Consolidating and Dispatching Truck
Shipments of Mobil Heavy Petroleum Products
DA N
O . B AU SCH
I NSIGHT .I" f.
19820 Villas e Office C""rt
Bel/d, On'goll 97702
GERALD G . BROWN
Opaa titJIIs Research (OR/ BW)
Naval Postgral1uatc ScI/l)ol
MOllterey, Clllifom iQ 93943
DAVID RONE N
School of 8 11 5;lIl'% Administration
Ulliversity of Missouri- St. LOll is
8001 Nat ural Rridge Road
St. [.oll is, Missouri 63121
Mobil Oil Corpo rat ion consolidates and dispatches tru ck shipments of heavy petroleum prod ucts-lubricants in pa ckages
and in bul k- from 10 lubricant plants nationwid e. It disp at ches
hundred s of orde rs daily eithe r ind ividu ally or as consolida ted
tru ckloads, usin g a very nonhom ogen eous fl eet of Mobi lcontro lled and cont rac t vehicles and commo n carriers. Shipmen t sche d ules may span severa l da ys and include stops to
pick up return ed drums or entire trailers. Shipping costs depend upon th e vehicle used , th e shipme nt size, th e location s of
th e stops, and th e route distance and time. Ca ndida te consolidations are ge ne ra ted autom ati cally or with disp at cher ass istance. The n, th e dispatcher uses optimization to select a mini ma l-cost set of sche d ules. Mo bil has been usin g thi s sys tem for
three yea rs, redu cing ann ua l transportation costs by abo ut $ 1
million (US).
Sta nd not upon the o rder of your gotng.
But go <I t onn'.-S ha kl'spl' a rl·, Macbeth
A
computer-as sisted sys te m consolidates and di spatches tru ck shi pments of pa ckaged and bulk lu brican t
C"I'HI~hl' 1'1'10" I n ~h t u lt ' l ". 0lwral">n' R""-'d,,-h
,m J lh., )"b n a ~l·n ... nl S...,.'nH"
UINI2W2/'1Sj2O,1l2/000ISll12O,
I hh pal"'" "d~ .. ,,,, .. 't'll
(lube) products at Mubil Oil Co rpor a tion .
The sys te m cons o lid ates deliveries automaticall y o r with dispatcher assistance,
creating a lar ge se t of promisin g cand id ate
sched ules cos ted for eac h ava ilable tru ck
typ e , The ca nd ida te sc hed ules ma y include
IN fl L'S 1RIFo., I'F.TROIJ'U\I/,I\, AlURAI GAo.,
lRANSI'OKTATlON -R()UH SLL I:C nON
INT ERf AC ES 25: 2 March -April 199 5 (pp. 1-1 7)
BAUSCH, BROWN, RONEN
many truckload and less -than -truckload
(LTL) shipment alternatives (or any given
order. may offer to ship orders earlier than
absolutely Ill'Ct'Ssary if this looks appeal ing, and may include stops to pick up re turned drums or entire trai lers , The system
then SOIVl'S a set -partitioning model to Sl' lect a least-cost portfoliu of schedules.
which it then converts into truck routes.
Ronen [forthcoming] gives .1 review of pTl··
vious literature on dispatching all varieties
of petroleum products.
Mobil's Lube Operations
Mobil Oil Corporation markets over
1,000 heavy petroleum products-i-lubc
usuallv reached before truck volume limits.
However. some products are light (for ex ample, flaked wax), and some han' bulky
packaging (for example, drums) .
There are about 10,000 customer ac counts, each assigned to a primary supply
source from one of the 10 lube plants. Mo bil may ship from .1 secondary source in
case of product shortage. Mobil reviews
primary source assignments periodically.
Dynamic sourcing is impractical because of
the limited availability of special products.
A customer order usually consists of
multiple products. Mobil fills as much of
oils, grl',lst.'S , and waxes-in over 2,000
product -package combinations. A small
number of these products are fast movers,
but the majority are slow movers and Spl' cial products. The most familiar products
are Mobil 1 motor oil, other Mobil motor
oils, and industrial greases. Mobil markets
these products to service stations, chain
stores, and industrial customers, such as
steel mills or automobile plants.
Mobil operates 10 lube plants in the
continental US (Figure 1). These plants re ceive their base oil stocks in bulk from rl'fineries and receive additives, mostly pa ck aged. from refineries and outside vendors.
Some lube plants blend products primarily
to stock, while others blend primarily to
order. Each plant blends products common
to all plants, and each blends specialty
products that it ships to the other plants
the order .1S possible, and back -orders the
remainder. Infrequently, it may n-assign
entire orders prior to dispatch to a second ary source. Most plants and distribution
warehouses have a local delivery region in
which they assign customers to regular de livery days during the week, Customers
not in a loca l delivery region may receive
shipments on any day of the week .
Mobil usually pays for shipping heavy
products. Some customers, however. prefer
to pick up their own orders at the lube
plant. Customer orders that are smaller
than a minimum size are shipped fn'ight
collect or picked up by the customer,
In addition to transporting products outbound , trucks transport inbound bulk and
packaged additives and packaging materials from suppliers, empty drums and trail ers returned from customers, and occa sional product returns from customers.
(or distribution . Each lube plant has a col located mixing warehouse that supplies
products to customers, distributors, pack agers, and other warehouses.
Most of these products have high weight
per uni t volume: Truck weight limits are
They haul the empty drums to recondi tioning facilities, which are not located at
the warehouses.
Cent ra lized Dispatch
Mobi l has centralized its order taking
and dispatching for heavy products at
INTER FACES 25:2
2
MOBIL
n
Cicero.
f>
jB o~to n
.>
.
wo~~ven ~)d;boro
Clevelan ~
Kansas City
•
Vernon
•
Beaumont
•
Tcim pa
•
Figu re 1: Mobil lubricant plan ts ar e locat ed natio nwide. Each ord er is sourced alo ne of these
sites a nd e ithe r s h ippe d individuall y or conso lidated into tru ck loads wit h other o rd er s.
Malvern, Pennsylvania . It tak es over
10,000 orders a mon th for packa ged a nd
bu lk products, main ly by telephon e. Mob il
deliv ers ab o ut three -qu arter s o f these orders, and customers pick up th e rest.
Mo bil disp atch es eac h lube plan t deli vl'ry a rea se pa ra tely . It may ship or ders ca rlier th an required by custome r service
guide lines if the products are in stock and
if it is economica l to do so.
Mobil o pe ra tes its ovv n fleet of tractors,
tank (bu lk) trailer s w hic h may ha ve multiple com pa rtme n ts, package trailer s (box
van s), a nd stra ight tru cks. It uses this fleet,
located at th e lub e pla nts, prima rily for lo ca l truckload an d LTL sh ipme nts, so me
long-ha ul tru cklo ad , and pickups. Th e Mobil flee t is o pe ra ted for a sing le d aily shift
(w ith overtime) five days a week. Th e fleet
is no t u niform: Tru cks may hav e different
le ngth s, com pa rtmen ts, and equ ipm ent
(Figu re 2). Mobi l also uses ded ica ted ca rrier tru cks to supplement its own fleet for
local deliv ery and lon g ha ul, and uses con tract a nd com mo n ca rriers for truckload
a nd LTL long-h aul s hi pme nts.
Mobil commits two se pa ra te disp atch es
eac h day for eac h lube plan t. one for bulk
orde rs with its fleet of tank tru cks and th e
othe r for packaged prod ucts. Th e overlap
between these two d isp at ches is m inimal;
however, th ey ha ve so me issu es in cornm on :
Wh a t modes of trans port should be
used ?
What mix of owned a nd hir ed veh icles
is best ?
\Vhich ca rriers a n' mo st attractive?
Whi ch orde rs can be consolidated?
Can pool or stop-off d eliveries save
March- April 1995
3
BA USCH , BRO W , RO EN
and
Outbound deliveries interspersed with
order pickups or a trai ler back haul.
Each of these sh ipment modes has its
own costs and operating rules . These poli cies and restrictions include
Truck and trailer capacity limits on
weight, volume, and number of drums;
Carrier limits on number of stop-efts
and the ext ra driving d ist a nce these
stop-efts require;
Interstate and intrastate restrictions;
Limits on the availability of special
equipment ;
Limits on operating radius:
Figure 2: Mobil has a mixed truck fleet. The
27-fool and 45-fool package haile rs sh own
may be equipped with specia l d eliver y eq u ipment. Th ere are ma n y other tru ck typ es.
monev?
Should any future orders be shipped
l'arly?
Bulk tank trucks may have cornpart me rits so that t hey can carry mult ipit.'
products. Must bulk shipments are lank
truckloads. Very few bulk loads require
multiple-stop delivery routes, and the lank
lrucks usually make multiple trips per day.
The major problem in bulk dispatching is
to coord ina te production planning with
disp atchi ng, that is, to make sure that the
bulk product will be available when the
truck shows up for loading.
A packaged order may \\'l'igh from ~l'\' ­
eral pounds up to a truckload . Mobil m.,y
co nso lidate and ship orders by any of the
fo llowing mo des:
Local delivery by owned trucks,
Local delivery by hired trucks,
Overnight delivery by owned tru cks,
Packaged good carriers (common ca r-
Hl'quirl'ml'nts fo r minimum empty
truck ca pacity before p ickup is permit ted; and
Time windows .
Mobil -owned and dedicated carrier
tru cks -the controlled fleet -must return
to their source at the end of a schedu le,
and there are ,1 nu m be r of ways to pla n fo r
this (Figure 3) . Contract carriers may acCl'pt a route with intermediate stops as a
truckload at .l redu ced truckload rate as
long as the stops art' not too far off -route
(Figure 4) . \ Vl' can ship individual orders
LTL via common carrier. but t his costs
more for good reason (Figure 5) .
Syste m D evelopment Hi story
Mobil began exploring the automation of
heavy products dispatch following its success with ce n tralized computer-assisted
rier, United Parcel Service, and so
dispatch of light products in the early
forth),
Truckload by contract carrier,
Truckload by contract carrier, with
stop-offs,
Truckload to pool point (and a trailer
switch), with local delivery beyond ,
19805, reported later by Brown, Ellis,
Graves, and Ronen [19871 and still in use
today . In 1984 , Mobil commissioned us to
help formulate the requirements for a
heavy-products dispatching system and to
determine the fl'asibility of acquiring or
TERFA CES 25:2
4
M OBIL
technol ogical com pone n t, an o pt im izing
heav y -p rodu cts di sp at ch module .
Al th ou gh in 19 84 Mobil ce nt ra lized or d er taking on a co m puter in Woodfi eld . Illinois, dispatc hing was manu al an d d ecen -
local O..i _ r Ar.
tralized at each lu be plant. Th e co m pany
assig ne d each customer locati on to a geograp hical region a nd with in that region to
a master delivery ro ut e . O n a given day of
the week. ea ch lube plant ma de deliveries
only to specified regio ns and within t hose
regions delivered customer or ders via the
master d elivery rou tes.
The objectives o f o ur prototy pic e ffort
were
To give Mobil a bet ter grasp of pote n tial cost savings an d the ir sources,
To pr o vid e a cleare r pictu re o f th e support required for a di sp at ching syste m ,
a nd
To eva luate th e feas ibility of usin g the
order-t akin g co m p u ters alread y in
... r,. .. ,
...""" ,...,
Figure 3: Propr ieta ry tru ck s and d edi cat ed
ca r ri ere-e-Ihe co n tro lle d fleet - gen erall y return to th eir so urces . Show n a re three ways
to fo rm tru ck sc he d u les th at do Ihi s. A loca l
d el iv ery a re a (show n a t th e lop ) ma y b e d efined wi thin so me geog ra p hic region or simply a radiu s from th e so urce. Ove rn igh t deliveries outside the loca l deli ve ry ar ea are
po..sib le (ce n te r). A co n tro lle d tru ck ca n operal e as a d edi cat ed rem ot e ca rr ier a n d b e suppli ed via lin eh aul 10 a pool loca tio n [bo tto m).
place fo r di spatch ing.
Th e protot yp e model clus tered orders
int o tru ckl oad s a nd assign ed tru ck lo ad s to
tru cks usin g a ge ne ra lize d assignment
mod el. However, the variety o f truc ks and
eco no m ic analysis. Mobil as ked us to b uild
,1 proof p ro toty pe of the mos t in novative
Fig u re oj: Contract carrie rs will accept tr uckload rout es wit h int ermediate stops, as lon g
as th e sto ps ad d no more than som e per centage (say 10 per cent) to th e direct di stance
from so urce to last stop. In this exampl e th e
direct di stan ce is 650 miles, perm itting a route
distan ce of 715 mil es. Th e ca rrie r will accept
this 700-mile sto p-o ff route as a tru ckl oad.
Mar ch- April 1995
5
develo ping such ..1 system. \Ve identified
sig n ificant po ten tial savings, b ut no offth e -shelf so ftware' package was av aila ble
to d o th e job . Followi ng so me addi tional
BAUSCH, BROW N, RO N EN
a
Bf------------~·
Sh ipper' s VieW
effort, Mobil appended new geographic
data to the orders to faci litate better man-
ua l d ispatches.
In 1989, Mobil centralized dispa tching of
heavy products at the same location as
light products in Valley Forge, Pennsylva nia and moved order taking to a new
Figure 5: Sh ipping LTL vi a commo n carrier
looks s imp le eno ug h. The carrier's view reveal s wh y l TL costs mo re: The LTL carrier
has to find its o w n opportunities for tru ck load conso li dation bu t ev entuall y deliv er ou r
o rde r.
transpo rtatio n alternatives, combined with
the co mplexity of the dispa tching environ me nt, necessitated refining the solutions
using a dozen heuristic steps. The proto-
mainframe computer. These changes resurrected the potential for computerized di spatch. The new mainfram e pr ovid ed
enough computing power to so lve more
aggressive mathematical models of the dis patch . Mobil decided to pursue a dispatch ing module hosted as a background trans action in its operating system.
In 1990 , Mobil started d evel opmen t of
user and database interfaces and as ked
INS IGHT to develop the dispatch module.
type was run with one month of actual
We put the system into production on
schedule in June 1991 , and it has been op-
d at a from one representative lobe plant
erational since. Mobil has since asked for
and co m pa red wi th the actual, indepen dent manu al dispatches . Poten tial transportation cost savings wert' in the rangl' of
seven to 10 percent. The prototype was
alsu tested for fleet size and mix decisions
(for example, what is the best size and mix
on ly one minor revision of a report in the
d ispa tching mod ule.
Syste m Design a n d Opera ti o n
The heavy-products computer-assisted
dispatch (HPCAD) system operates with
Mobil 's heavy-products system (HPS),
where the orde rs reside. All user and cor-
of Mobil's controlled fl eet on a given day?) .
Although the prototype was successful ,
the next step posed significant technical
problems. The order-taking computers
turned out to have no working scientific
computer language. and connecting them
to microcomputers (for data download,
porate database and systems interfaces, JS
we ll as the additiona l data files need ed fo r
this new application, have been developed
by Mobil information system personnel in
close cooperation with the dispatching staff
at Valley Forge.
co mputation, and upload) was infeasible.
The centerpiece o f H PCAD is the
In addition, the existing co mpute rs were
already becomi ng overloaded and were
INSIGHT dis patching modu le, w hic h con sists of a dispatch data importer, a sched -
due for replacement at any time . Developing a dispatching system was put on hold.
pe nd ing upgrade of the host computers. In
the meantime, as a result of the prototypic
ule generator, d rater, an optimizer, and a
dispatch solution exporter. The dispatch
dat, (Table I) are checked for completeness and consistency-this is important
TER FAC ES 25:2
6
MOB IL
So u Tel;'
bec au se IfPCAD int egrat es a va riety of
data types and sources that would not normall y reside together. Th e sys tem diag-
no ses a nd treat s minor da ta problem s by
applying default rule s with a ppropriate
pr escriptive messages. Major data problem s result in error messages and mu st be
externally correc ted before th e disp at ch
ca n resume.
The sche du le ge ne rato r aggregate s tru cks
int o tru ck typ es; tru cks within a tru ck typ e
are essentially identical for th e work a t
hand . For ea ch tru ck type, it selects all
com patible orders (deli veries a nd pickups)
and from th ese genera tes a ll cand ida te fea sible wo rk sched ules (rou tes), Although
Mobil pr efers tu include> a ll alternate
sche d ules, their number ca n be limited by
en forcing quotas on th e number of ca nd idat e sche d ules for each tru ck typ e, or for
eac h truck category, or for eac h order, and
so forth . Thi s ha s been necessar y in practice only for loca l deliveries from th e larg es t lub e plan t.
A work sched ule may consist of severa l
con secutive trip s, ea ch starting a nd ending
at th e origin . When the sched ule gene ra tor
cons ide rs work schedu les with multiplestop trip s, it gene ra tes th e trip s by a sw eep
heuri stic [Gillett and Miller 1974J. Each
sweep collects wurk by defining a ra y from
the ori gin to a starting see d ord er a nd th en
ro tating th e ray about th e origin clockwise
(or counte r-cluc kwise) until the tru ck is
full. A sepa ra te s weep is perf ormed for
eac h com pa tible seed ord er. Each s\v('ep
usually results in mor e than one fea sibl e
combination becau se as the sweep progresses, subsets of order s a lso form feasible
com bina tions. For exam ple, if a tru ck typ e
is limited tu three slups per trip, a nd we
number orders enco unte red in a sw eep I,
2, and 3, and these orders will fit on the
tru ck, th e followin g feasibl e com bina tions
Marc h-April 1995
7
lJi~p.ltrh d.lIl'
Bul k ur p,J(".lgl'
dl~p.lkh
Source nM1W
l.nc a tum
SPI·I'd -bv · di~ l.l IKt'
Dicp atch
tabh-
IN.. ion
1.1...·,11 d i"p,lk h pol icy p.H,lmdl'rs
Orders
C us tomer .111(\ order identification
Ik liH'ry! r ic" u p indic a tor
Sd 1l'du l.'d J "t,l
l trip. ...t.mdard Ji..,t<llKl' . and tim l' :
Loca tion . i n.-l ud ing ..,t,llt'
\\\'i ~h t.
vulurne, drums
P rt'ft'rrt'd truc kload common r,u rit'r
l ruckload I'll."
P referred L'l l. common c,u rier
LTL w.,t
AIIt'TnJI,' ..,,,urn' 1..(.l lion (pool point trailer switch . rr.rn ..h-r
p"i nl )
[s rnalk-r p,K", lg.· (fOT '>',1I11pll" L:I'Sj n .... l :
[ tim e win dow :
l"'pI: n .ll t'qulpnll'n t:
1pn 'i1....ignt· d n-qum-ment for a nv of th t' (oll.,w ing : C.uTIl'T ,
truck . trip. ..,top;
( )pI1lnl /('T .,ugg .... tion f" T date. ea rner. tr uc k. trip. ,1,,1'
Tru c.....
ldvn t rfica tion
Sta rt lor ,lti lfll , if nol ' t'urn' location
[ret u rn 10 start IUt:<1 lioll ind lr,llo r :
l'.lr ",l);.' or bul k IWc"
0pt' r,lI1l1~ radiu .. Mou nd ... l...rt location
Con tract t\'F'I ' : propnctarv. dedu-a n-d . common earner
truc kload. o r common c.rrrw r 1.11.
[can do plf "Up" :
In lr......ld lt', inter..t<111', or both
\\' I' i ~h t. volume, drum c,lp <lcil\' (p ar",l);t'), o r \'oltlm.' -by
rom part rnent (bu l")
S pt'(i.11 equipmen t
Cost-, r't' r dav (mini m um), hour, d l..t.uue, ""I', overnight.
un der -, ov er tinn- hou r
S hift hour.. u nder , ovcrtirne. m uurnum . rnavunum
D i... t.mcv mnurnu m , m ax im u m
M.n .im u Ol number of ..1111''' pt'r trip
Ceoreterence
Ma p for dl' h'r m i n; n ~ ]\>( -,111011 III location d i..t.mccs and
tmu -,
Future wor kd ays
C <111'n d.H for p ru\ llll.lIt' (UIUH' or der..
Table 1: D ispa tch dat a are int egr ati ve a nd
vo lu mi no us . Some op tio na l fields a re lis ted in
cu rly br aces, so me other fields need not always be d efin ed , HP C AD may ed it so me
fields , a nd optimizer suggestions are outpu ts.
BAUSCH , BROWN, RONEN
will be ge ne rated : I ; I , 2; I, 2, 3. Th ,'
g~ n ­
era tor genera tes and ret ain s o nly fe~l si bl l'
combinations: for instance, int erstate or -
ders cannot be added to a combina tion on
an intrastate truck type.
Unfortunately, trip cos ts for co m mo n
carrier tru cks defy app roximation as a sim ple fun ction of distance, weight, tim e. or
number o f stops- they a n' neither concave
nor COIl \'l' X fun ctions o f th ese (for exa m ples, rev iew Figures 4 and 5). The sc he d ule
generator Sl"q ul-'nces fea sible order co m binations into stups wit hin each trip to mini m ize di stan ce o r time eit her by Iull enu .
rneration (two or f ew er sto ps ) or by a '-Iu,] dratic assi gnment heuristic. Th ese
sequen ces are constrained by di spatch pol icy . For instance, the di stan ce be tween ,lny
successi ve pair o f sto ps mu st no t exceed a
maximum by truck typ e. Also , seq ue nc ed
truckload trips for commercial ca rriers
m ust have a total route distan ce to th e last
sto p th at is no grea ter than a gi ve n ~1l'r ­
ren tage of the direct distance from d vparture to the last sto p (Figure 4). Poli cies
such as these help crea te face-valid routes
that will be accepted and dri ven . Give n ca -
ticu lar tru ck typ e; the rated sch edules are
th en sen t along w ith elas tic penalty cos ts
to th e X - S yst ~m [I : S IG I IT 199°1 in th e
form of an elastic set -partitioning model
(append ix). The dispatch solution exporter
breaks truck types ba ck up into individual
tru cks and sugges ts d at e, ca rrier, tr ip, and
s top for ea ch order , giving the detailed
sc he d ule o f sto ps , distances, hours, and
cos t. For eac h tru ck type and ea ch tru ck
ca tegory (Mo bil. dedi cat ed . com mo n carri er
tru ckload . and co m mo n carrier I.TL), it di splays a su mm,u y of the number of orders
di spatched . the total cost, a nd the average
cost P!" order. Overall gaug es of dispatch
performance include cos t per di stance, cost
per wei ght. cos t pl'r wei ght-di stance, cos t
p,'r vol u me , a nd penalty cost s.
Figure 6 shows th e di spat ching proCl' ss.
Dispatching begins a fte r di spatchable or dcrs-e-thosc pa ssin g cred it checks and for
which inventory is availab le-an' extracted
Th e fleet is not uniform.
from liPS o pe n o rders . Th ese an' passed
pa cities by tru ck type, sto ps for d eliveries
and pickups must al so be fea sibl e in th e
sl'quenCl' driven . For controlled tru ck typ es
th a t re turn to known locations (that is,
p ro p riet ar y and d edi cated trucks), straigh t
driv ing dista nce, time, and number of
stops suffice for cost ca lcu lations . For
other tru ck types, th e s~q u ~nc~ is ende d
throu gh " svs te m ca lled RATETRA C,
which appends to ea ch o rder its preferred
carriers and rates.
Because order and truck data change
dai ly, .1 pre view of order workload and
trucks available is always ca lled for , with
possible adjustment of di spatch poli cy p,l-
at an anchor order that ha s that truc k
Minimal manual da ta en try is required. but
di spatch er ass is tanc e is alw ays wel come .
Fur instance , the dispatcher may ad d ,
change, and rerate orders after the batch
type as its preferred carrier and thus
co n trib u tes a pr eferred rate to use for trip
cost calculation .
Each work schedu le generated is sen t to
a ra te r w hic h calculates costs for that par-
TERFAC ES 25:2
rarn etcrs and co rrection of d ata blemishes.
proCl'SS through RATETRAC. Orders can
also be manually preassigned to a carrier,
8
M OBIL
HPCAD Functions
HPS Functions
Preview by
Dispatcher
Dispatchable
Ord ers
Overnight
Batch
Schedule
Generation
RAT ETRA C
1·2
minutes
Dispatch Data
Source
Orders
(with Carriers/Costs)
Trucks
Georeference
Wo rkdays
Schedule
Rating
Opt im ization
Review by
Dispatcher
No
Preview by
Dispatcher
Commit
Figure 6: Heavy products computer-assisted dispat ch (HPeAD), Every day, for every lube plan t
nationwide, for package and bulk products, Mobil 's heavy products s ystem (HPS) provides or ders, and RA TETRA C suggest s for each th e best common carrier tru ckload , l Tl ca rrier, and
cost. Th e entire dispat ch data scenario is asse m b led for dispatch er prev iew. Sch edul e generation, sc h ed u le rating, and optimization take about 15 com p u te secon ds, y ie ld ing a response
time of just over a min ute or so. Mo st im por ta n t, th e di spatcher ca n eas ily review suggested
so lu tion s, compare solu tion s, save, restore, or navigate among an y ten tat ive so lu lio ns, and
manu all y pr eassi g n anything. Dispa tch com m it m en l p rinls shipping documen ts at th e sup p ly
s ite.
or to a particular truck, or trip, or stop, or
any combination of these.
A shift is then submitted for dispatch .
\Vithin a minute or two. the d ispatcher rc -
pursue and compare multiple parallel no tions about what will work best that dJY .
Development Challenges
Several collateral topics have required ef-
ceives an optimized result . A grea t d ea l of
effort has been invested in II PCA D to
make it easy and intuitive for the dis -
fort. Am on g these an> mec han isms to p ro vide driving d istances a nd times, carrier
rates and delivery costs, consideration of
patcher to accept a dispatch, reject it and
start over, or amend part or all of a prior
future orders for early delivery, and appro -
dispatch and try again . The dispatcher can
priate solution technology.
Truck routes begin at sources and go to
M arch - April 19 9 5
9
BAUSCH, BROW , RONEN
customer locations but m~lY continue with
mu ltiple additional stops: Trip standards
art' available that give driving distances
a nd tim es between sources an d customer
pair of locations in the sa me zone or
neighboring zones, the truck travels di rectly from loca tion to location . Otherwise.
locations, but it is im practical to keep records of distan ces and times between l'Vt'TV
pair o f custo mers. \Ve d esigned a geo reference system wit h the he lp of the dispatch ers that divides the country intu dispatch
zones. Each zone is a small contiguous
area , perhaps several miles across, with a
cen ter location a nd one OT more neighbor
zones di rectly connec ted to it for purpOSl'S
of tru ck tra ns port. Every cus to me r loca tion
is code d wit h a zo ne . For tri ps betwe en iI
d is tan ce dri vin g pa th fro m locati on to
neighborin g zo ne ce nter and hen ce via legs
we construct a shortest -ti me o r shortest -
between successive neig hb or ing zone cen ters u n til the truck can drive from ,1 zone
center neighboring the destination zone di rectly to the destination location (Figure 7).
\Vl' estimate driving times based on a table
giving speed as a function of leg distance
(longer d istances have high er overall a ve rage speeds). Thr ou gh exte ns ive testing we
have va lidated tha t these rou tes are rea lis-
I rnpassble Bay
•
Stop 1
Z31
Z33
Figure 7: "C eo-zones" a re d esign ed by di spa tch er s. Do ts sho w zon e cen te rs. T rucks can drive
from eac h zo ne d irec tly to nei gh bor zo nes. The barrie rs s how con tig uo us zo nes that are no t
neighbors. Dri ving routes begin at a locat ion , th en pass th rough success ive neighbor zo ne
centers until they reach a zon e center nei ghboring th e d estination locati on , from whi ch th ey
proceed directl y to th e de stination.
INTER FACES 25:2
10
MOBIL
tic and tha t the route distan ces and times
good future -ord er ca ndidate, we ma y in -
are reasonably accurate, whi ch mak es
clude it with a curre nt-o rder co mbination .
se nse in light of th e dispersion of orders
H ow ever, fu ture orders do not hav e to be
over a relativ ely large geographic area.
mo ved up : Each future o rde r is give n a
Common and contract carriers are an
o ption fur virtually all o rde rs. Carrie r rates
are numerous, complex , change con stantly,
and depend on a va riety of factors, includ ing the carrier, produ ct, shipmen t size, ori -
gin , and destination . I Il' CAD probably
Manual disp at ching is
staggering ly complex.
penally for not s hipping , which is its co m mon carrie r cost divided by the number o f
workdays left until th e order mu st be
sh ippe d (that is, the number of remaining
dai ly opportunities to ship the or der). Thi s
heuristic alwa ys pe rmits the future order to
be ignored at a modest penalty, un less it
appears in a sc hedule with oth er o rde rs at
an e ve n more attractive cost.
base and can only process on e o rde r per
invocation . Mobil provides an HPS proce -
Heuristi c methods ca n be helpful in
speeding co ns truc tion o f co m patible orde r
co mbinatio ns , in seque ncing these into
face-valid ca nd ida te sched ules, a nd in lim iting the ex po ne ntial numbers o f cand idate
sc he d ules wh en this is necessary . How e ve r, heuristic s have not proven reliable
for selecting whi ch particu lar sch ed ule s to
dispatch . For this we have had to resort to
optimization : In particular, we so lve set
partition int eger linear progra ms, and these
optimizations require care (appendi x).
Evaluati on
dure th at ex trac ts so urced , dispatch abl e o rders and then submits eac h order to
ye ars, us ing it at lea st o nce each da y for
co uld not accommodate such a large database a nd still o pera te relia bly and respon sivel y. Manu al ext ractio n of rates for dis-
pat ching is impossibl y tedi ou s. Fortuna tely,
wh en this issu e arose Mobil wa s putting
th e finish ing tou ch es on RATETRA C, a
sys tem that maintains current carrier rate s
for ot her a pplications. RATETRAC manipula tes a large and rath er unwieldy dat a-
RATETRAC in a n o ve rn ight process. Il reco mme nds a best tru ckload a nd LTL carrier
Mobil has been usin g IIPCAD for three
Future o rde rs may be sche d uled early if
the produ cts are available and if it mak es
sen se to move the work up (that is, if a
tru ck is nut full but is sched uled to pa ss in
the vici nity of a co m patible future deliver y). But shipping too man y orders ea rly
may starve the con trolled fleet in the fu -
pa ck aged products ,1Od se pa rate ly for bulk
at eac h lube plan t. Dispatch ers usu ally ex perim ent several times before co mmitting a
di spatch , es pec ia lly with pa cka ged prod ucts, whi ch are hard er to dispat ch . Individ ual dispat ch es invol ve as man y as 40
tr uck s and 250 or ders.
In 1992 , Mobi l performed a thorough
aud it of HP CAD, including independent
manual and HP CAD -assisted dispat ching
ture, leaving too little w or k to keep prl' -
of the sa me workload . Originally. we fore -
co m mitted trucks and drivers busy . Ac co rdingly, w he n the s weep enco unters a
cas t th at IIPCAD would o ffer potential
sav ings of ab out $700 th ou sand an n ua lly.
Marc h-April 1995
II
and rat e for each orde r.
BAUSCH , BROWN, RO N EN
The audit revealed annual savings of about
$1 million .
About 77 percent of dispatches with
III'CAD di ffer significantly from manual
di spat ch es. III'CAD loads more we ight
a nd mak es mo re stops pt.-·f trip on com-
routes arouse initial curiosity until it be clear that I IPCA D can afford to cus-
(VOll'S
tomize each trip for each truck typl' , rather
than laboriously build a general-purpose
trip by hand first an d th en find a truck to
p ut it 011 . For exa mple, Itre A D suggl'sts
pany-controlled trucks. Manual d ispatchers
tend to schedule straight -Iine trips. making
all deliveries on the way out to the last
Gin
stop. or on the way back; trips from
I II' CA D include cloverleaf patterns and
than use LTL, HPCAD includes more or ders as stop-offs on truckload shipments:
some total surprises. For example, Figure 8
This difference alone accounts for savings
in the ra ngl' of $ -104to-$300 for each dis -
s hows that, cou nter to in tu ition and cum -
trips that only company-controlled trucks
drive, because they cross boundaries
that commercial carriers will not. Rather
mon practice, it may mak e perfect sense to
bui ld tru ckloa ds wit h I ~lfg l' early deliveries
and small deliveries la ter. III'CAD trips
may look funny at first, but they are drive-
patch . II I'CA D ma kes l'a rly d eli ver y of fu about $600 .
Additional benefits include
able and they save money. Other III'CAD
-
tun' orders, which for one or der SJVl'd
Fewer dispatchers needed (especially to
30,000 Ibs
1,000 100
Source I'--------------....;:~ Stop 2
'1""0 indhidu:.a1 shipmenls
Onl' shipment with Slop-off
Stop 1 TL
$450.00
Stop 2 LTL = $150.00
Total
$600 .00
Stop 1 Drop
stop 2 TL
Total
$ 50 .00
= $500 .00
= $550 .00
Figure 8: Cost-based routes ma y not be intuiti ve. This route violates the co nventio na l rul e of
thum b th at the heaviest deliveries should be last on the route. Here, paying a full truckload
rat e for 1,000 pounds and dropping off 30,000 pounds for a small stop-off cha rge is cheaper
th an paying for two individ ual shipments.
TERFA C ES 25:2
12
MOB IL
seq Ul-'n ce r out es),
with heu risti cs, we ha ve littl e co n fidence
More consistent service (orde rs are as-
tha t heurist ics will reliably, globally exploit
the o ppo rtunities th ese sched ules offer.
Optimi zation is key for succ ess, So metimes co mmo n sense, experience. and heu ristic met hods su ffice, som etimes not. The
signed to co mpa tible truc ks),
Reduced lead tim e for cus tomer o rders,
Faster trainin g for new dispatchers,
and
An sw ers tu qu esti ons abo ut th e size
and mi x o f the co nt rolled truc k fleet.
S u m m a ry and In si ghts
How d o you save mo nt')' in a n intensely
co m p etitive in d ust ry in wh ich tru ck 0per,l tors are efficient, di spatch ers are sma rt a nd
good at wh at they do , and ev ery bo dy .11 ready works hard? Two of the bigge st
problems art' lack of information and littl e
tim e to act o n information : IIPCAD trans forms these problems int o opportunities.
Manual di spatching is stagge ring ly co rnplex a nd is alwa ys performed und er severe
tim e pressure. Perhaps th e mo st innova tive
co n tribu tio n of o ur work is cos t visibility ,
Dispatcher s can now gras p the cos ts of
th eir decisio ns- thi s cost visibili ty has
never been pract ical befor e. \Vht'n dis pat chers start talking abou t sched uling in
terms of cost, rath er than fea sibility, man -
important point is that th ere is no way to
know for sure . If th e o ptim um is nut
known , sooner or lat er so me o ne will dis co ve r a better so lution . Once that happens.
and only once will su ffice, cred ibility is
permanently co mpro mised .
It's hard to save money when operations
are already fine -t un ed and efficie nt. Wit h out optimization , it is difficu lt and risky to
HPCA D is intended to help
di spa tchers, no t replace th em .
try to assess su btle trad e -offs and distin gui sh between close alt ernatives.
Shipping goods by truck is a n essential
activity in a developed t'conomy and on e
that most people tak e fo r g ra nted-as lon g
as s hipme nts co ntin ue uninterrupted . In
1991 , 1.2 million trac tors a nd 3.6 million
full or se mi trail ers co nveyed abo ut 2.7 billion ton s o f goods between US cities at a
cost of $ 16 7 billion (that is, about three
age rs are pleased .
Traffic fo lks, th e o nes w ho nego tiat e
rat es, benefit from thi s approa ch . The n' a re
adva ntages to looking at the big bu siness
picture, rather than focu sing cvc lusivcly
l.m e-by-Iane on po int s per h und red weig ht
mill' . It's as important to know what sh ippin g ca pabilities to ne gotiate for as it is to
negotiate th e rat es.
o no ptimizing heuristic methods an>
eas ily explained and ca n be fast , but in o ur
prototypic experience. th eir performan ce
and reliability depended upon ass um ptions
we ca nnot make about our costs, orders, o r
trucks. Even if we build good sched u les
pe rce nt of the gro ss domestic product
[C DI' D. Local tru ck deliveries cost anot her
$110 billion (two percent of GDI') . l'ctroleurn produ cts accounted for 27 billion
ton -mil es IT rall sport at itm itl A mrrj eQ 1993].
Clearl y, improving th e e fficienc y of tru ck
s hipping ha s significan t eco nom ic impact.
Mobil ha s been usin g IIPCAD for severa l years to dispat ch orders for heav y
prod ucts in bu lk and pa ckages from lu be
plants to cus tome rs. II PCAD has not onl y
March- April 1995
13
BAUSCH, BROWN, RO E
saved Mobil con sid erable amoun ts of
mo ney, it has helped Mobil to improve its
cus to mer se rvice. HP CA D qui ck ly gener·
at es large numbers of attractive, face -valid
alternate shipment schedules-sets of orders sequen ced as feasible routes for particular trucks in a heterogen eous fleet; dis patc hers select a globa l, minimum -cost dis -
pat ch from these by quick ly so lving a set partitioning problem . HP C AD is int ended
to help d ispat ch ers, no t replan' them . Dispa tchers can contribute their o wn idea s
an d compa re alt ernatives; they co ntrol all
as pects of a dispatch and have th e final
au thority to commit it.
Acknowledgments
We th ank Hal Schwartz of Mobil Oil
Corporation , whose fores ight and persis te nce brough t abou t this application;
Rich ard Powers of INSIG HT lnc., who
fac ilita ted wor k o n th is project; Rick
Rosen th al of the Naval Postgrad ua te
School, who was deeply invol ved in till'
ea rly protot y pe wo rk; Ro b Dell , Tom
Halwach s, and Kevin Wood of th e Nava l
WP,., WP,. penalties for under-. overperforming order w ;
TRUCKS, Number of trucks o f truc k type
TP TP, pe nalties for under-, overusing
tru "ck type I .
Decision variabl es:
binary deci sion variabl e equals on e
when using sc hedule S,
~U" wu' elastic constraint violat ion va riable s
fo r und er-, overpe rforma nce of order w;
a nd
II, 7, ela stic co ns traint violation variables
for under-, overutilization of tru ck type t ,
ESP Mod el formulation:
su b ject to
y~
L
Ys + ~ll'
-
wu'
(1)
'Vw,
~ES",
L: y, + ! , -
T,
= TRUCKS,
VI,
(2)
,,{:s,
(3)
(4 )
minimi ze
Pos tgrad ua te School for scrupulous manu script re vie ws; and Ron Fiano, Andy
G ib bo ns, Terr y Ha mlin , Jo h n Mak ho ul,
and th e rest of th e Mobil pro ject tea m
I;
and
+ L:
(TP,r,
+ TP,T,).
(5)
S, sc hed ules requiring tru ck typ e I.
Da ta :
COST, cost of sc hedu le s:
Each partitioning co nstraint ( 1) seeks to
sched ule an order; a lo wer violation represe nts a co mmon carrier ship men t (w he re
permiss ible, at the appropriate LT L or UPS
cos t), while an upper vio latio n results in a
high disruption penalty (which is worth
an al yzing if it happens). Each cardinality
cons traint (2) seeks one sche dule pl'r truck
of truck type t; w here a lo wer vio lation
rep resents idleness o f suc h trucks (at a
penalty represent ing the appropriate idleness cos t), and an uppt..'r vio lation incurs a
sch edule disruption penalty (more tru cks
may be ne eded). Stipulations (3) and (4)
respectively spec ify d iscr et e sch edule
selectio n and. no nn egative e lastic logical
INTERFACES 25:2
14
w ho mad e thin gs happen .
APP ENDI X
The elastic se t-partitio ning model (ESP)
selects a least-cost po rtfolio of delivery
sche dules for each truck type.
Indices:
w E W or de rs (de liveries, pick -u ps):
l ET tru ck typ es: and
s E 5 a lternate sc hed ules .
Ind uced index sets:
51.< ' sc hedules including order w ; and
MOBIL
va riables. TIll' ob jective function (5) in eludes the transport ation cos t o f se lected
sc hed ules as we ll as penalties.
Each alternat e schedule s is associated
wit h .1 truck typt.' t and con veys a se t of ord ers tha t co nst itutes o ne ur more trips or
routes o f seq uenced stops . The deriva tion
o f COST, includes findin g for eac h feasibl e
truckload co mb inat io n o f o rders a minimal -di stance fl'a sible sl'q ul' ncl' that can be
driven as a trip rou te, wit h stop-by -stop
d eli veri es and pickups. If tru ck typ e t re turns to its sta rting location , multi ple trips
may be co ncatenated into o ne shift. Each
route is costed even t by even t, with COSTs
th e tota l cos t o f ,111 trip s a nd sto ps in th e
sh ift sc hed ule.
A typi cal problem ma y have 250 orders
and 40 trucks, which tra nsl a te into about
275 co ns train ts and se ve ra l thou sand binary selectio n va riables . These probl em s
are rl'1i,Jbly SOIVl'd in ,J minute or 50 , usin g
an int egrality toleran ce (best incumbent
obj ective cos t less lower bound on this
cos t, expressed as a per centage of objectiv e
cost) of 0 .1 percent using the X-Systl'm
IINSIGI IT 19901.
The X-Systl·m omploy s se ve ral nontra ditional so lu tio n methods to produ ce
these results, including ela stic cun strain ts, row factorization, cascade dproblem so lu tion, prereduction . co ns traintbran ching enumeration , and a fast du al
simplex procedure .
Elas tic co ns train ts m.1Y be vio lated at a
give n linear pen alty cost pl'r unit o f viola tion . Every co ns traint here is elas tic. The
X-System represents the elas tic variabl es
and penalties logicall y and ex plo its elas ticity durin g optimiza tion , co nce n trating o n
the acti ve , o r taut , co ns traints. Se tting
th es e e las tic pen alti es w arrants som e
th ou ght: Here, so me o f th e penalties play ,1
direct roil' in the di spatch (for exam ple,
WP•. is th e LTL or UPS cos t for o rder w ).
Even when the penalties represent a high
mod el disrupti on cost, one w ant s pen alties
tha t are meaningful wh en they are neces -
sary and neither too low (soft ) nor too high
(hard). Mod eration is a virtu e. Fast. good qu ality so lut ions are the reward .
Row factorization ide ntifies and exploits
sets o f co ns traints tha t sha re a co mmo n
speci a l str uct u re. Brown and Ol son 11 9941
g ive se t-pa rtitio n exa m ples along w ith a
number o f othe r a p plica tio ns to d emonstrate the va lue o f this approac h in co m pari son to th e trad itio nal method s used by
well-known co mme rcial o p tirnize rs. Co n stra ints (2) hav e at most one unit coeffi cie n t associa ted with each variabl e and
th us qu al ify as ge ne ral ize d upper bou nd s.
Exploiting this factor ization reduces co m pu tatio n tim e dramati call y.
Even the linear programming relaxations
o f ESP (that is, where s tip ula tio ns (3) for
binary variable values are relaxed to co n tinuou s unit bounds) can be difficult to
so lve directl y. Casca de d problem so lutio ns
permit a particularly difficult mod el to be
so lved increm entally: we solve a seque nce
of su b models. anal yze su bsolutions and
maintain records for the ro le played by
ea ch co ns train t and ea ch variab le, ma in tain ing variables that wou ld otherwise no t
be part of a su brnodel at thei r last-kno wn
values . Eventuall y, we can use recorded
variable valu es as an ad vanced starting
point for so lving the entire model. Hen',
we follo w th e advi ce o f Bausch [19821 and
d efin e subproblems by labelin g co ns traints
and variabl es as foll ows: So rt the co n stra in ts (1) by ca rd ina lity o f S•. and th en
break th ese sorted cons train ts up into , say ,
five roughl y eq ua l-sized components and
label each co ns train t with its com po ne nt
number (tha t is, se pa rate orders with fe we r
sched ules from tho se with more ). Lab el
eac h variable y. with the minimum incid ent co m po nen t number (tha t is , label
eac h sched u le 5 with the com po ne nt nurn ber o f the o rde r which is included in the
fewest other sched u les). Label a ll co n stra in ts (2) " 0." Nex t, so lve th e following
sl'que nce o f subproblems, where each of
th ese is identified by " (m in-la bel, ma x-
Mar ch - Apr il 1995
15
BAUSCH , BROW , RO N E
la b el )" : (0, I ), (2, 2), (0, 2), ... , (0, 5).
Pre-eduction o f mod el insta nces prior to
optimi zati on, th at is, seeking and re mov ing
s truc tu ra lly redundant features. ca n re veal
hidden pr obl em structure and speed up
co m puta tio n. For exam ple, suppose some
o rde r w is presen t only in a single sc hedu le
s, the n the bina ry va riable y, ca n be fixed
to o ne an d the constraints (1) for order il'
and all o the r o rders acco mpanying 1( ' on
sch ed u le 5 ca n be rela xed a nd ign ored . Removing suc h isola ted order s may isolat e
mort' o rde rs, permi tting furth er reductions.
A num be r o f we ll-know n redu cti on s like
th is o ne are easy to apply. \\'e prefer that
th e prob lem ge ne rator be smart enough to
det ect a nd un am biguo usly d iagnose such
redundan cies while crea ting th e mod el.
Aft er all , th e ge n e rator knows a lo t mor e
a bo ut th e d at a and th e p ro blem than the
op timize r d oes . For ins tance, the example
a bove may act ua lly be du e tu an order that
requi res special equipment available only
o n one truc k ty pe . An othe r reductio n is
trivial for t he ge ne ra to r to ex p lai n b u t rc quires dualit y for a mathematical justifica tion : A sched ule will n e ver be selected if
its cost exceeds th e su m of the custs to ship
its orders as indiv idual packages via LTL or
UPS . We use the X-Sys tem prereduce
fun ction to tell us in a fraction of a second
wh ether th e probl em ge nerator is ge ne rat ing " good" models . O ur goal is mod els
that ca n not be pren-duccd at al l.
Constraint br an ching is a va ria tion of
branch -and -bound in tege r e n umerat io n
that selects a branch variable o n the basis
o f its di rect influence and the indirect effects uf the va lues it w ill induce for other
s truc tu rally d epend ent variables. For in s ta nce. co ns tra in ts ( 1) di ctate th at if a
sc h ed u le s for order U' is fixed to o ne, th en
a ll other sched u les ca rry ing that o rde r
(t hose in the se t 5 14.\5) may be set to zero.
Constra in t bra n ch in g speeds up intege r
e n u mera tio n, Bran ch va riables are selected
fur res triction based on an es timate of th e
full elastic cos t co nsl'q ue nces o f suc h re -
IN TERFAC ES 25:2
striction (that is, a beneficial interaction
exists bet wee n elas ticity a n d co ns tra in t
b ran ching).
Finally, thi s model h J S far fewl'r co n st rai n ts tha n va riables, and ou r du a l sim plex pr ocedure so lves it a bo u t 10 tim es as
fast .15 the primal. (Th is also tu rns out to
hold for the pa rtitio ning examples sol ved
with primal by Brown and O lso n 11994).)
Overa ll, th es e specia l tech niques p e rform reliabl y o n Mob il' s heav y p rodu ct
d ispatch es hundred s of lim es dail y. In
Iact , a personal co m p uter is mor e th an
adeq uate for solving such proble ms in a
minute or two.
References
Hau-ch . D. O . 1982, " Co mpu tatio nal adva nces
in the solution uf large-scale set (overing an d
se t partition ing problems." MS the sis, Nava l
Postgradu ate School. Mon terey, Ca lifornia.
October.
Brown, G. G.; Ellis, C. I. Graves. G. IV.; and
Roncn . D. ICJ8 7, " Real-time, wide an-a dis patch of Mobil tank trucks ," Ilftafact':', Vol.
17, No . L pr. 107-120.
Bro wn , G . G . an d Olson . M. P. 199-l, " Dyn amic
facto rizat ion in large -scale optimization mod cls." Mathelllll ti cal PrtlxrammiHS:. Vol. 64, Series A. No . L PI'. 17- 5 L
Gilll>tt, B. E. and ~ 1iI1l'f . I.. R. 1974. " A heuristic
algorithm for the vehicle-dispatch problem,"
OpaQt;(lII ~ Rt':,('arch, Vol. 22. ; o . 2, pp . 340349 .
INSIGH T, Inc. 1990, " XS(F) mat hematica l program ming sys tem," Alexan d ria. Virginia .
Ron en. D. for thcoming. " Dispatchin g petroleum
prod ucts: ' Opaat;tl/1 5 Research,
Tran sportutinn i ll Ama;cQ 1993, Eno Tra ns po rta tion Foundation . Land sdowne. Virginia .
w. R. Bnu lkwill II. Su pe rv iso r. Transpor ta tion Progr am s, USS &L Logist ics Su p port,
Room 6A -Y09 , Mobil O il Co rporation,
3225 Ga llow Road, Fairfax, Virginia
22037-000 1, writes, " \\' e have re viewed
the a rticle submitted to you a nd have
fo u nd it to be acc u ra te in its d escr iption of
o ur busi n ess . We insta lled the HI'CAD op-
16
MOBIL
tirnize (HI'CAD stands for Heavy Prod ucts Cum pute Assisted Dispatch) in 199 1
and it is working out \'ery well for us. This
optimi zer has allowed us to reduce head count in the disp atching fun ction and im pro\'e ou r distribution eco no mics. Thi s .1 1go rithm h.1S pr ovided a very satis factory
return on our initial investment and since
implementa tion , w e hav e had to do vcry
few en hancemen ts ."
March-April 1995
17
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