A PROGRAMMED LOADING PROCEDURE FORCONTAINERIZED CARGO SHIPS

Tran Quang Thieu

>Javai PosturaauaTe Scnool

Monierey, California 93940

NAVAL POSTGRADUATE SCilQOL

Monterey, California

THESls•

A PROGRAMMED LOADING PROCEDURE FOR

CONTAINERIZED CARGO SHIPS

by

Tran Quang Thieu

June 197 5

The sis Advisor

:

James P. Hynes

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A Programmed Loading Procedure forContainerized Cargo Ships

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Master's ThesisJune 19758. PERFORMING ORG. REPORT NUMBER

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Tran Quang Thieu

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LogisticsContainerizationSealift

20. ABSTRACT (Continu* on r«v*r** »ld» It nmcfmry Mid Idmntlty by block numbtr)

A programmed loading procedure for containerized cargo shipsis developed. The model requires input information on the con-tainers to be loaded, the ship's design and hydrostatic proper-ties, and the specific order of port calls to be made in thevoyage.

The purpose of the programmed procedure is to minimize time

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20. Continued

spent in ports for unloading and loading. Requirements for shiptrim, list, and stability, safety regulations governing hazardouscargo stowage are taken into account.

The procedure is presented in simple flowcharts and in a detailedFORTRAN IV program. An illustration, which was made as realisticas possible was given and the complete computer printout areattached

.

DD Form 1473, 1 Jan 7?

S/N 0102-014-G601 SECURITY Classification of this PAGE(T»Ti»n Dat* Eni»i»d)

A Programmed Loading Procedure forContainerized Cargo Ships

by

TRAN QUANG THIEU

Submitted in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCE IN MANAGEMENT

from the

NAVAL POSTGRADUATE SCHOOLJune 1975

UDfrirv

Nava. Postsraauate bcnout

Momerev. California 93940

ABSTRACT

A programmed loading procedure for containerized cargo

ship is developed. The model requires input information on

the containers to be loaded, the ship's design and hydro-

static properties, and the specific order of port calls

to be made in the voyage.

The purpose of the programmed procedure is to minimize

time spent in ports for unloading and loading. Requirements

for ship trim, list, and stability, safety regulations

governing hazardous cargo stowage are taken into account.

The procedure is presented in simple flowcharts and in

a detailed FORTRAN IV program. An illustration, which was

made as realistic as possible was given and the complete

computer printout are attached.

TABLE OF CONTENTS

I. DEVELOPMENT OF CONTAINERIZATION 8

II. THE PROBLEM 9

III. INTRODUCTION OF A PROPOSED PROCEDURE 10

IV. ASSUMPTIONS 11

A. THE CONTAINER 11

B. THE SHIP 11

^ C. THE VOYAGE 11

D. THE CARGO 13

V. THE MODEL 15

A. MATHEMATICAL PROGRAMMING APPROACH 15

B. HEURISTIC APPROACH 15

1. Loading Principles 16

a. Higher-sooner 16

b. Higher- lighter 16

c. Left-right Equality 17

d. Heavy Aftward 17

2. The model 19

a. System of Coordinate 19

b. Loading Procedure 19

3 . Calculation 25

a. Ship Trim 25

b. List and Stability 29

VI. THE GENERAL FLOW CHART 30

VII. THE SUBROUTINES • 32

A. SORT 3 2

' B. POST 33

C. TRIM AND CURVE 36

VIII. THE MAIN PROGRAM 40

IX. ILLUSTRATION . 41

X. FEASIBILITY OF THE MODEL AND RECOMMENDATIONSFOR USE 47

XI. IMPLICATION FOR FURTHER STUDY 50

A. TESTING AND ANALYSIS 50

B. MODEL EXPANDING 50

APPENDIX A 52

APPENDIX B 54

COMPUTER OUTPUT 56

COMPUTER PROGRAM 8 9

BIBLIOGRAPHY 97

LIST OF INITIAL DISTRIBUTION -98

LIST OF FIGURES

FIGURE 1: A five port voyage 12

FIGURE 2: Loading Heuristics 18

FIGURE 3: System of coordinates 20

FIGURE 4: Example address of a container 21

FIGURE 5: Grouping of containers 23

FIGURE 6: Loading pattern 24

FIGURE 7 : Partially occupied stacks of containers '-- 26

FIGURE 8 : Matching of containers and addresses 27by selected heuristics

FIGURE 9: General flow-chart 31

FIGURE 10: Flow-chart, Subroutine "Post" 34

FIGURE 11: Estimation of a curve 39

FIGURE 12: Illustrating voyage —42

FIGURE 13: A specific hatch 48

I. DEVELOPMENT OF CONTAINERIZATION

In 1929, a new idea was developed in the transportation

field. Some of the ships operating in coast-wise and con-

tiguous trade were specially outfitted to carry the trucks,

trailers and railroad freight cars. Unfortunately, the

great potential of this concept was not fully developed due

to the lack of standardization. It was not until the mid-

nineteen fifties that the next step in the development

occurred. Ships were specially designed to carry standard

containers. Cargo was stuffed into containers before ships

entering the port. Loading and unloading became much more

easy, and in the nineteen-sixties containerization was fully

developed. Common cargo containers were fully transferable

among the various modes of transportation. However, ships

were the most important container carriers; in 1966 the

first fully-containerized ship entered into the foreign

trade market, and later on, the second generation American

containerized ship, the LANCER class, commenced operations

in 1968-1969.

8

II. THE PROBLEM

Generally speaking, when containers have been assigned

to a specific ship the following factors must be considered.

a. Proper grouping of a consignee's cargo and container

accessibility in the marshalling yard.

b. The order of the port calls in the voyage, i.e.,

containers must be stowed in such a way that there should

be no overstow of cargo for a later port over cargo for an

earlier port call.

c. Special stowage requirements for hazardous types of

cargo or reefer containers requiring access to electrical

outlets.

d. Arrangement of weights to meet the ship trim, list,

and stability requirements.

Satisfying all these conditions simultaneously becomes a

very complex task when there are several loading ports in

the voyage. Years after the beginning of containerization,

there remains to be developed an effective load planning

procedure that can handle all factors. The actual methods

now being used vary from company to company. Most of them

are manual and based on "trial and error" procedure. They

are all time-consuming and consequently leave something to

be desired.

III. INTRODUCTION OF A PROPOSED PROCEDURE

In the past, the old "trial and error" methods were more

or less adequate to handle the problem. Now that larger

ships are being built, changes must be made in order to

promote more efficient use of the investment in a vessel.

In general, our objective is to reduce the time in port of

a ship for loading and unloading. The time would be mini-

mized if the unloading does not require extra movement of

containers aboard the vessel, and this, of course, is

accomplished by avoiding overstow. Certainly all the factors

mentioned in the previous section must be met. In short,

to minimize the time in port of a ship means to minimize

the overstow, subject to loading constraints. With the

assistance of a computer, the goal is attainable. In the

next chapter a loading procedure is proposed; calculations

of ship's trim, list and stability will be introduced in

another chapter. The procedure then is translated into

FORTRAN IV language and a somewhat realistic illustration

with a complete computer print-out will be given.

This chapter and Appendix A, were based on a previousstudy by Dewey E. Beliech, Jr.

10

IV. ASSUMPTIONS

We shall first assume the following conditions for the

model.

A. THE CONTAINER

A container is a box containing cargo. All containers

are assumed to be the same size for this procedure.

B. THE SHIP

In general it is not required the ship have any special

form. However, for purposes here, it will be assumed that

2the ship has nine different cargo holds. Holds vary in

sizes, but all can be vertically accessed to any place. In

other words, the hatches are as large as the holds. This

is generally not a restrictive assumption.

C. THE VOYAGE

The order of port calls in the voyage must be specific

and fixed. We can assume, without losing generality, that

the ship is making a "circle" trip from port-1 to port-n

and after that returning to port-1, (not port-n-1) .See

Figure 1.

It is assumed that containers are unloaded and loaded

at each port in the voyage. Also, it is assumed that the

number of containers to be loaded at a port will never be

2The reason for assuming nine holds will be explained

in the assumptions about labeled cargo mentioned later inthis chapter.

11

>rt 3

Port 2

Port 5 Port 1

Figure 1: A five port voyage

12

greater than the number unloaded at the port. This latter

assumption is needed to insure that there is always suffi-

cient space available for loading.

D. THE CARGO

Both labeled and common cargo can be carried, and are

classified into the following nine types:

3Type-1 Explosives.

Type-2 Inflammable compressed gas (RED GAS) e.g..

Butane, LPG, Acetylene.

Type-3 Inflammable liquids (RED LABEL)

.

Type-4 Inflammable solids/oxidizing materials

(YELLOW LABEL)

.

Type-5 Hazardous articles.

Type-6 Non-inflammable compressed gas CGREEN LABEL)

e.g./ Oxygen, Freon, Helium.

Type-7 Poisonous articles (BLUE LABEL)

.

Type-8 Corrosive liquids (WHITE LABEL)

.

Type-9 Common cargo.

The first eight types of cargo listed are labeled.

Based on Department of Transportation regulations for stowage,

most of the labeled cargo types can not be stowed in the same

hold. There is no restriction on common cargo. However,

type-2 and type-5 cargo are required to be stowed on deck.

Refrigerated cargo could be classed as an other type and

stowed into a separate hold, however, in this study we

3Type number were arbitrarily selected for programmingpurpose,

13

neglect that by assuming as far as refrigerated cargo and

containers are concerned, each container is a refrigerator

itself, and accessibility to electrical outlets is assumed

available around the ship. For more detailed rules of

stowage for the labeled cargo, see Appendix A.

14

V. THE MODEL

A. MATHEMATICAL PROGRAMMING APPROACH

As stated briefly in the introduction/ the ultimate

objective is to minimize the in-port time of the ship in

order to maximize the productivity of the vessel. Port

time for a ship is dependent on the number of container

movements required aboard the vessel to discharge con-

tainers for the port, and to load containers from the port.

As previously pointed out, this is accomplished by mini-

mizing overstow. So in terms of a mathematical programming

approach/ the problem can be stated as:

Objective Function: Minimize (number of overstow

containers)

Subject to: - Storage regulations

- Ship's trim, list, stability requirements,

Conceptually/ it appears that the problem can be solved

using an Integer-Programming technique. Unfortunately,

an initial investigation revealed that for a vessel of even

small size, the number of variables would far exceed the

capacities of contemporary software and computing machinery.

Therefore/ it was assumed that pursuing simple mathematical

programming approaches would not be fruitful in the short

run.

B. HEURISTIC APPROACH

While the mathematical programming is reluctantly dis-

counted, a heuristic approach appeared to be more productive

15

way of initially grappling with the problem because there

exists a set of loading heuristics which simplify the

problem. These heuristics, or rules of thumbs, are detailed

below. They may not always lead to an optimal solution, but

at worst they can be used to get a solution which is more

or less optimal. In this sense, the emphasis here is on

obtaining workable solutions which more or less minimize

overstow. This, of course, is a reflection of the heuristic

4"philosophy" of problem solving.

1. Loading Heuristics

a, Higher-Sooner

To eliminate, or minimize, overstow the well

known "last-in-first-out" procedure is used here. Suppose

that containers are being loaded at port-1 (see Figure 1)

then all containers destined to port-5 should be at the

bottom of each container stack on the vessel. The con-

tainers at the top of a stack should be destined to port-2.

It can be said that to eliminate overstow, containers for

the same POD should be stowed together in the same stack,

however, if they cannot all be in the same stack, then the

containers for earlier ports should be above the containers

for later ports.

b. Higher-Lighter

Ship's stability will be assured if, in any

stack of containers, the higher the container is, the

Murray A. Jeisler & Wilber A. Steger, "The Combinationof Alternative Research Techniques in Logistics SystemsAnalysis," Management Technology, May 1963, pp. 68-77.

16

lighter it is. A heavy container loaded below the ship's

gravity center tends to lower the gravity center and

therefore, increase the righting moment. If not required

by regulations, the "higher-lighter" principle is applied

here.

c. Left-Right Equality

The ship has no list if equal weights are

distributed symetrically with respect to the ship center-

line.

d. Heavy-Aftward

Another factor that must be considered is the

ship's trim. Usually a slightly deeper aft-draft Ctrim

by the stern) is preferred to keep the ship easily under

control. Ship's configurations and ship arrangement vary

a great deal. It is almost impossible to set up a general

principle regarding distribution of weight along the

transverse direction of the ship. However, most ships

are constructed such that there are more cargo holds in

the forward part than in the aft part. Heavier weights

are, therefore, likely to be stowed closer to the stern.

Nevertheless, that is not a guarantee. Ship's trim must

be calculated before containers are actually being loaded.

The difference between aft and forward draft must be

within tolerance, or be adjustable by ballasting. The

above principles are illustrated through simple examples

in Figure 2.

17

EDC

R

A _J

CL

B

w

Stern

A

Be

(a) (b)

2 3Stack 1

;tern \

//1

Bow

Figure 2 : Loading Heuristics

(a) If all containers are being sentto the same port of destination thenWeight (A) > Weight (B) ^ . . . :^ Weight (E)

If those containers are being sent todifferent ports then; Container E shouldbe destined to an earlier port than con-tainer A.

(b) Container A and container B should havethe same weight.

(c) Stack-1 should have sufficient weightto counter the weight of stack-2 and 3.

l&

2. The Model

a. System of Coordinates

By using the above heuristics we can develope

a loading procedure. For reference purposes, a system of

coordinates is first defined. (Figure 3)

Let the XOY plane be the horizontal plane of

the lowest deck where containers can be stowed.

Let the XOZ plane be the vertical plane

perpendicular to the ship center-line and tangent to the

ship stern.

Let the YOZ plane be the vertical plane

parallel to the ship center-line and tangent to the left

most point of the ship.

Each container storage location, or cell, has

an address specified by row, column, and tier. A row of

containers is a group of containers having the same Y

coordinate. A column of containers is a group of containers

having the same X coordinate. A tier of containers is a

group of containers having the same Z coordinate.

For example, the container A in Figure 4 has

address (4,4,2). In other words, it is at row-4 , column-4,

tier-2

.

b. Load Planning Procedure

Applying the heuristics previously discussed,

containers are first sorted into decreasing order of weight.

After that, containers are grouped by order of ports of

destination and then sub-grouped by types of cargo. This

19

z <

Upper Deck

Lowest Deck

Ballast

^

Ballast" Y

Figure 3: System of Coordinates

20

AZ (tier)

UnitContainer "y (row)

4 '^ X (column)

Figure 4 : Example Address of a Container

5(

procedure is illustrated by Figure 5, After grouping,

containers destined to the last port are assigned to stacks,

and assigned to separate holds, depending upon the types

of cargo. As an example, containers of type-1 cargo could

be assigned to hold (N-1) , type-2 cargo assigned to hold

(N-2) , etc. Now, recall that type-2 and type-5 cargo con-

tainers are required to be stowed on deck and common cargo

(type-9) can be stowed anyplace; therefore, after type-2

and type-5 cargo containers have been assigned deck spaces,

there are "empty holes" left underneath those labeled

containers. The holes will be filled up by common cargo

containers which have the same (or lower) port of destination,

Ship list is controlled by assigning spaces in

a column to the right to the center-line and then assign-

ing spaces in a column to the left, with the same distance

from the center line. The total weight of those two

columns is generally not the same and a list moment exists,

but it is generally slight and can be adjusted by ballasting.

If not, stacks can be reassigned before actual loading.

In general, labeled cargo containers are

assigned first, following the pattern described above, and

illustrated in Figure 6 (b) . This typically leads to

partially occupied stacks, or columns, of containers, and

there exist the holes; either underneath or above, which

can be filled by common cargo containers.

22

Containers to Qn-r-hor] i rrl-r)

be labeled at Port-1 DecreasingWeight

\'

> f y * \f i

2nd 3rd 4 th 5th

POD POD POD POD

Figure 5: Grouping of Containers

23

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After all containers destined to a POD have

been loaded, the containers to the next-to-the-last POD

are assigned. The same principles are applied, and

addresses assigned to a container only if it has been

checked to make sure that there is no over stow. See

Figure 7.

Another way to look into the model is illustrated

in Figure 8. In general, the heuristics are used for con-

tainer sorting, grouping, address assignment and matching.

In the next chapter these tasks will be explained in detail

by flow-charts, computer programs and subroutines. How-

ever, some words should be said about the matching. An

address can be preoccupied by a container or a ship

structure. In this case, the address is automatically

rejected, and other addresses will be searched, checked,

and matched with the container. This feature allows the

model to be independent to ship configuration, and allows

the model to be applied at every port in the voyage.

3. Calculations

As mentioned in the above paragraphs, the heuristics

here do not guarantee that an optimal solution can be reached

and, moreover, ship trim and stability must be calculated

to assure that the loading is acceptable.

a. Ship Trim

The inclinations in the transverse direction

are measured by the difference between the forward and the

aft drafts. This difference in drafts is defined as trim.

25

MainDeck

B

Figure 7: Partially Occupied Stacksof Containers

A: above hole

B: underneath hole

26

Containers

Output

Containerand

Address

Container

Address

<-

AddressAssignment

o•HPCO

•rH

u

0)

Figure 8: Matching of Containers andAddresses by Selected Heuristics

27

Where the draft aft is greater than the draft forward, the

ship is said to be triimned by the stern, otheirwise the ship

is trimmed by the bow.

When a container is loaded onboard, the trim

changes, and the change of trim is defined as the change

in difference between the drafts forward and aft. To cal-

culate this change we need to define some new terms:

Moment to change trim one inch, MTI , is the

moment required to produce a change of trim by one inch.

This value varies depending upon the displacement of the

ship and therefore, upon the mean draft. It is often

found as a curve in the "Curves of the form." When such

a curve is not immediately available, MTI can be computed

by the formula:

BM' X WMTI

12 L

Where

:

BM' = longitudinal metacentic radius (in feet)

W /= displacement (in ton)

L = ship length (in feet)

- Center of flotation (CF) : The geometric center

of the waterline plan is called the center of flotation.

For ship trim, it inclines about an axis through the center,

For practical purposes, flotation center is assumed at mid-

ship or at a point with a distance d from midship; where

^NAVPERS 91067, Principles of Stability in Ship Loading ,

page 69, Bureau of Naval Personnel, 1949.

28

d is the average distance of distances from the midship

to the points on the locus of flotation center.

Thus, if a container with weight equal to w,

is loaded at a distance t from CF, the change of trim is;

T = Change in trim = ^,^^-^ .

MTi

and, by the system of coordinates previously defined

New draft, aft = new mean draft - T/2

.

New draft, fwd = new mean draft + T/2,

A subroutine to compute these values after each

container is assigned to a space is described in the next

chapter and is the principal calculation needed to be

attached to any loading plan.

b. List and Ship Stability

Experience has shown that the "higher-lighter"

and the "left-right equality" heuristics tend to keep

ship stability and ship list within limits. Actually, with

the same distance from the ship centerline, a right column

of containers which are assigned first, is likely to be a

little heavier than a left column because the containers

are sorted into decreasing order of weight. However, this

list moment is assumed negligible for practical purposes,

and can be adjusted by ballasting. If an accurate list is

desired, it can be computed in almost the same manner as

ship trim. The same holds true for stability. An accurate

computation involves a complicated read-in of the cross-

curves and lengthy adjustments.

29

VI. THE GENERAL FLOW-CHART

In the previous chapter the model has been described

by words. In this chapter it is depicted by a general

flow-chart and by FORTRAN IV language in full details.

A somewhat realistic example, with five loading ports, 946

containers and the CB-1 containership, is introduced for

purposes of illustration.

The general flow-chart depicts the principal steps

of the loading plan. First of all, data involving the

ship, the voyage, and the containers are read by the

program. The addresses which are already occupied either

by containers or by ship objects, are registered. Con-

tainers are then sorted into decreasing order of weight,

grouped by ports and types. The containers already on-

board are listed with their addresses. Ship trim affected

by those containers is computed and stored.

Next, new containers are selected, assigned addresses,

ship trim is computed and accumulated. The addresses of

all containers are then printed as a manifest. If any

labeled container is not in a proper hold, or if any one

overstowed, then its serial number and characteristics

are printed out for human interference. Unoccupied

addresses, if any, are also listed in relative port order

according to containers partially occupying the stacks.

To carry out these tasks, a main program is used with

four subroutines. These subroutines are generally described

as follows.30

(_Start_) ORead in

Data

RegisterOccupiedAddresses

Sort & Groupcont

Into POD

roup ContCnto Types

SelectCarriedCont

ComputeTrim

*0

Select NewCont

IAssign

Addresses

ComputeTrim

Print OutAddresses

List AllCont Not InAppro

Print Un-loaded Contand TTnorg . |

^addx^e^ses

PrintShip'sTrim

+>u(a

Xio?o•Hfa

u<o

c0)

o

0)

u

•Hfa

•^i END. )

31

VII. THE SUBROUTINES

A. SORT

Subroutine "Sort" is used to sort the containers into

decreasing order of weights. Data related to a container

include: serial number, port of loading, port of distina-

tion, cargo type, gross weight, and if already loaded,

row-column-tier-address. The weight is used to compare

containers with each other; the heaviest container, with

all its related data, will be moved to the first place of

computer storage. In any later processing, such as address

assignment or manifest listing, the heavier containers are

considered first.

The data are read by the main program. Following is

the list of variable names. Note that "NCONT" includes

containers already loaded, "dummy containers", which are

merely ship-objects having addresses but no weight or

serial number. In fact, NCONT is equal to total number

of possible addresses on the ship.

List of Important Variable Names

ICOL(I) = Column address of container (I).

IPDEP(I) = Number assigned to a port on the route

where the container was loaded.

IPARR(I) = Number assigned to a port where the

container is destined.

32

IROW(I) = Row address of container (I).

ISER(I) = Container (I) serial number.

ITIER(I) = Tier address of container (I)

.

ITYPE(I) = Number assigned to the type of cargo

stuffed inside the container.

WEIGHT (I) = Gross weight of container (I).

A number of variable names, such as NC, WES, are

defined internally, they are used only as temporary

storage and do not have any special meaning. For a

complete variable name list, see Appendix B. The sub-

routine is listed in the "Computer Program" Appendix.

B. SUBROUTINE POST

The most important and complicated subroutine is

"POST". It is used to assign newly loaded containers.

It checks all requirements, all constraints posed by

regulations and loading heuristics.

First, a general flow-chart is illustrated in Figure 10.

As said before, containers are grouped by types of cargo.

The main program has specified the appropriate hold for

each type of labeled cargo. This subroutine's first step

is to check if the hold is full. If it is full, containers

will be stowed in a common hold for manual inspection.

The program does not determine in which case stowing is

tolerated and in which case it is not. If the appropriate

hold is not full, the next address in a well-defined

sequence will be offered to the container. The matching

33

( start J

No

Yes

No

No

(Return )

AssignAddress

Move toCommonHold

Yes

RegisterGivenAddress

f Return J

Figure 10: Flow Chart, Subroutine"POST".

34

will be checked against regulations and if compatible, the

address will be registered and returned to main program.

If an address is not acceptable, the next address will

be examined. The "next address" is defined as the same

row, same column, one-unit-higher tier.

If the new tier address is greater than the maximum,

then the new address is one-unit-forward row, same column,

tier =1.

If one-unit-forward takes the row address out of the

hold, then the new address is most aftward row, symetric

with respect to C/L of old column address, tier = 1.

The data for "POST" are also read by the main program.

The following is a list of important variable names.

List of Important Variable Names

K = Order of a port under the loading

process, where the loading port is

assigned number 1. The variable K

is relative to the loading port,

therefore it is different from IPARR(I)

which is a constant while K varies.

The loading port can be any port on the

route

.

L = Index assigned to a hold where type-L

cargo is stowed.

JC = Column address under processing.

JR = Row address under processing.

JT = Tier address under processing.

35

JL = First tier address on deck.

KRORIG = Maximum row address of a hold.

MAXROW(L) = Number of rows in a hold. Note that

"dummy rows" which are ship objects,

must be assigned to an adjacent hold.

MTIER = Maximum value of tier address.

MAXCOL = Maximum value of column address.

MAC = Midship column address.

MLOWER = Maximum value of tier address underneath

the main deck.

LOG(JC/ JR, JT)= Address characteristics

- LOG(JC,JR, JT) = denotes an un-

occupied address.

- LOG (JC, JR, JT) = K denotes a container

occupying the

address which will

be unloaded at port-

K, with respect to

this loading port.

The complete subroutine is listed in the "Computer

Program" Appendix.

C. SUBROUTINES "TRIM" AND "CURVE"

"TRIM" is a subroutine used to compute ship trim. To

evaluate mean drafts and MTI's with respect to displacement,

an auxiliary subroutine, "CURVE", is needed. The curves

of the form are expressed by linear estimation. They are

36

divided into ten segments, each segment as a linear function

of displacement. (AA,BA) , (AB,BB) , . . . , (AJ,BJ) are ten

ordered pairs of ten points on the draft curve, and (AA,CA)

,

(AB,CB) / . . . , (AJ,CJ) are ten points on the MTI curve. The

coordinates of those points are read by the main program

and transmitted to "CURVE" through "TRIM".

For a general curve, the coordinates of those ten

points are: (XO, YO) , (XI, YI) , . . . , (X9 ,Y9) . See Figure 11.

In addition to the variables mentioned above, the

following variable names have been used in the subroutines,

"TRIM" and "CURVE".

List of Variable Names

A

CL

DIFF

DISP

DRAAFT

DRAFWD

SHLGTH

SHMEAN

SHMTI

T

W

D

= Container position and equals row address.

= Container length, in feet.

= Difference of mean drafts after a con-

tainer is loaded.

= Displacement.

= Aft draft.

= Forward draft.

= Overall ship length, measured by number

of rows of containers.

= Mean draft, in feet.

= Moment of trim by one inch.

= Total trim when a container is loaded,

= Gross weight of a container being loaded.

= Distance from midship to flotation center,

positive if C.F is forward of midship,

negative otherwise.

37

BALI = Distance from gravity center of aft bal-

last to midship. Note that if there are

more than one aft ballasts, then the

gravity center is the center of all

ballasts.

BAL2 = Distance from gravity center of forward

ballast to midship. See above note.

38

Y I

9 9 ^ "1 I *

XO XI X2 X3 X4

Figure 11: Curve Estimation

39

VIII. THE MAIN PROGRAM

The main program has been generally depicted by the

flow-chart illustrated in Figure 10. Although every state-

ment is important, no attempt is made here to explain each

statement. A complete list of variable names is attached

in Appendix B, and some brief explanations are integrated

into the program to describe its main functions. A numeric

example in the next section is used as an illustration.

A careful observation of results will help to understand

the main program. However, it is recommended that the

main program be read both before and after the illustra-

tion. It also should be checked during each computation

explanation.

40

IX. ILLUSTRATION

Here is an example which is somewhat close to reality.

Data for a C.B-I cargo vessel is used and we suppose that

the ship is making a route from LOS ANGELES to SAN FRANCISCO,

TOKYO, HONG KONG, SAIGON and then return to LOS ANGELES.

There are five ports, NP=5, and the ports are numbered in

Figure 12.

It is also supposed that containers are being loaded

on the ship at San Francisco, thus, the number of loading

port is 2,NL0ADP = 2, and containers to SAIGON will be

loaded first because there are no containers destined to

Los Angeles. The ship can handle 8 columns, and 6 tiers

of containers (4 tiers under the main deck) . There are

totally 2640 addresses but only 946 containers can be

loaded. The other addresses are permanently occupied by

ship objects. The data mentioned above are read by state-

ment 004.

The total number of rows (equals 55 in this case) are

divided into 9 holds. For this example the numbers of rows

in the holds are: 9,2,6,2,12,2,6,2,8. Note that these

figures can be rearranged, i.e., any number can be zero

or any two or more holds can be combined into one hold

for stowing one type of cargo. These data are read by

statement 005 with format (1015)

.

All data related to individual containers (including

dummy containers) are read next by statement 007. These

41

lOKYO = 3

HONG KONG

SAIGON = 5

SAN FRANCISCO = 2

LOS ANGELES = 1

Figure 12: Illustrating Voyage

42

data are punched on a card, format (110 , 315 ,F10 .3 , 110 , 215)

.

For dummy containers and containers which have been already

loaded, addresses in row, column, and tier must be specified,

Next, ship data, (displacement, aft-draft, forward

draft, ship length by containers, container length in feet,

position of flotation center, position of ballast gravity

centers, and coordinates of points on the draft and MTI

curves) , are read.

Not much is necessary to say about "CALL SORT",

Initialization, and Registration of addresses, except

what we mean by LOG (JC, JR, JT) . Suppose that a container (I)

is being sent from Los Angeles to Hong-Kong; its port of

destination IPARR(I)=4, see Figure 12. At San Francisco,

this container has been already been labeled, and also

suppose that it is stowed at column JC , row JR, tier JT,

Keep in mind that the location LOG ( JC , JR, JT) has been

occupied by a container to Hong-Kong which is the third

port on the route, relative to loading port, San Francisco.

In the process of registration, this relative order is

needed so that overstow can be prevented. The absolute,

unchanged order IPARR(I) of the container is used to

compute the relative order; see statements 026,027,028.

Note that any dummy container has that relative order

equal to NP (latest call port) so that any real container

can be stowed over it.

The first computation is to determine the address

of the center column. Columns of containers are assigned

43

from the left most and from the right most to the center-line

For a maximum of 8 columns the sequential column address is:

8,1,7,2,6,3,5,4. That means the right most column, 8, then

the left most column, 1, are assigned first. The last

column to be stowed is column-4, and we have to determine

this number, MAC, before the main program can call sub-

routine POST. Depending on whether MAXCOL is odd or even,

then:

MAC = (MAXCOL + l)/2

or MAC = MAXCOL/2 (8/2 = 4, for this example.)

In the grouping process, there is no difficulty to group

containers by cargo types. Type-1 cargo containers are

considered first. Any container with ITYPE(I) not equal

to 1 will be dropped out, and so on. However, it would

be a little more complicated to group containers by order

of port calls. We can not use IPARR(I) because this

variable gives the absolute, unchanged value assigned to

each port. What we need is the relative order with respect

to the loading port. We start by considering containers

of the latest call port. The variable K, the relative

order of considered port, and then NARRP , the permanent

number assigned to the considered port, are determined and

computed. If IPARR(I) is not equal to NARRP, then the con-

tainer will be dropped out of the grouping process. State-

ments 034 and 035 compute K and NARRP. The variable K

has the sequential values: 5,4,3, and 2, because for the

loading port NLOADP = 2, NARRP has the sequential values:

1,5,4, and 3. In this case port-1 is the latest call port.

44

After all carried containers have been selected and

listed on the manifest/ the new containers are then

assigned. First, the address to the lower-right most

aft corner is offered. For this example it is (8,1,1).

The address is examined and, in this case, is pre-occupied

by ship configuration. The next address is then offered

and checked; the step from one address to the next has

been explained previously. Actually, the first acceptable

address is (7,4,2). See computer print-out page 58,

Based on the order that has been determined by compu-

tation, the addresses and related data of all containers

destined to port-1, port-5, port-4, port-3 Cin that order)

are printed. There are no containers from San Francisco

to Los Angeles here, therefore, only the headlines are

printed.

The last part of the print-out is a summary. First,

the boundary of each hold is determined; each container

which is in an unacceptable hold, is listed. Sometimes,

depending on the nature of the cargo, "sharing" can be

tolerated. If it is not tolerated, decisions to relocate

or drop-out the containers must be reached before con-

tainers are actually loaded.

All addresses and containers are also investigated.

Any container which has not been assigned an address,

or any address which has not been occupied, are listed.

Along with an unoccupied address is the relative order

45

of the POD of the container which is stowed at the lowest

location of the stack on deck. There are addresses un-

occupied because there are containers required to be stowed

on deck. These containers are for a POD whose relative

order is high, therefore, the common containers of other

ports can not be used to fill those "lower holes". Again,

human interpretation is necessary. In this example, newly

loaded common cargo containers destined to Saigon (port-5)

which have been assigned addresses somewhere in the same

hold should be re-assigned to those unoccupied addresses,

and there will be no overstow.

Data related to the containers in the example have been

generated by a random number process based on assumption

that a certain percent of containers are of type-I,

(I = 1,9) and a certain percent of containers from a

port-J are sent to a port-K. (K = 1,5; K ^ J) . Certainly

overstow depends on the number of containers required to

be stowed on deck. With 4%, it is likely that about 1%

might be over stowed without manual adjustment.

In the last part of the printout summary are the

results related to ship's trim. Note that the weight of

water used to balance the ship must be smaller than the

capacities of the involved ballasts. This figure is used

to identify whether the load plan is feasible. If it is

not acceptable, then manual corrections are needed.

For complete results, see the computer printout.

46

X. FEASIBILITY OF THE MODEL AND RECOMMENDATIONS FOR USE

The model was developed through a heuristic approach,

and many assumptions had to be made. As a result, the

model's overall capacities are subject to some limitations.

The heuristic approach does not always yield an optimal

solution. The model assumes that containers are of a single

size.

The model does not depend on ship form and ship objects,

however, an assumption has been made about the vertical

direct accessibility to any address on board. This means

that if only one stack of containers under the main deck

is to be unloaded, then all containers on the deck, over

the hatch, must be removed. In this case, the solution

reached may become less meaningful as far as overstow is

concerned. However, this problem could be accommodated

with multiple-removable-container-sized-auxiliary hatches

as shown in Figure 13.

The model is not 100% computerized. Due to a variety

of regulations requiring separation of labeled cargo, a

ship loaded with all nine types of cargo might not have

enough separate holds for each type of cargo; or in some

cases, a hold reserved for a specific type of cargo is full.

Manual adjustment are also needed in the cases where there

is overstow which the program cannot avoid, or in the cases

where ship trim, stability, or list is unacceptable.

47

HatchMultipleRemovable

tainer-sizediliary hatch

Figure 13: Specially Designed Hatch.

48

Changing the locations of some container stacks is not very

difficult with data available from the computer printout.

The model only shows where containers should be stowed,

it does not point out which stack of containers should be

loaded first and which one second, etc. If we follow the

order printed, the ship might be sunk in port. The loading

officer should load stacks of containers in a way such that

the ship stay afloat after any container is loaded.

The model can be used in the pre-loading stage. Con-

tainers should be arranged in the marshalling area such

that they are easy to access. A good solution is to arrange

them in the same way as they will be stowed on board, except

in each stack the order is reverse.

The last point here is completely technical. To make

the model more applicable, all data related to the ship and

the voyage can be stored on tape or a data cell, but data

related to containers should be punched on cards. Output

related to each carried container is needed as input for

next loading port, therefore, an extra card output is

necessary.

49

XI . IMPLICATION FOR FURTHER STUDY

A. TESTING AND ANALYSIS

The model has been used with a variety of different data,

and results were acceptable. However, the model should be

further tested with greater ranges of data by changing the

ship, the route, and the generating program, the number of

port calls, total number of containers to be loaded, ship

characteristics, percentage of labeled cargo, percentage

of cargo to each port, etc. Using these variables as

independent variables, the model can be tested to provide

dependent variables such as number of containers overstowed,

number of addresses which must be re-considered, and the

number of cases where ship trim is unad justable . The

results could be analyzed by multi-variable statistics

in order to draw firm conclusions about the feasibility

of the model. The loading program itself requires almost

3 minutes CPU time on an IBM360/67, therefore the process

of testing which includes data generating, loading, and

analysis, will be costly and time-consuming.

B. MODEL EXPANDING

Only the trim computation has been included in the model.

Ship list and stability have been neglected based on the

belief that these effects are generally not a problem.

Another subroutine should be developed and added to the

program, at least for testing and assuring the feasibility

of the solution,

50

The program can be modified to take into account

the effect of the hatches on over stow. This development

would lead to more realistic solutions.

Like celestial navigation, which provides a better and

more accurate position from an estimated position, the

model can be developed such that the result after the

first loading attempt can be revised and used for the

second attempt, etc. As seen in the illustration, the

summary has included assignments that must be reconsidered

and a number of containers that have not been loaded. The

model can be revised such that the program will "automatic-

ally" take these considerations into account, reassign some

addresses to some containers, and repeat the procedure until

an acceptable solution is reached.

The concept of containerization has been in existance

for quite some time, but is still an area requiring quan-

titative research. The model here and its proposed appli-

cations are no exception to this.

51

APPENDIX A

BASIC RULES FOR STORAGE OF CARGO

Type-1: EXPLOSIVES

Must not be stowed with any other labels.

Type- 2: INFLAMMABLE COMPRESSED GAS (RED GAS )

Must be stowed on deck.

Cannot be stowed over a red label hatch.

Must be 2 5 feet from any other hazardous cargo.

Must have the deck house between it and explosives.

Type-3 : FLAMMABLE LIQUIDS (RED LABEL)

Must not be stowed in the same hatch with inflam-

mable solids, oxidizing materials, corrosive liquids,

poisons, or cotton.

Must not be stowed in the same hold over non-

inflammable compressed gases.

Many red label items require between deck storage,

therefore no red label is to be stowed in a lower

hold or deep tank without checking the regulations.

Must have a full hatch or midship house intervene

between it and explosives.

Type-4: INFLAMMABLE SOLIDS/OXIDIZING MATERIAL (YELLOW LABEL)

Must not be stowed in the same hold or compartment

as red label, corrosive liquids, poisons, or cotton.

Must no be stowed in the same compartment over non-

inflammable compressed gases.

52

Must have a full hatch or midship house intervene

between it and explosives.

Type-5: CORROSIVE LIQUIDS (WHITE LABEL)

Some are permitted under deck storage. General

policy is to stow on deck at all times.

Must not be stowed adjacent to or over any poisonous

articles or hazardous items.

Must not be stowed on the square of the hatch.

Must have a full hatch or midship house intervene

between it and explosives.

Type-6 : NON-INFLAMMABLE GASES (GREEN LABEL)

Must not be stowed with explosives.

Must not be over stowed with corrosive liquids,

inflammable solids, oxidizing material, poisons,

or hazardous articles.

Type-7 : POISONOUS ARTICLES (BLUE LABEL)

Must not be stowed in the same compartment with

explosives, inflammable liquids, inflammable solids,

refrigerated cargo, or cotton.

Must not be stowed adjacent to corrosive liquids.

Must not be stowed over compressed gases.

Type-8: HAZARDOUS ARTICLES

Must not be stowed in any compartment with explosives

Type-9: COMMON CARGO

Can be stowed any place.

53

APPENDIX B

LIST OF VARIABLE NAMES USED IN COMPUTER PROGRAM

A = Container position and equals to row address.

BALI = Distance from gravity center of aft ballasts

to midship.

BAL2 = Distance from gravity center of forward ballasts

to midship.

CL = Container length, in feet.

D = Distance from midship to flotation center,

positive if CF is forward of midship, negative

otherwise.

DIFF = Difference of mean draft after a container is

loaded.

DISP = Displacement.

DRAAFT = Aft draft.

DRAFWD = Forward draft.

ICOL(I) = Column address of container I,

IPDEP(I)= Number assigned to a port where the container

was loaded.

IPARR(I)= Number assigned to a port where the containter

is destined.

IROW(I) = Container row address

ISER(I) = Container serial number.

ITIER(I)= Container tier address

ITYPE(I)= Number assigned to the type of cargo stuffed

inside the container

.

54

JC = Column address under processing.

JR = Row address under processing.

JT = Tier address under processing.

JL = First tier address on deck.

K = Relative order of a port under processing.

KRORIG = Maximum row address of a hold.

L = Index assigned to a hold where type-L cargo is

stowed.

LOG = Address characteristics, zero denotes unoccupied

address.

MAC = Midship column address

MAXCOL = Maximum value of column address

MAXROW(L)= Number of rows in the hold L.

MLOWER = Maximum value of tier address, on deck,

MTIER = Maximum value of tier address.

NCONT = Total number of possible addresses,

NARRP = Number assigned to the port under processing.

NLOADP = Number assigned to the port where containers

are being loaded.

NP = Number of ports on the route.

SHLGTH = Overall ship length, measured by number of rows

of containers.

SHMEAN = Mean draft, in feet.

SHMTI = Moment trim by one inch.

T = Total trim when a container is loaded.

W = Gross weight of a container being loaded.

WEIGHT (I) = Gross weight of container I.

WATER = Water added in ballasting process.

55

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3. DOD Project Manager for Surface Container Systems,Draft Master Plan for Surface Container-SupportedDistribution Systems, Department of the Army, Head-quarters United States Army Materiel Command,Washington, D.C., March, 1972.

4. Maritime Administration, Challenge and Opportunity,U.S. Department of Commerce, Washington, D.C. October,1970.

5. Office of Federal Register, National Archives andRecords Services, General Service Administration, Codeof Federal Regulations-46 , Shipping, Parts 146 to 149(Revised as of January 1, 1972), U.S. GovernmentPrinting Office, Washington, 1972.

6. Saurbier, Captain Charles L. (USNR) , Marine CargoOperations , John Wiley & Sons, New York, 1956.

7. Murray A. Jeisler & Wilber A. Steger,"The Combinationof Alternative Research Techniques in Logistics SystemsAnalysis," Management Technology , May, 1963.

8. Dewey E. Beliech, Jr., A Proposed Method for EfficientPre-Loading for Containerized Cargo Ships, Naval Post-graduate School Thesis, June, 1974.

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