797

1 INTRODUCTION

The given cargo annual throughput of a container

terminal

and the known average container dwell

time

dwell

 enable to estimate one‐time storage

capacity

needed to store containers:

365

dwell

EQT

.Thestandardcontainersprovide

the possibility to stack them in several tiers, thus

reducingtheareafortheirallocationinthecontainer

yard, since the area measured in terminal ground 

slotsis

sEh

.Ontheotherhand,thehigheristhe

operational height of the stack, the bigger moves

neededtoselecttherequiredboxfromthestack.Both

the area for the stack allocation and extra shuffling

moves cause the financial losses, so in order to

determinetheoptimalvalueofthe

operationalheight

one needs to find a balance between these costs, as

Fig.1shows.

Box Selectivity in Different Container Cargo-handling

Systems

A.L.Kuznetsov,A.V.Kirichenko&A.D.Semenov

dmiralMakarovStateUniversityofMaritimeandInlandShipping,St.Petersburg,Russia

ABSTRACT:Theboxselectivityinoperationalstackofcontainerterminalisaquitecommonandlongstudied

question. The pure random choice is governed by the theory of probability offering some combinatorial

estimations. The introduction of operational rules like

 import/export separation, storage by shipping lines,

sortingbyrailortruck transportationetc.,aswellasthemostnotorious‘sinking’effect,i.e.coveringofboxes

arrivedearlierbynextcargoparties–alltheseblurtheclearalgebraiсpictureandleadtoappearanceofmany

heuristic outlooks of the problem.

A new impetus to this problem in last decades was given by the rapid

developmentofIT,AIandsimulationtechniques.Therearequitemanyexamplesofthemodelsdescribedin

the scientific publication reflecting many real and arbitrary terminals, which embed very advanced and

complicatedmechanisms reflecting selected features and

 strategies. Unfortunately,these models usually are

created ad hoc, with some pragmatic objectives and under the demand of closest possible proximity to the

simulating objects. There are much less models designated to pure scientific study of the deep inner

mechanismsresponsiblefortheprimalbehavioroftheoperatingcontainerstack,

enablingtointroducestepby

stepnewrulesandrestrictions,providingregularproving ofeverynextstage’sadequacyandeasytouse.This

paperdescribesoneattemptofthiskindtocreateanewtheoreticaltooltoputintotheregulartoolkitofthe

containerterminaldesigner.Thestudystartswith

mathematical(combinatorial)considerations,proceedswith

somerestrictionscausedbyphysicalandtechnologicalcharacteristics,andendsupwiththesimulationmodel,

whichadequacyisconfirmedbypracticalresults.



http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 13

Number 4

December 2019

DOI:10.12716/1001.13.04.12

798



Figure1. Cost of area against cost of moves in total

operationalcost.

The assessment of the operational areas needed

under different cargo‐handling systems and

calculation of the relevant costs are relatively well

studied,whilethequestionoftheselectivityremains

vague[1,2,3].Thispaperinputssomeconsiderations

tothisdomain.

2 CONTAINERSELECTIVITY

Theselectivityisusuallydefinedasthe

ratiobetween

thenumberofcommercial(productive)movestothe

total number of moves, productive and non‐

productive [4, 5, 6]. Since for one container there is

only one productive move which brings money for

theterminaloperator,thisdefinitioncouldbewritten

like

Selectivity:

move





The containers needed to be selected (usually

referred to as ‘hot’ ones) dwell somewhere in the

body of the stack, covered by some ‘cold’ boxes

blocking the direct access. Different container

handling systems (or, more exactly,  the operational

featuresoftheequipmentusedinthesesystems)need

to shuffle either

only one ‘column’ containing the

requiredbox,or‘digout’throughsomeajarspacein

thestack,asFig.2illustrates.



Figure2.Theoperationalzoneforselection

Theselectivityinthesesystemsdiffersgreatly.The

way how equipment accesses the boxes in the stack

divides all container handling systems in two main

categories: with top accesses (Rail Mounted Gantry,

RubberTyredGantry,StraddleCarrier)andwithside

access(FrontLoader,SideLoader,Reachstacker).The

former systems here we

 will refer to as the gantry

type,thelatter–theloadertype.Fig.3and4givea

generaloutlookofthesemachines.

a)



b)



c)



a)Railmountedgantry;b)Rubbertyredgantry;с)Straddle

carrier

Figure3.Gantry‐typecontainerhandlingequipment

a) 

b)



c)



a) Reachstacker b) Mast front loaderс) Empty container

handler

Figure4.Loader‐typecontainerhandlingequipment

799

Therefore, in the context of this study we would

distinguish between only two main types of these

machines:providingthetopandsideaccessesforthe

boxesinthestack(seeFig.5).



Figure5.Theequipmentprovidingthetopandsideaccess

tothestack

ThefirstgroupincludesRTG,RMG,SCandASC,

the second‐FL, RS, ECHsystems. The top access

system we will refer to as gantry type one, the side

accesssystem–asfrontloadersystem. 

3 THETHEORETICALSELECTIVITYINTHE

GANTRYTYPESYSTEMS

Letusassumethatwehave

acontainerstackwiththe

average operational height

. The upper boxes in

thesesystemscouldbeselectedinonemove,theones

belowit–withtwomoves,thelowerboxes–with



moves each. Consequently, the theoretical average

numberofmovespercontainerwouldbe



 

move



4 THETHEORETICALSELECTIVITYINTHE

LOADERTYPESYSTEMS

The loader systems demand to remove not only the

boxes on top of the required one, but clear the way

throughtherows between the machine and column.

In case of pure front loader, i.e. with mast forklift

trucksand empty

containerhandlers,the number of

movesneededtoselecttheboxisgivenbyFig.6.



Figure6.Theoperationalzoneforselection

Accordingly,thetotalamountofmovesneededto

handle the stack with the height ofheight

 tiers

andwidthof

 rowsis







 



22222

11 1

22 2

01 w1

hh h

Nhhhhh

hhhw

hw h

hhwwwh

hw hw

hwhwhw hw

 



   



     



  



  



 

    





Consequently, the average number of moves per

containerinthiscaseis







move

Nhw



The selection of container in case of the

reachstackersneedsthetotalamountofmovesinthe

stackgivenbytheexpression

  



13311

Nhhw hhh

wwh





   





    



Thisformulacouldbededucedfromconsideration

ofmovesasshownbyFig.7.

800

1 2 4 9 14 19 24 29

24 7 12 17 22 27 32

3 6 10 15 20 25 30 35

     

4 8 13 18 23 28 33 38

510 15 20 25 30 35 40

1 12 124 1249 124914 12491419 1249141924 124914192429

2 2 4 2 4 7 2 4 712 2 4 71217 2 4 7121722 2 4 712172227 2 4 71217222732

3 3 6 3 610 3 61015 3 6101520 3 610152025 3 61015202530 3 6101520253035

4 4 8 4 813 4 81318 4 8131823 4 813182328 4 81318232833 4 8131823283338

5 510 51015 5101520 510152025 51015202530 5101520253035 510152025303540



Figure7.Formuladeduction

The average number of moves per container in

caseofreachstakeris





move



Fig.8showsthecomparisonofaveragenumberof

movespercontainerindifferentsystems.



Figure8.Numberofmovesindifferentsystems

5 EQUIPMENTPRODUCTIVITY,TECHNICAL

ANDCOMMERCIAL

Theprimalobjectiveofanycargo‐handlingsystemsis

in optimal processing of the cargo passing through

the terminal. In this respect not the total number of

moves needed to access a required box matters, but

how many these “productive” moves could be

accomplished within

 the given interval. In other

words,weneedtoassesstheproductivityindifferent

systems.

Let us assume that an average full cycle of the

spreader takes the time

move

[sec]. This value

usually is reported by the manufacturer of the

equipment and enables to calculate its technical

productivity

3600

theory

move



.

Theterminaloperatoranditsclientsareinterested

not in the technical, but in commercial

productivity

3600 ( )

efficient mov e m ove

PNT



theory

sP

. This characteristic shows how many

client’sboxes the equipment could retrievefromthe

stack in one hour. The working cycles of different

equipment differ, with some typical values as

250

move

T 

 secforfrontloadersand

120

move

T 



secforgantrytypeequipment,providethepossibility

to calculate the commercia l productivity of different

equipment. Fig. 9 shows the results  of these

calculations based on the above‐studied selectivity

andtypicalworkingcycles.



Figure9.Commercialproductivityindifferentsystems

As one can see at this figure, the commercial

productivityoffrontloadersdropsdramaticallywith

the increase of the operational  height. This explains

whythestackwidthinthesesystemsislimitedby2‐4

rows only (with the access from both sides) if the

boxes are treated individual and

 not anonymous.

Anotherpointtonoticeistheconvergenceofallfront‐

loadersproductivity:tocleartheaccessoneneedsto

removeincreasingnumberofverticalrows,withthe

differenceofmovesonlyinthelastone.

Usually it is not a problem to assess the cost of

operational hour

for any cargo handling equipment.

Havingthesedone,itispossibletoestimatetheself‐

cost of one commercial move in different systems.

Providedthatthecostofoperationalhourisgivenby

Fig. 10, the correspondent self‐cost of one moves is

representedbyFig.11.



Equipment RS RTG ECH

Сhour

USD/motor‐

h

21 24 18

Figure9. Typical cost of one motor‐hour for different

equipment



801



Figure10. Self‐costs of commercial moves in different

systems

In the beginning,  with low average height of the

stack, the reachstacker as the handling machine is

betterdueto itsabilitytoworkoverthefirstrawof

boxes,butfurtheronthisadvantagedeterioratesdue

tothehigheroperationalcostofonehourandnearly

thesameamountof

moves.

The study above assumes the pure stochastic

mechanism of box selection from the stack. The

specialists in container business are aware of the

unpleasant fact that ‘hot boxes’ needed for selection

tendto‘sink’tothebottomofthestackbeingcovered

by‘coldboxes’arrivinglaterandexpected

todwellin

thestackforsometime.Thislabor‐addedmechanism

istobestudiedinthenextpaper.

6 CONCLUSIONS

1 Inmanycasesthecomplexbehaviorofbigsystems

is the result of big collection of simple but

interactingprocesses.

2 The identification and resultative study of these



mechanism require the regular methodological

approachfromsimpletocomplexperception.

3 The problem of the box selectivity is well

recognized and studied, but the results of these

researches cannot be acknowledged as complete

andfinal.

4 The paper deals with the most primal

mathematical mechanisms responsible for the

selectivity

of boxes from the stack, taking into

account specific features of generalized cargo

handlingsystems.

5 Thestudyendsupwithsimpleformulawhichcan

be used for practical purposes and theoretical

studiesofcontaineroperations.

6 The labor‐added mechanism is not taken into

accounthere,aswellasthe

procedureof putting

boxesintostack.

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