigh exchange pla o ms. We
sugges u he esea ch on ou ALNS implemen a ion o imp o e he
pe o mance o la ge se s o ins ances. Simila ly, aluable insigh s can
be gained by pe o ming a sensi i i y analysis o he ALNS pa ame e s
o e alua e hei impac on a ious p oblem a ian s and by explo ing
al e na i e me hods o cons uc ing ini ial solu ions. On he o he
hand, he SMDPDPMTWPD is a p oblem ha inco po a es ealis ic
ea u es in o he anspo a ion sys em, such as mul iple ime windows,
mul iple depo s, and non-manda o y o de selec ion. In his ega d,
he anspo a ion sys em deals wi h la ge sou ces o unce ain y, such
as s ochas ic anspo a ion imes, se ice imes, and las -minu e can-
cella ions. Consequen ly, u u e esea ch can be conduc ed o de elop
s ochas ic op imiza ion app oaches o handle he unce ain y in he
anspo a ion sys em.
CRediT au ho ship con ibu ion s a emen
Daniël Roelink: W i ing – e iew & edi ing, W i ing – o iginal
d a , Visualiza ion, Valida ion, So wa e, Resou ces, Me hodology, In-
es iga ion, Fo mal analysis, Da a cu a ion, Concep ualiza ion. Gio-
anni Campuzano: W i ing – e iew & edi ing, Visualiza ion, Valida-
ion, Supe ision, So wa e, Me hodology, In es iga ion, Fo mal anal-
ysis. Ma ijn Mes: W i ing – e iew & edi ing, Visualiza ion, Supe -
ision, Resou ces, Fo mal analysis. Edua do Lalla-Ruiz: W i ing –
e iew & edi ing, Visualiza ion, Valida ion, Supe ision, Resou ces,
Me hodology, In es iga ion, Fo mal analysis, Concep ualiza ion.
Decla a ion o compe ing in e es
This is o ce i y ha he e is no con lic o in e es ega ding he
submi ed wo k.
Acknowledgmen s
The esea ch o D . G. Campuzano is unded by he Chilean Na-
ional Agency o Resea ch and De elopmen (ANID)/Schola ship P o-
g am/DOCTORADO BECAS CHILE/2019 unde G an 72200288. This
inancial suppo is g a e ully acknowledged.
Appendix A. Simula ed annealing me aheu is ic amewo k
Algo i hm 4 desc ibes he Simula ed Annealing (SA) me aheu is ic
amewo k implemen ed in he expe imen s o Sec ion 5.5. The inpu
pa ame e s a e s a ing (𝑇𝑠𝑡𝑎𝑟𝑡) and ending (𝑇𝑒𝑛𝑑 ) empe a u es, he cool-
ing a io (𝛼), he numbe o i e a ions 𝑁𝑖𝑡𝑒𝑟 a a gi en empe a u e, he
coun e o solu ions ejec ed wi hin a neighbo hood s uc u e (𝑟), and
he maximum compu a ional ime (𝛿𝑇). Addi ionally, 𝑡𝑖𝑚𝑒𝑖𝑛𝑖𝑡 and 𝑡𝑖𝑚𝑒𝑒𝑛𝑑
a e ime e mina ion c i e ion handle s, 𝑥′ ep esen s a neighbo ing
solu ion, 𝑇 is he cu en annealing empe a u e, 𝜙 is a andom numbe
gene a ed in he in e al (0,1), 𝑙(⋅) is he 𝑙 h neighbo hood s uc u e,
|𝑁| ep esen s he o al numbe o neighbo hoods, and 𝑓(⋅) p o ides
he objec i e alue o a gi en solu ion. The calib a ion o he pa ame e
alues o SA is p esen ed in Sec ion 5.1. The neighbo hood s uc u es
𝑙(⋅) implemen ed in SA a e desc ibed in Appendix A.1.
The ini ializa ion phase (lines 1–4) s a s by es ablishing he de aul
alues o he annealing empe a u e (line 2), he ime e mina ion
handle s 𝑡𝑖𝑚𝑒𝑖𝑛𝑖𝑡 and 𝑡𝑖𝑚𝑒𝑒𝑛𝑑 (line 3), and building an ini ial solu ion
ha is s o ed in 𝑥 and 𝑥∗ (line 4). The heu is ic p ocedu e o build
an ini ial solu ion is he same as he one implemen ed by ALNS (see
Sec ion 4.2). Then, he i e a i e phase (lines 5–19) is applied un il
ei he he maximum compu a ional ime eaches 𝛿𝑇 o he annealing
empe a u e equals 𝑇 (line 6). In e e y i e a ion o he main while-loop,
i.e., a each gi en empe a u e 𝑇, he algo i hm explo es a maximum
o 𝑁𝑖𝑡𝑒𝑟 solu ions (lines 7–17). Thus, in e e y i e a ion o he o -loop,
he SA algo i hm andomly selec s a neighbo hood o explo e (line 8),
and hen explo es he 𝑙 h neighbo hood 𝑙(⋅) un il ei he he maximum
numbe o ejec ed solu ions 𝑟 is eached o a easible solu ion is ound
and s o ed in 𝑥′ (line 9). A e ha , he new solu ion 𝑥′ is s o ed in
𝑥 i he objec i e unc ion alue is imp o ed (lines 10–11). O he wise,
he SA accep ance c i e ion is applied (lines 12–15). Thus, a andom
numbe is gene a ed and s o ed in 𝜙 (line 13). I 𝜙 < 𝑓(𝑥′)−𝑓(𝑥)
𝑇 he new
solu ion is accep ed and s o ed in 𝑥 (lines 14–15). Nex , 𝑥′ is compa ed
o he incumben 𝑥∗ and s o ed in 𝑥∗ i he new objec i e unc ion
alue ou pe o ms he incumben (lines 16–17). Once ou side o he
o -loop he annealing empe a u e is upda ed (line 18), as well as he
ime handle 𝑡𝑖𝑚𝑒𝑒𝑛𝑑 (line 19). Finally, he SA me aheu is ic e u ns he
bes solu ion ound du ing explo a ion 𝑥∗.
Algo i hm 4: SA
Da a: (𝑇𝑠𝑡𝑎𝑟𝑡, 𝑇𝑒𝑛𝑑 , 𝛼, 𝑟, 𝛿𝑇)
1Ini ializa ion Phase:
2𝑇←𝑇𝑠𝑡𝑎𝑟𝑡;
3𝑡𝑖𝑚𝑒𝑖𝑛𝑖𝑡, 𝑡𝑖𝑚𝑒𝑒𝑛𝑑 ←𝑡𝑖𝑚𝑒 ();
4𝑥, 𝑥∗←Cons uc i e_Heu is ic(𝑟);
5I e a i e Phase:
6while 𝑡𝑖𝑚𝑒𝑒𝑛𝑑 −𝑡𝑖𝑚𝑒𝑖𝑛𝑖𝑡 < 𝛿𝑇and 𝑇 > 𝑇𝑒𝑛𝑑 do
7 o 𝑁𝑖𝑡𝑒𝑟 do
8𝑙←𝑟𝑎𝑛𝑑(|𝑁|);
9𝑥′←𝑙(𝑥, 𝑟);
10 i 𝑓(𝑥′)> 𝑓(𝑥) hen
11 𝑥←𝑥′ ;
12 else
13 𝜙←𝑟𝑎𝑛𝑑(0,1) ;
14 i 𝜙 < 𝑒 (𝑓(𝑥′)−𝑓(𝑥))
𝑇 hen
15 𝑥←𝑥′ ;
16 i 𝑓(𝑥′)> 𝑓(𝑥∗) hen
17 𝑥∗←𝑥′ ;
18 𝑇=𝑇⋅𝛼;
19 𝑡𝑖𝑚𝑒𝑒𝑛𝑑 ←𝑡𝑖𝑚𝑒 ();
Resul : 𝑥∗
A.1. Neighbo hood s uc u es
In his sec ion, we lis he neighbo hood s uc u es 𝑙(⋅) imple-
men ed in he SA me aheu is ic:
•Exchange: This neighbo hood s uc u e andomly selec s an as-
signed o de om one ehicle’s ou e and inse s i in o he ou e
o ano he ehicle. The pickup loca ion is placed i s a a andom
posi ion, ollowed by he deli e y loca ion, which is also placed
andomly a e he pickup o ensu e ou e easibili y.
•Swapping: This neighbo hood s uc u e andomly selec s wo
ehicles and wo o de s, hen swaps he pickup and deli e y
loca ions o he selec ed o de s be ween he wo ehicle ou es.
In his s uc u e, he wo selec ed o de s can belong o he same
ehicle ou e.
•Inse ion: This ope a o a emp s o inse an unassigned o de
in o one o he ehicle ou es. Vehicles a e explo ed in lexico-
g aphic o de , wi h he pickup and deli e y loca ions placed a
andom posi ions wi hin he selec ed ou e.
•Remo al: This ope a o andomly selec s an assigned o de and
emo es i s pickup and deli e y loca ions om he ehicle’s ou e.
Appendix B. Compa ison o me aheu is ic app oaches
Tables B.16, B.17, and B.18 p esen a compa ison o ALNS and SA
o he p o i maximiza ion wi h CO2 emissions, he so ime windows
p o i maximiza ion, and he so ime windows p o i maximiza ion
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
19
D. Roelink e al.
Table B.16
A e age esul s o he ALNS and SA me aheu is ic o he p o i maximiza ion wi h CO2 emissions SMDPDPMTWPD.
Exp. Da a ins ance ALNS SA
𝑍 (e)𝑍𝜎𝛥𝑍𝐼𝑛𝑖𝑡 (%) Time (s) 𝑍 (e)𝑍𝜎𝛥𝑍𝐼𝑛𝑖𝑡 (%) Time (s)
P o i
maximiza ion
wi h CO2
emissions
D-1-25 912.26 295.15 161.09 114.13 −186.45 869.53 23.44 15.80
D-1-50 2763.26 99.05 322.88 67.44 −44.05 627.41 48.66 10.08
D-1-100 4188.22 60.67 552.67 478.79 2842.07 696.16 593.54 23.41
D-1-250 2503.01 791.78 326.01 663.44 1500.81 1061.98 300.64 22.23
D-2-25 282.47 222.05 159.56 79.28 2823.97 1907.85 344.81 72.47
D-2-50 2064.63 96.59 263.57 92.16 1658.02 1837.87 407.02 16.51
D-2-100 3497.12 57.16 445.19 300.11 1511.52 1302.64 154.64 97.66
D-2-250 5889.08 43.80 499.88 1576.42 4139.53 2439.01 967.86 113.02
D-4-25 27.80 131.92 101.71 128.54 4144.22 2155.05 2656.99 74.72
D-4-50 1223.24 122.66 227.73 224.22 −40.31 1375.49 100.24 28.63
D-4-100 2567.32 279.95 227.92 608.01 2929.72 3227.99 459.55 135.39
D-4-250 5552.79 265.73 12 409.16 1815.13 2890.34 1577.52 196.61 82.18
SFT1-C25-16-2 −161.45 7.17 76.23 108.57 −611.82 120.44 20.06 190.57
SFT2-C25-16-2 −474.47 0.00 44.31 101.37 −690.26 76.65 17.56 205.65
SFT1-C50-24-3 733.43 0.00 198.95 434.29 −227.31 570.84 70.72 210.60
SFT2-C50-24-3 126.54 24.50 114.26 270.91 −626.77 243.87 31.36 200.80
SFT1-R25-20-2 372.00 27.22 148.13 258.78 −320.81 316.34 60.76 91.38
SFT2-R25-20-2 −120.53 0.00 80.00 308.71 −444.94 130.28 42.53 109.13
SFT1-R50-30-3 302.49 0.00 123.64 506.83 −627.30 287.89 41.85 155.11
SFT2-R50-30-3 −421.56 0.00 63.74 218.05 −765.20 127.67 36.52 161.08
SFT1-RC25-20-2 63.29 8.54 108.85 276.48 −450.34 273.23 43.58 118.77
SFT2-RC25-20-2 93.75 0.00 112.94 103.54 −415.10 274.94 50.94 122.66
SFT1-RC50-30-3 544.97 0.00 157.97 643.69 −429.36 206.65 47.17 153.92
SFT2-RC50-30-3 1215.84 0.00 553.75 624.38 −61.20 365.90 140.19 125.92
SFT1-R100-50-5 −6.65 18.32 99.58 1058.85 −1072.34 321.68 35.97 233.64
SFT2-R100-50-5 163.12 1.33 107.63 975.11 −1183.14 257.43 35.11 260.50
SFT1-R100-75-7 804.84 15.70 138.84 1813.81 −1274.72 333.52 44.85 366.27
SFT2-R100-75-7 769.91 62.23 132.75 1812.31 −1169.40 375.91 45.50 335.28
A e age 1267.03 93.98 641.39 559.41 492.84 834.35 250.67 133.33
Table B.17
A e age esul s o he ALNS and SA me aheu is ic o he so ime windows p o i maximiza ion SMDPDPMTWPD.
Exp. Da a ins ance ALNS SA
𝑍 (e)𝑍𝜎𝛥𝑍𝐼𝑛𝑖𝑡 (%) Time (s) 𝑍 (e)𝑍𝜎𝛥𝑍𝐼𝑛𝑖𝑡 (%) Time (s)
So ime
windows p o i
maximiza ion
D-1-25 2 151.40 98.65 734.96 288.01 2154.18 83.83 463.85 56.34
D-1-50 4374.31 496.34 477.09 553.65 4149.23 586.42 473.39 68.53
D-1-100 5713.38 702.21 2172.67 1580.92 4483.24 1065.48 2138.71 139.79
D-1-250 11400.9 931.02 1108.71 1830.02 5221.18 1744.42 316.08 138.14
D-2-25 2332.36 69.69 365.11 766.82 1793.85 1672.33 293.96 933.19
D-2-50 4377.11 430.95 508.76 756.82 1072.09 2666.23 269.23 689.71
D-2-100 5916.66 330.98 496.84 1785.17 2296.80 2541.07 292.79 801.30
D-2-250 15056.69 818.46 1686.16 1850.71 2552.78 4058.61 181.49 423.34
D-4-25 11697.05 133.03 615.42 497.03 3498.05 2926.87 248.76 706.75
D-4-50 5848.25 507.06 371.90 559.77 5453.65 6615.57 407.80 851.42
D-4-100 8322.08 461.53 256.43 1383.13 6450.43 6029.66 555.88 1441.61
D-4-250 21007.81 1749.52 1514.70 1847.80 6391.77 5403.95 331.92 1311.95
SFT1-C25-16-2 −163.68 11.71 92.02 93.22 −1247.89 301.03 39.67 1825.87
SFT2-C25-16-2 −470.83 0.00 80.55 71.96 −1298.41 171.97 47.40 1830.10
SFT1-C50-24-3 823.10 0.00 134.52 1257.33 −798.68 386.46 66.93 1846.81
SFT2-C50-24-3 137.72 9.91 105.03 341.04 −1360.71 502.09 50.31 1856.73
SFT1-R25-20-2 496.36 21.15 123.23 733.93 −542.98 718.43 77.30 1825.56
SFT2-R25-20-2 −97.67 0.00 96.80 467.15 −1478.95 566.44 49.67 1787.09
SFT1-R50-30-3 348.32 0.00 108.68 998.98 −1800.69 545.54 53.40 1836.09
SFT2-R50-30-3 −407.92 0.00 91.16 281.96 −2541.71 480.81 43.62 1835.35
SFT1-RC25-20-2 218.73 0.00 109.52 700.81 −974.13 464.45 59.75 1764.64
SFT2-RC25-20-2 115.42 10.33 104.58 124.39 −1300.82 421.89 51.22 1817.27
SFT1-RC50-30-3 760.70 13.59 123.30 1811.56 −1860.83 821.32 42.04 1835.92
SFT2-RC50-30-3 1321.22 17.11 145.89 1629.35 −815.28 1176.07 75.36 1820.59
SFT1-R100-50-5 124.27 13.00 101.87 1821.86 −4130.38 849.75 38.88 1858.42
SFT2-R100-50-5 205.19 40.89 102.91 1624.80 −3521.02 1125.97 50.39 1858.08
SFT1-R100-75-7 930.67 13.57 109.89 1854.96 −4806.75 658.08 46.16 1880.25
SFT2-R100-75-7 974.40 36.77 111.78 1856.67 −4566.10 1230.85 44.43 1887.85
A e age 3696.93 247.05 430.37 1048.92 445.43 1636.27 243.23 1318.88
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
20
D. Roelink e al.
Table B.18
A e age esul s o he ALNS and SA me aheu is ic o he so ime windows p o i maximiza ion wi h CO2 emissions SMDPDPMTWPD.
Exp. Da a ins ance ALNS SA
𝑍 (e)𝑍𝜎𝛥𝑍𝐼𝑛𝑖𝑡 (%) Time (s) 𝑍 (e)𝑍𝜎𝛥𝑍𝐼𝑛𝑖𝑡 (%) Time (s)
So ime
windows p o i
maximiza ion
wi h CO2
emissions
D-1-25 2103.84 73.25 216.29 290.89 2063.46 78.90 218.59 58.05
D-1-50 4365.57 523.75 630.03 579.93 4153.57 817.93 556.29 66.25
D-1-100 5293.50 672.41 839.20 1382.85 4755.95 726.71 1301.77 123.56
D-1-250 10866.02 2073.13 1 002.91 1822.73 5150.54 707.06 503.09 119.43
D-2-25 2170.93 88.38 872.63 783.08 1659.98 2645.59 190.83 762.27
D-2-50 4122.57 522.10 371.30 769.88 855.29 2527.88 1771.70 585.07
D-2-100 5894.24 151.60 1 335.15 1817.71 2560.31 3761.47 547.22 560.84
D-2-250 15068.48 868.89 1 579.17 1876.24 3041.85 3093.63 389.91 748.34
D-4-25 11522.68 270.33 506.83 498.75 6465.42 5420.24 343.47 1472.04
D-4-50 6032.62 477.71 65 031.87 565.61 3857.04 4580.54 270.49 695.71
D-4-100 7853.49 1017.51 1 912.80 1473.26 4123.17 3141.55 215.61 901.32
D-4-250 22099.22 704.64 660.93 1855.18 6373.11 4647.49 556.13 1209.93
SFT1-C25-16-2 −310.32 430.29 83.77 149.62 −1239.14 460.84 42.17 1818.39
SFT2-C25-16-2 −474.47 0.00 80.80 80.50 −1464.24 333.26 39.62 1835.18
SFT1-C50-24-3 759.64 28.17 130.54 1095.36 −1146.37 567.72 53.89 1852.39
SFT2-C50-24-3 115.81 11.88 104.11 336.25 −1646.75 415.24 42.49 1849.51
SFT1-R25-20-2 480.37 0.00 121.20 698.73 −839.77 575.78 63.39 1819.47
SFT2-R25-20-2 −120.53 0.00 95.98 483.35 −1518.40 457.48 49.94 1817.53
SFT1-R50-30-3 303.17 0.00 107.40 1113.40 −2238.02 591.28 47.79 1859.98
SFT2-R50-30-3 −421.56 0.00 91.14 274.57 −2612.44 765.39 45.26 1833.28
SFT1-RC25-20-2 175.54 5.14 107.14 680.87 −1092.60 402.64 54.76 1801.88
SFT2-RC25-20-2 97.34 7.57 103.49 139.72 −1215.48 398.51 54.02 1807.80
SFT1-RC50-30-3 648.31 40.10 119.40 1809.07 −1595.77 730.92 53.80 1827.86
SFT2-RC50-30-3 1220.40 13.22 140.00 1562.95 −742.49 1106.22 76.77 1822.18
SFT1-R100-50-5 64.21 14.68 101.00 1822.23 −3704.98 975.73 44.38 1874.93
SFT2-R100-50-5 168.30 2.52 102.31 1581.87 −4587.05 954.15 37.50 1863.48
SFT1-R100-75-7 846.64 36.71 109.26 1852.04 −5074.93 712.79 44.21 1877.29
SFT2-R100-75-7 864.31 34.50 110.66 1891.32 −5155.22 1036.06 37.80 1877.61
A e age 3636.08 288.16 2 738.12 1046.00 328.07 1522.61 273.32 1312.20
Table C.19
Compu a ional esul s o he compa ison be ween ALNS and he MILP model.
Exp. Da a ins ance ALNS 𝛥MILP (%) Time (s)
Max A g Min 𝜎A g 𝜎Max A g Min 𝜎
P o i maximiza ion
D-1-5 −617.75 −673.33 −731.83 52.14 −9.00 8.44 4.65 4.30 4.13 0.19
D-1-10 609.75 538.33 406.25 92.38 −11.71 15.15 26.54 25.90 25.04 0.51
D-1-15 1155.25 1045.15 406.25 228.71 −9.53 19.80 89.60 82.18 42.09 14.18
D-1-20 1155.25 895.35 406.25 339.69 −22.50 29.40 110.93 88.03 45.92 29.09
D-2-5 −1313.58 −1388.67 −1427.67 51.55 −5.72 3.92 8.64 8.53 8.37 0.08
D-2-10 −86.08 −164.43 −289.58 87.46 −91.01 101.60 35.14 33.70 31.69 1.00
D-2-15 459.42 124.62 −289.58 358.09 −72.88 77.94 48.61 43.35 37.86 3.41
D-2-20 459.42 256.82 −289.58 290.21 −44.10 63.17 73.31 66.06 55.41 6.68
A e age 227.71 79.23 −226.19 187.53 −33.30 39.93 49.68 44.01 31.31 6.89
wi h CO2 emissions SMDPDPMTWPD, espec i ely. Each ins ance is
execu ed 10 imes, and he a e age esul s o bo h ALNS and SA a e
epo ed. The columns o he ables lis he a e age objec i e alue (𝑍),
s anda d de ia ion (𝑍𝜎), pe cen age o imp o emen o e he ini ial
solu ion (𝛥𝑍𝐼𝑛𝑖𝑡), and compu a ional ime in seconds. The bes a e age
objec i e alues a e bold- aced.
Appendix C. Pe o mance e alua ion o ALNS and MILP model
Table C.19 p esen s he esul s o compa ing he MILP o mula-
ion and ALNS me aheu is ic on small da a ins ances. The columns
epo he maximum (Max), a e age (A g), minimum (Min) and s an-
da d de ia ion (𝜎) objec i e alues o he ALNS. Nex , he a e age
(A g) and s anda d de ia ion (𝜎) o he pe cen age di e ence be ween
he ALNS and MILP solu ions a e depic ed. These a e compu ed as
𝛥𝑀𝐼𝐿𝑃 =𝑍𝑀𝐼𝐿𝑃 −𝑍𝐴𝐿𝑁𝑆
𝑍𝑀𝐼𝐿𝑃
⋅100, whe e 𝑍𝑀𝐼𝐿𝑃 and 𝑍𝐴𝐿𝑁𝑆 ep esen
he bes solu ions o he MILP o mula ion and ALNS me aheu is ic,
espec i ely. Finally, he maximum (Max), a e age (A g), minimum
(Min) and s anda d de ia ion (𝜎) o he un ime a e shown.
Appendix D. Compu a ional de ails on he ALNS pe o mance o
he SMDPDPMTWPD a ian s
Tables D.20, D.21, D.22, and D.23 p esen he esul s o he ALNS
me aheu is ic o (i) he p o i maximiza ion (HTW), (ii) he p o i
maximiza ion wi h CO2 emissions cos s (HTW + CO2), (iii) he so ime
windows (STW) and (i ) he so ime windows wi h CO2 emissions
cos s SMDPDPMTWPD (STW + CO2) espec i ely. The columns epo
he in o ma ion o he objec i e alues 𝑍 (e), he ini ial solu ion 𝑍𝐼𝑛𝑖𝑡
(e), he imp o emen pe cen age (𝛥𝑍𝐼𝑛𝑖𝑡) o 𝑍 compa ed o he ini ial
solu ion, and compu a ional imes (s). In hese ca ego ies, we epo he
a e age (A g) and s anda d de ia ion (𝜎) alues and o he objec i e
unc ion alue also he maximum (Max) and minimum (Min).
Da a a ailabili y
Da a will be made a ailable on eques .
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
21
D. Roelink e al.
Table D.20
De ailed esul s o he ALNS me aheu is ic o he p o i maximiza ion SMDPDPMTWPD (HTW).
Exp. Da a ins ance 𝑍 (e)𝑍𝑖𝑛𝑖𝑡 (e)𝛥𝑍𝐼𝑛𝑖𝑡 (%) Time (s)
Max A g Min 𝜎A g 𝜎A g 𝜎A g 𝜎
P o i maximiza ion
D-1-25 1155.25 979.05 406.25 304.55 −203.12 770.11 154.39 80.94 112.69 33.59
D-1-50 2908.25 2830.15 2703.75 87.65 316.01 1201.15 423.41 423.47 69.68 4.77
D-1-100 4339.50 4268.95 4211.67 52.89 −504.78 1075.51 850.03 1046.49 507.58 43.74
D-1-250 3145.92 2602.08 1387.33 821.66 −634.74 767.08 427.68 222.50 637.18 552.20
D-2-25 459.42 256.82 −289.58 290.21 −1185.07 796.82 149.82 50.89 71.35 7.14
D-2-50 2212.42 2142.69 2007.92 93.80 −1042.89 1634.26 269.38 195.57 88.82 2.31
D-2-100 3643.67 3573.12 3515.83 52.89 −693.59 1610.16 1993.35 5291.01 280.68 8.20
D-2-250 6053.33 5997.39 5960.50 40.58 −1957.48 1045.07 1478.04 3271.07 1811.42 7.65
D-4-25 278.83 92.22 −128.17 151.07 −1543.20 1112.90 113.90 28.50 119.15 3.47
D-4-50 1470.92 1302.13 1062.92 158.97 −2899.57 1570.77 147.52 20.05 210.53 3.13
D-4-100 2902.17 2746.90 2570.83 135.70 −2733.58 879.83 216.44 58.26 583.18 10.14
D-4-250 5934.08 5643.23 5485.17 192.66 −3389.09 969.17 284.89 76.03 1800.19 19.57
SFT1-C25-16-2 −150.08 −156.88 −172.75 10.95 −688.70 170.88 75.53 7.99 99.86 5.63
SFT2-C25-16-2 −470.83 −470.83 −470.83 0.00 −867.16 63.41 45.43 4.23 94.76 8.32
SFT1-C50-24-3 773.92 773.92 773.92 0.00 −848.97 297.77 206.96 55.97 391.45 22.30
SFT2-C50-24-3 165.92 127.62 122.25 13.51 −945.84 234.13 114.29 3.92 238.35 6.24
SFT1-R25-20-2 451.83 396.63 382.83 29.09 −673.83 295.95 171.91 35.51 234.08 10.66
SFT2-R25-20-2 −97.67 −97.67 −97.67 0.00 −722.59 135.17 86.00 2.94 281.90 6.26
SFT1-R50-30-3 342.75 342.75 342.75 0.00 −879.93 293.73 144.03 18.05 464.49 21.04
SFT2-R50-30-3 −407.92 −407.92 −407.92 0.00 −1216.03 98.60 66.26 2.76 189.05 4.84
SFT1-RC25-20-2 120.25 106.08 100.00 9.78 −759.72 136.99 114.43 3.44 250.82 4.59
SFT2-RC25-20-2 107.42 107.42 107.42 0.00 −654.57 219.73 118.49 7.14 93.45 2.99
SFT1-RC50-30-3 614.00 614.00 614.00 0.00 −958.58 172.40 165.88 11.40 575.42 11.04
SFT2-RC50-30-3 1286.50 1286.50 1286.50 0.00 −899.96 372.66 313.28 229.84 558.48 24.01
SFT1-R100-50-5 74.50 50.98 47.75 8.37 −1757.43 219.57 102.98 0.89 935.13 13.87
SFT2-R100-50-5 206.92 206.72 205.92 0.42 −1843.42 175.52 111.31 1.09 862.80 21.67
SFT1-R100-75-7 941.83 910.60 904.75 11.84 −2223.03 370.52 142.27 8.88 1814.59 9.14
SFT2-R100-75-7 939.00 804.97 596.75 92.41 −1996.33 263.53 140.80 6.15 1816.05 9.32
A e age 1407.22 1322.49 1186.79 91.39 −1228.83 605.48 308.17 398.75 542.61 31.35
Table D.21
De ailed esul s o he ALNS me aheu is ic o he p o i maximiza ion wi h CO2 emissions SMDPDPMTWPD (HTW +CO2).
Exp. Da a ins ance 𝑍 (e)𝑍𝑖𝑛𝑖𝑡 (e)𝛥𝑍𝐼𝑛𝑖𝑡 (%) Time (s)
Max A g Min 𝜎A g 𝜎A g 𝜎A g 𝜎
P o i
maximiza ion
wi h CO2
emissions
D-1-25 1105.96 912.26 357.46 295.15 −452.94 728.67 161.09 64.18 114.13 34.30
D-1-50 2853.43 2763.26 2648.93 99.05 −526.86 1232.19 322.88 151.32 67.44 1.15
D-1-100 4255.46 4188.22 4127.62 60.67 300.87 1666.20 552.67 510.46 478.79 19.79
D-1-250 3081.55 2503.01 1340.29 791.78 −255.89 1084.21 326.01 185.23 663.44 596.58
D-2-25 410.12 282.47 −338.37 222.05 −1194.69 758.23 159.56 68.29 79.28 6.20
D-2-50 2157.60 2064.63 1953.10 96.59 −1715.75 1336.02 263.57 139.64 92.16 5.63
D-2-100 3559.62 3497.12 3431.79 57.16 −1362.26 1640.95 445.19 561.62 300.11 3.91
D-2-250 5941.85 5889.08 5849.01 43.80 −2163.96 916.31 499.88 405.76 1576.42 492.86
D-4-25 197.52 27.80 −209.48 131.92 −2240.50 1001.75 101.71 7.43 128.54 6.49
D-4-50 1394.72 1223.24 986.72 122.66 −2395.47 2037.72 227.73 219.25 224.22 4.71
D-4-100 2796.74 2567.32 1865.83 279.95 −1965.62 1571.13 227.92 70.94 608.01 42.33
D-4-250 5792.12 5552.79 5144.48 265.73 −2778.24 1942.47 12 409.16 38161.53 1815.13 13.55
SFT1-C25-16-2 −159.18 −161.45 −181.85 7.17 −718.15 159.64 76.23 6.81 108.57 5.10
SFT2-C25-16-2 −474.47 −474.47 −474.47 0.00 −855.62 60.08 44.31 3.73 101.37 3.25
SFT1-C50-24-3 733.43 733.43 733.43 0.00 −912.79 359.73 198.95 55.81 434.29 17.33
SFT2-C50-24-3 154.62 126.54 99.39 24.50 −922.62 212.10 114.26 3.71 270.91 5.30
SFT1-R25-20-2 423.40 372.00 354.40 27.22 −815.36 184.29 148.13 12.77 258.78 14.10
SFT2-R25-20-2 −120.53 −120.53 −120.53 0.00 −672.92 200.83 80.00 8.09 308.71 13.60
SFT1-R50-30-3 302.49 302.49 302.49 0.00 −1303.77 178.15 123.64 3.60 506.83 25.77
SFT2-R50-30-3 −421.56 −421.56 −421.56 0.00 −1180.52 148.89 63.74 4.87 218.05 6.86
SFT1-RC25-20-2 79.49 63.29 59.24 8.54 −755.18 187.42 108.85 2.32 276.48 8.40
SFT2-RC25-20-2 93.75 93.75 93.75 0.00 −819.18 223.33 112.94 6.58 103.54 4.76
SFT1-RC50-30-3 544.97 544.97 544.97 0.00 −1030.73 305.02 157.97 20.29 643.69 30.51
SFT2-RC50-30-3 1215.84 1215.84 1215.84 0.00 −790.52 434.24 553.75 925.00 624.38 18.62
SFT1-R100-50-5 40.99 −6.65 −33.00 18.32 −1672.12 231.47 99.58 1.17 1058.85 33.62
SFT2-R100-50-5 163.95 163.12 161.20 1.33 −2162.17 224.73 107.63 0.88 975.11 10.40
SFT1-R100-75-7 847.08 804.84 796.52 15.70 −2158.94 391.03 138.84 10.08 1813.81 7.71
SFT2-R100-75-7 837.03 769.91 674.91 62.23 −2366.58 240.61 132.75 3.42 1812.31 8.22
A e age 1350.28 1267.03 1105.79 93.98 −1281.73 702.05 641.39 1486.24 559.41 51.47
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
22
D. Roelink e al.
Table D.22
De ailed esul s o he ALNS me aheu is ic o he so ime windows p o i maximiza ion SMDPDPMTWPD (STW).
Exp. Da a ins ance 𝑍 (e)𝑍𝑖𝑛𝑖𝑡 (e)𝛥𝑍𝐼𝑛𝑖𝑡 (%) Time (s)
Max A g Min 𝜎A g 𝜎A g 𝜎A g 𝜎
So ime
windows p o i
maximiza ion
D-1-25 2 234.93 2 151.40 2019.15 98.65 −472.93 1243.92 734.96 1113.89 288.01 9.93
D-1-50 4 783.28 4 374.31 3672.87 496.34 −456.82 1527.30 477.09 343.02 553.65 46.59
D-1-100 6175.70 5 713.38 4495.08 702.21 −111.47 1744.49 2172.67 4929.72 1580.92 391.18
D-1-250 12 682.02 11 400.91 10040.92 931.02 432.88 2487.89 1108.71 611.64 1830.02 24.79
D-2-25 2 400.93 2 332.36 2185.15 69.69 −1985.37 1196.09 365.11 361.72 766.82 60.73
D-2-50 4 704.83 4 377.11 3594.42 430.95 −2324.73 1659.62 508.76 803.53 756.82 62.52
D-2-100 6097.25 5 916.66 5004.12 330.98 −2251.47 1720.37 496.84 281.59 1785.17 105.91
D-2-250 16 242.73 15 056.69 14543.18 818.46 −1937.93 1992.43 1686.16 1832.78 1850.71 30.20
D-4-25 11982.95 11 697.05 11563.67 133.03 −3574.20 1773.41 615.42 491.15 497.03 106.25
D-4-50 6 454.68 5 848.25 5140.77 507.06 −3618.41 2736.00 371.90 328.06 559.77 46.00
D-4-100 8903.33 8 322.08 7844.12 461.53 −5778.85 1854.55 256.43 44.76 1383.13 324.30
D-4-250 23 699.88 21 007.81 19368.65 1749.52 −3681.07 1410.89 1514.70 2791.30 1847.80 31.47
SFT1-C25-16-2 −150.08 −163.68 −172.75 11.71 −2059.42 109.56 92.02 0.80 93.22 13.33
SFT2-C25-16-2 −470.83 −470.83 −470.83 0.00 −2432.27 169.48 80.55 1.48 71.96 10.70
SFT1-C50-24-3 823.10 823.10 823.10 0.00 −2411.45 271.76 134.52 3.84 1257.33 49.10
SFT2-C50-24-3 165.92 137.72 134.58 9.91 −2775.67 257.13 105.03 0.86 341.04 48.97
SFT1-R25-20-2 508.80 496.36 450.72 21.15 −2181.32 320.14 123.23 3.72 733.93 30.49
SFT2-R25-20-2 −97.67 −97.67 −97.67 0.00 −3058.59 172.83 96.80 0.18 467.15 21.70
SFT1-R50-30-3 348.32 348.32 348.32 0.00 −4039.08 344.14 108.68 0.68 998.98 43.16
SFT2-R50-30-3 −407.92 −407.92 −407.92 0.00 −4641.04 378.93 91.16 0.76 281.96 59.28
SFT1-RC25-20-2 218.73 218.73 218.73 0.00 −2331.43 296.99 109.52 1.23 700.81 50.80
SFT2-RC25-20-2 127.42 115.42 107.42 10.33 −2560.61 343.57 104.58 0.74 124.39 23.07
SFT1-RC50-30-3 767.12 760.70 726.23 13.59 −3301.58 353.74 123.30 2.74 1811.56 6.47
SFT2-RC50-30-3 1326.63 1321.22 1 272.52 17.11 −2917.40 373.51 145.89 5.27 1629.35 126.73
SFT1-R100-50-5 145.27 124.27 104.53 13.00 −6647.26 384.94 101.87 0.21 1821.86 14.14
SFT2-R100-50-5 221.72 205.19 89.15 40.89 −7117.25 437.00 102.91 0.63 1624.80 185.71
SFT1-R100-75-7 947.73 930.67 913.02 13.57 −9428.40 394.54 109.89 0.40 1854.96 28.58
SFT2-R100-75-7 1055.37 974.40 929.73 36.77 −8296.17 494.53 111.78 0.79 1856.67 35.69
A e age 3996.15 3696.93 3 372.89 247.05 −3284.26 944.64 430.37 498.48 1048.92 70.99
Table D.23
De ailed esul s o he ALNS me aheu is ic o he so ime windows p o i maximiza ion wi h CO2 emissions SMDPDPMTWPD (STW +CO2).
Exp. Da a ins ance 𝑍 (e)𝑍𝑖𝑛𝑖𝑡 (e)𝛥𝑍𝐼𝑛𝑖𝑡 (%) Time (s)
Max A g Min 𝜎A g 𝜎A g 𝜎A g 𝜎
So ime
windows p o i
maximiza ion
wi h CO2
emissions
D-1-25 2 153.62 2 103.84 1937.84 73.25 44.18 1308.70 216.29 123.57 290.89 4.75
D-1-50 4 713.47 4365.57 3 608.04 523.75 −713.81 1410.04 630.03 582.60 579.93 11.62
D-1-100 6069.25 5293.50 4 404.20 672.41 −69.07 1534.14 839.20 914.68 1382.85 372.14
D-1-250 12 589.78 10866.02 5411.38 2073.13 −190.35 1585.85 1 002.91 802.93 1822.73 12.46
D-2-25 2 273.27 2 170.93 2057.49 88.38 −732.08 1228.27 872.63 1 812.28 783.08 63.95
D-2-50 4 628.21 4122.57 3 522.79 522.10 −1364.37 1547.94 371.30 217.33 769.88 33.19
D-2-100 5984.00 5894.24 5 552.92 151.60 −1258.48 2056.14 1 335.15 2895.80 1817.71 8.95
D-2-250 16 078.04 15068.48 14395.43 868.89 −1934.77 1245.82 1 579.17 1727.99 1876.24 34.61
D-4-25 11809.23 11 522.68 11 072.53 270.33 −3087.20 907.39 506.83 136.60 498.75 112.98
D-4-50 6 323.25 6032.62 5 014.32 477.71 −3775.13 2168.38 65 031.87 204749.56 565.61 37.02
D-4-100 8834.78 7 853.49 6 205.03 1017.51 −3498.85 2084.26 1912.80 4945.19 1473.26 296.61
D-4-250 23 436.02 22099.22 21753.42 704.64 −4451.25 1487.98 660.93 226.04 1855.18 26.44
SFT1-C25-16-2 −159.18 −310.32 −1534.58 430.29 −1936.79 161.86 83.77 22.68 149.62 193.51
SFT2-C25-16-2 −474.47 −474.47 −474.47 0.00 −2482.22 175.69 80.80 1.35 80.50 10.84
SFT1-C50-24-3 773.00 759.64 706.20 28.17 −2493.37 151.60 130.54 1.71 1095.36 48.66
SFT2-C50-24-3 133.23 115.81 108.43 11.88 −2850.50 255.86 104.11 0.73 336.25 42.41
SFT1-R25-20-2 480.37 480.37 480.37 0.00 −2288.60 247.00 121.20 2.20 698.73 35.07
SFT2-R25-20-2 −120.53 −120.53 −120.53 0.00 −3015.63 222.52 95.98 0.29 483.35 23.55
SFT1-R50-30-3 303.17 303.17 303.17 0.00 −4124.09 363.51 107.40 0.65 1113.40 53.91
SFT2-R50-30-3 −421.56 −421.56 −421.56 0.00 −4770.52 278.57 91.14 0.52 274.57 38.16
SFT1-RC25-20-2 177.97 175.54 165.79 5.14 −2491.29 278.31 107.14 0.95 680.87 38.21
SFT2-RC25-20-2 111.70 97.34 93.75 7.57 −2827.46 342.21 103.49 0.53 139.72 24.12
SFT1-RC50-30-3 666.47 648.31 548.40 40.10 −3376.66 333.68 119.40 2.45 1809.07 6.32
SFT2-RC50-30-3 1 230.49 1 220.40 1 201.27 13.22 −3177.33 624.17 140.00 9.22 1562.95 63.02
SFT1-R100-50-5 95.48 64.21 49.54 14.68 −6490.16 292.98 101.00 0.27 1822.23 14.50
SFT2-R100-50-5 170.63 168.30 164.50 2.52 −7295.54 347.42 102.31 0.12 1581.87 168.97
SFT1-R100-75-7 900.46 846.64 787.16 36.71 −9158.63 474.17 109.26 0.56 1852.04 36.27
SFT2-R100-75-7 935.59 864.31 831.73 34.50 −8132.07 499.79 110.66 0.74 1891.32 27.32
A e age 3917.70 3 636.08 3136.59 288.16 −3140.79 843.37 2 738.12 7827.84 1046.00 65.70
Re e ences
[1] CBS. 2023, h ps://openda a.cbs.nl/#/CBS/nl/da ase /83101NED/ able? s=
1712140961134. [Accessed 03 Ap il 2024].
[2] CBS. 2024, h ps://openda a.cbs.nl/#/CBS/nl/da ase /83760NED/ able? s=
1712142139308. [Accessed 03 Ap il 2024].
[3] CBS. 2024, h ps://openda a.cbs.nl/#/CBS/nl/da ase /83077NED/ able? s=
1712140231380. [Accessed 03 Ap il 2024].
[4] Sa K, Ghadimi P. A sys ema ic li e a u e e iew o he ehicle ou ing p oblem
in e e se logis ics ope a ions. Compu Ind Eng 2023;177:109011.
[5] El Bouyahyiouy K, Bellabdaoui A. The selec i e ull uckload mul i-depo ehicle
ou ing p oblem wi h ime windows: Fo mula ion and a gene ic algo i hm. In J
Supply Ope Manag 2022;9(3):299–320.
Ope a ions Resea ch Pe spec i es 14 (2025) 100342
23
D. Roelink e al.
[6] Li Y, Yang J. The las -mile deli e y ehicle ou ing p oblem wi h handling cos
in he on wa ehouse mode. Compu Ind Eng 2024;190:110076.
[7] El Bouyahyiouy K, Bellabdaoui A. A new c osso e o sol e he ull uckload
ehicle ou ing p oblem using gene ic algo i hm. In: 2016 3 d in e na ional
con e ence on logis ics ope a ions managemen . GOL, IEEE; 2016, p. 1–6.
[8] El Bouyahyiouy K, Bellabdaoui A. An an colony op imiza ion algo i hm o sol -
ing he ull uckload ehicle ou ing p oblem wi h p o i . In: 2017 in e na ional
colloquium on logis ics and supply chain managemen . LOGISTIQUA, IEEE; 2017,
p. 142–7.
[9] El Bouyahyiouy K, Bellabdaoui A. A mixed-in ege linea p og amming model
o he selec i e ull- uckload mul i-depo ehicle ou ing p oblem wi h ime
windows. Decis Sci Le 2021;10(4):471–86.
[10] El Bouyahyiouy K, Bellabdaoui A. An am-TSPTW ans o ma ion and a RTS
algo i hm o commodi y selec ion and ehicle ou ing planning in ull uckload
indus y. In: 2022 14 h in e na ional colloquium o logis ics and supply chain
managemen . LOGISTIQUA, IEEE; 2022, p. 1–6.
[11] El Bouyahyiouy K, Bellabdaoui A. A gene ic-based algo i hm o commodi y
selec ion and ull uckload ehicle ou ing p oblem. In: Digi al echnologies and
applica ions: p oceedings o ICDTA’23, Fez, Mo occo, olume 2. Sp inge ; 2023,
p. 806–16.
[12] A che i C, Spe anza MG, Vigo D. Chap e 6: Pickup-and-deli e y p oblems o
goods anspo a ion. In: Vehicle ou ing: p oblems, me hods, and applica ions,
second edi ion. SIAM; 2014, p. 161–92.
[13] Ve donck L. Collabo a i e logis ics om he pe spec i e o eigh anspo
companies (Ph.D. hesis), Uni e si ei Hassel ; 2017, A ailable a h ps://
documen se e .uhassel .be/bi s eam/1942/23685/1/Doc o aa Lo eVe donck.
pd .
[14] Dumas Y, Des osie s J, Soumis F. The pickup and deli e y p oblem wi h ime
windows. Eu opean J Ope Res 1991;54(1):7–22.
[15] Jung S, Haghani A. Gene ic algo i hm o a pickup and deli e y p oblem wi h
ime windows. T ansp Res Rec 2000;1733(1):1–7.
[16] Alaïa EB, D idi IH, Bouch iha H, Bo ne P. Op imiza ion o he mul i-depo &
mul i- ehicle pickup and deli e y p oblem wi h ime windows using gene ic
algo i hm. In: 2013 in e na ional con e ence on con ol, decision and in o ma ion
echnologies. coDIT, IEEE; 2013, p. 343–8.
[17] Ropke S, Pisinge D. 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. T ansp Sci 2006;40(4):455–72.
[18] K ajewska MA, Kop e H, Lapo e G, Ropke S, Zaccou G. Ho izon al coope a ion
among eigh ca ie s: eques alloca ion and p o i sha ing. J Ope Res Soc
2008;59(11):1483–91.
[19] Dahl S, De igs U. Coope a i e planning in exp ess ca ie ne wo ks—An empi ical
s udy on he e ec i eness o a eal- ime decision suppo sys em. Decis Suppo
Sys 2011;51(3):620–6.
[20] Baldacci R, Ba olini E, Mingozzi A. An exac algo i hm o he pickup and
deli e y p oblem wi h ime windows. Ope Res 2011;59(2):414–26.
[21] Heilig L, Lalla-Ruiz E, Voß S. Po -IO: an in eg a i e mobile cloud pla o m
o eal- ime in e - e minal uck ou ing op imiza ion. Flex Se Manu J
2017;29(3–4):504–34.
[22] Adi TN, Bae H, Iskanda YA. In e e minal uck ou ing op imiza ion using
coope a i e mul iagen deep ein o cemen lea ning. P ocesses 2021;9(10):1728.
[23] Alaïa EB, D idi IH, Bouch iha H, Bo ne P. A pa icle swa m op imiza ion o
he mul i-depo s pick-up and deli e y p oblems wi h ime windows and mul i-
ehicles. In: In e na ional con e ence on indus ial enginee ing and sys ems
managemen IESM. 2017, p. 623–8.
[24] Ha baoui D idi I, Ben Alaïa E, Bo ne P, Bouch iha H. Op imisa ion o he mul i-
depo s pick-up and deli e y p oblems wi h ime windows and mul i- ehicles
using PSO algo i hm. In J P od Res 2020;58(14):4201–14.
[25] Ting C-K, Liao X-L. The selec i e pickup and deli e y p oblem: Fo mula ion and
a meme ic algo i hm. In J P od Econ 2013;141(1):199–211.
[26] Ting C-K, Liao X-L, Huang Y-H, Liaw R-T. Mul i- ehicle selec i e pickup and
deli e y using me aheu is ic algo i hms. In o m Sci 2017;406:146–69.
[27] Al Chami Z, Manie H, Manie M-A. New model o a a ian o pick up and
deli e y p oblem. In: 2016 IEEE in e na ional con e ence on sys ems, man, and
cybe ne ics. SMC, IEEE; 2016, p. 001708–13.
[28] Al Chami Z, Manie H, Manie M-A. A lexicog aphic app oach o he bi-objec i e
selec i e pickup and deli e y p oblem wi h ime windows and pai ed demands.
Ann Ope Res 2017;273:237–55.
[29] Al Chami Z, Manie H, Manie M-A, Fi ou i C. A hyb id gene ic algo i hm o sol e
a mul i-objec i e pickup and deli e y p oblem. IFAC- Pap 2017;50(1):14656–61.
[30] Al Chami Z, El Fli y H, Manie H, Manie M-A. A new me aheu is ic o sol e a
selec i e pickup and deli e y p oblem. In: 2018 4 h in e na ional con e ence on
logis ics ope a ions managemen . GOL, IEEE; 2018, p. 1–5.
[31] Al Chami Z, Manie H, Manie M-A. A new compac wo-index o mula ion o
a pickup and deli e y p oblem. 2018, A ailable a h ps://www.openscience. /
IMG/pd /is e_ o18 1n1_1.pd .
[32] Al Chami Z, El Fli y H, Manie H, Manie M-A. Mul i-pe iod pickup and deli e y
p oblem wi h ime windows and pai ed demands. In: 2018 15 h in e na ional
con e ence on con ol, au oma ion, obo ics and ision. ICARCV, IEEE; 2018, p.
337–42.
[33] Al Chami Z, Becha a B, Manie H, Manie M-A. A obus pickup and deli e y
p oblem wi h unce ain a el ime. In: 2018 IEEE 30 h in e na ional con e ence
on ools wi h a i icial in elligence. ICTAI, IEEE; 2018, p. 940–6.
[34] Al Chami Z, Becha a B, Manie H, Manie M-A, Sleiman M. A GRASP-
ALNS combina ion o obus pickup and deli e y p oblem. In J P od Res
2022;60(12):3809–28.
[35] Li Y, Chen H, P ins C. Adap i e la ge neighbo hood sea ch o he pickup and
deli e y p oblem wi h ime windows, p o i s, and ese ed eques s. Eu opean J
Ope Res 2016;252(1):27–38.
[36] Gans e e M, Küçük epe M, Ha l RF. The mul i- ehicle p o i able pickup and
deli e y p oblem. O Spec 2017;39:303–19.
[37] Peng Z, Al Chami Z, Manie H, Manie M-A. A pa icle swa m op imiza ion
o selec i e pickup and deli e y p oblem. In: 2018 IEEE 30 h in e na ional
con e ence on ools wi h a i icial in elligence. ICTAI, IEEE; 2018, p. 947–52.
[38] Peng Z, Al Chami Z, Manie H, Manie M-A. A hyb id pa icle swa m op imiza-
ion o he selec i e pickup and deli e y p oblem wi h ans e s. Eng Appl A i
In ell 2019;85:99–111.
[39] Sun P, Veelen u LP, Hewi M, Van Woensel T. Adap i e la ge neighbo hood
sea ch o he ime-dependen p o i able pickup and deli e y p oblem wi h ime
windows. T ansp Res Pa E: Logis T ansp Re 2020;138:101942.
[40] Ben-Said A, Mouk im A, Guibadj RN, Ve ny J. Using decomposi ion-based mul i-
objec i e algo i hm o sol e selec i e pickup and deli e y p oblems wi h ime
windows. Compu Ope Res 2022;145:105867.
[41] Baklagis D, Dikas G, Minis I. The eam o ien ee ing pick-up and deli e y p oblem
wi h ime windows and i s applica ions in lee sizing. RAIRO- Ope Res- Rech
Opé 2016;50(3):503–17.
[42] Liu C, Aleman DM, Beck JC. Modelling and sol ing he senio anspo a ion
p oblem. In: In eg a ion o cons ain p og amming, a i icial in elligence, and
ope a ions esea ch: 15 h in e na ional con e ence, CPAIOR 2018, Del , he
Ne he lands, June 26–29, 2018, p oceedings 15. Sp inge ; 2018, p. 412–28.
[43] San ini A, Plum CE, Ropke S. A b anch-and-p ice app oach o he eede ne wo k
design p oblem. Eu opean J Ope Res 2018;264(2):607–22.
[44] Nadizadeh A. Fo mula ion and a heu is ic app oach o he o ien ee ing
loca ion- ou ing p oblem. RAIRO- Ope Res 2021;55:S2055–69.
[45] Eu osende . How o calcula e LDM o shipping? 2023, h ps://www.eu osende .
com/blog/en/calcula e-ldm-shipping/. [Accessed 31 May 2024].
[46] HST G oep. Logis iek Ja gon. 2024, h ps://www.hs .nl/logis iek-ja gon/.
[Accessed 31 May 2024].
[47] Schul e F, Lalla-Ruiz E, González-Ramí ez RG, Voß S. Reducing po - ela ed
emp y uck emissions: a ma hema ical app oach o uck appoin men s wi h
collabo a ion. T ansp Res Pa E: Logis T ansp Re 2017;105:195–212, URL
h ps://www.sciencedi ec .com/science/a icle/pii/S1366554516300801.
[48] Fe nández Gil A, Lalla-Ruiz E, Gómez Sánchez M, Cas o C, e al. A e iew o
heu is ics and hyb id me hods o g een ehicle ou ing p oblems conside ing
emissions. J Ad T ansp 2022;2022.
[49] Co ona-Gu ié ez K, Nucamendi-Guillén S, Lalla-Ruiz E. Vehicle ou ing wi h
cumula i e objec i es: a s a e o he a and analysis. Compu Ind Eng
2022;169:108054.
[50] Azue o-O iz J, Ga i ia-He nández M, Jiménez-Rod íguez V, Vale-San iago E,
González-Nei a E. Design o a hyb idiza ion be ween abu sea ch and PAES
algo i hms o sol e a mul i-depo , mul i-p oduc g een ehicle ou ing p oblem.
Decis Sci Le 2023;12(2):441–56.
[51] Ma a STW, No cahyo R, Jodiawan P, Lusian o o L, Ri ai AP. A su ey o
adap i e la ge neighbo hood sea ch algo i hms and applica ions. Compu Ope
Res 2022;105903.
[52] Azi N, Gend eau M, Po in J-Y. An adap i e la ge neighbo hood sea ch o a
ehicle ou ing p oblem wi h mul iple ou es. Compu Ope Res 2014;41:167–73.
[53] A ci MG, A ci M. An adap i e la ge neighbo hood sea ch app oach o mul iple
a eling epai man p oblem wi h p o i s. Compu Ope Res 2019;111:367–85.
[54] Oda T, Liu Y, Sakamo o S, Elmazi D, Ba olli L, Xha a F. Analysis o mesh ou e
placemen in wi eless mesh ne wo ks using iedman es conside ing di e en
me a-heu is ics. In J Commun Ne w Dis ib Sys 2015;15(1):84–106.
[55] Pe ei a DG, A onso A, Medei os FM. O e iew o F iedman’s es and pos -hoc
analysis. Comm S a is Simula ion Compu 2015;44(10):2636–53.
[56] Boyacı B, Dang TH, Le ch o d AN. Vehicle ou ing on oad ne wo ks: how good
is euclidean app oxima ion? Compu Ope Res 2021;129:105197.
[57] Eu opean Commission. 2023, h ps:// oad-sa e y. anspo .ec.eu opa.eu/eu- oad-
sa e y-policy/p io i ies/sa e- oad-use/sa e-speed/a chi e/cu en -speed-limi -
policies_en. [Accessed 13 July 2023].
[58] Rie eld P, Zwa B, Van Wee B, an den Hoo n T. On he ela ionship be ween
a el ime and a el dis ance o commu e s. Ann Reg Sci 1999;33:269–87.
[59] Ho ns a RP, Sil a A, Roodbe gen KJ, Coelho LC. The ehicle ou ing p oblem
wi h simul aneous pickup and deli e y and handling cos s. Compu Ope Res
2020;115:104858.
[60] Taş D, Dellae N, Van Woensel T, De Kok T. Vehicle ou ing p oblem wi h
s ochas ic a el imes including so ime windows and se ice cos s. Compu
Ope Res 2013;40(1):214–24.
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