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APPLICATION OF THE
SEQUENTIAL UNCONSTRAINED MINIMIZATIONTECHNIQUE IN A
SYSTEMATIC CONTAINERSHIP DESIGN
Robert Malcolm Fortson
DUDLEY KNOX LIBKAK1
NAVAL POSTGRADUATE SCHOUL
MONTEREY. CALIFORNIA 93940
APPLICATION OF THE
SEQUENTIAL UNCONSTRAINED MINIMIZATION
TECHNIQUE IN A
SYSTEMATIC CONTAINERSHIF DESIGN
by
ROBERT MALCOLM FORTSON, III
B. S. United States Naval Academy
- - - - " (1969)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF MASTER OF SCIENCE
MAY 10. 1974
z'i*
IWONTEREY, CAL irn-H°°'-
APPLICATION 0? THE SEQUENTIAL UNCONSTRAINED
MINIMIZATION TECHNIQUE IN A
SYSTEMATIC CCNTAINERSHIF DESIGN
by
ROBERT M. PORTSCN, III
Submitted to the Alfred P. Sloan School of Management onMay 10, 197^i in partial fulfillment of the requirementsfor the degree of Master of Science in Management.
ABSTRACT
This paper investigates the preliminary ship designprocess. The thesis begins by looking at methodologiesfor ship design and concludes that a different outlook onthe overall process could provide an improvement, In par-ticular, possible modifications were identified in theowner's requirements as traditionally given to the designer.After the new design procedure was developed, effortshifted to implementing the procedure for a containershipdesign.
A preliminary ship design model is developed. Thismodel was then used in a test design problem in which anowner desires a single ship to add to an existing traderoute. The design model was used to identify acceptableship alternatives.
The determination of attractive designs was accom-plished by a version of an optimization method known asa Sequential Unconstrained Minimization Technique. Thismethod employs a barrier penalty function to handle theproblem constraints. The search method was found to beeffective in identifying design alternatives. In parti-cular, it behaved well with the discontinuities imposedby the discrete engine selections involved with gas tur-bine power plants.
Thesis Supervisor: Thomas L. MagnantiTitle: Assistant Professor
ACKNOWLEDGEMENT
My many thank go to Professor Magnanti for the time
he spent reviewing the content and suggesting changes in
problem areas. Needless to say, a great deal of personal
appreciation goes to him for being encouraging at times
when it v/as needed most.
My thanks also to Professor Mandel for giving me the
inspiration for the thesis topic and for the time he spent
in guiding my efforts.
Thanks also to Professor Chryssostomidis for the
technical assistance and for reviewing the technical con-
tent.
Last, but not least, my appreciation and thanks to
my wife, Martha, who typed the thesis twice and for the
untimely hours she spent changing mistakes, editing and
listening to my complaints.
TABLE 0? CONTENTS
Pagetai
TITLE PAGE 1
ABSTRACT 2
ACKNOWLEDGEMENTS 3
TABLE OF CONTENTS 4
LIST OF FIGURES 7
LIST 0^ TABLES 9
INTRODUCTION 10
I. OCEAN TRANSPORTATION SYSTEM 14
1.1 Elements1.2 Subsystem Interactions
II. SHIP DESIGN PROCESS 19
2.1 General2.2 Normative Design Process2.3 Proposed Design Frocess
I I I. PROBLEM STATEMENT 31
3.1 Scenario3.2 Design Problem
IV. SHIP DESIGN CRITERIA 34
4.1 Criteria4.2 Measures of Effectiveness4.3 Measure of Economic Criteria
4.3.1 General4.3.2 Net Fresent Value4.3.3 Capital Recovery factor4.3.4 Required "reight Rate
V
.
ALTERNATIVES 48
5.1 Decision Variables5.2 Design Alternatives
Page
5.2.1 Engine Arrangements5.2.2 Ballast5.2.3 Full Load Condition5.2.4 Volume5.2.5 Containers5.2.6 Terminal Interactions5.2.7 Propeller Alternatives
VI. DECISION MODEL 56
6.1 Objective Function6.2 Constraints
VII. OPTIMIZATION TECHNIQUES 60
7.1 Basic Search Routines
7.1.1 Random Search7.1.2 Climbing Techniques
7.2 Sequential Unconstrained Minimization Technique
7.2.1 General7.2.2 Newton-Raphson Method7.2.3 Golden Section Search
7.3 SUMT Computer Frogram
VIII. DEFINITION 0? THE OBJECTIVE SURFACE 75
8.1 General8.2 Required Fropulsive Fower8.3 Discrete Fower Plant Selection8.4 Payload Configuration8.5 Input Parameters
IX. ANALYSIS 90
9.1 Program Validation9.2 Frogram Inputs9.3 Procedure9.4 SUMT Trajectories9.5 Ranking the Alternatives9.6 Discontinuities9.7 Sensitivity
X. CONCLUSIONS AND RECOMMENDATIONS HO
10.1 General10.2 Optimization in the Design Process
5
Page
10.3 Experience with SUT.T
10.4 Areas for Additional Study10.5 Applications
XI. FOOTNOTES 119
XII. BIBLIOGRAFHY 120
XIII. APPENDICES 125
APPENDIX A 126APPENDIX 3 130AFFEKDIX C 139APPENDIX D 1^0APPENDIX E 161
LIST 0? FIGURES
Figure Page
1. OCEAN TRANSPORTATION SYSTEM 15
2. SHIP DESIGN PROCESS 20
3. INFORMATION PLOWS IN A NORMATIVE DESIGN PROCESS 22
4. MODEL 0? THE PROPOSED SHIP DESIGN PROCESS 28
5. SIMPLE CAPITAL DECISION MODEL 40
6. CASH FLOW MODEL AND NPV CALCULATION 43
7. CRF AND R"R CALCULATIONS 47
8. MATHEMATICAL STATEMENT OF THE CONTAINERSHIFDESIGN PROBLEM - 59
9. PENALTY FUNCTION 64
10. NEV/TON-RAPHSON PROCEDURE 70
11. SEARCH INTERVAL 71
12. UNIMODAL FUNCTIONS 72
13. OBJECTIVE SURFACE FLOW CHART (A) 78
14. OBJECTIVE SURFACE FLOW CHART (B) 79
15. OBJECTIVE SURFACE FLOW CHART (C) 80
16. FEEDBACK LOOP DIAGRAM 81
17. OBJECTIVE SURFACE PROFILE FOR ALTERNATIVE 4 105
18. OBJECTIVE SURFACE PROFILE FOR ALTERNATIVE 3 106
19. SPEED REDUCTION FACTOR 133
20. MACHINERY WEIGHT 13^
21. COST OF MACHINERY 135
22. SPECIFIC fuel CONSUMPTION 137
Fage
23. SFC CURVES FOR MARINE GAS TURBINES 138
Zk, PROGRAM DATA DECK STRUCTURE 152
25. SAMPLE DATA CARDS FOR SUMT PROGRAM 153
26. SAMPLE DATA CARDS FOR DESIGN MODEL 15^
27. SAMPLE OUTPUT OF DETAILED DESIGN 156
28. SAMPLE OUTPUT OF SUMT PROGRAM 15?
8
LIST 0F_ TABLES
Table
1. CATALOG 0? CRITERIA
2. DECISION VARIABLES
3. A.S.A STANDARD CONTAINER DIMENSIONS AND WEIGHTS
4. PROGRAM INPUT FARAMETERS
5. PROGRAM INPUT PARAMETERS (CONT.)
6. MODEL VALIDATION
7. IDENTIFICATION OF ALTERNATIVES
8. SOLUTION TRAJECTORY FOR ALTERNATIVE 3
9. SOLUTION TRAJECTORY FOR ALTERNATIVE 4
10. SOLUTION TRAJECTORY FOR ALTERNATIVE 6
11. SOLUTION TRAJECTORY FOR ALTERNATIVE 8
12. RANKING OF ALTERNATIVES
13. SENSITIVITY ANALYSIS
14. DEFINITION OF TERMS
15. INPUT PARAMETERS FOR NNSB VALIDATION
16. INPUT PARAMETERS FOR BIW VALIDATION
17. INPUT PARAMETERS ^OR G.G. SHARP VALIDATION
18. INPUT PARAMETERS "OR SCENARIO PROBLEM
Fase
35
48
59
88
89
91. 92
95, 96
98
99
100
101
103
109
127
140, l4l
142, 143
144, 145
146, 147
INTRODUCTION
Through the years, ocean transport systems have provi-
ded a common forum in which the businessmen and engineers
could participate as a team. The complexity of the present
systems as well as the sophistication of their design has
not evolved without numerous growing pains. Over the years,
society has developed the framework in which each party
operates. The boundaries of responsibility for the two are
not always well defined nor are their liabilities. This
vagueness extends to their interaction with the rest of soc-
iety. The results of past efforts to formalize their rules
with respect to the ship design process can be found in
rules of the American Board of Shipping and of many insur-
ance companies. These rules guide the engineer/designer
in his task so that the final ship design will meet certain
minimum standards. These standards have been developed over
the years and are based on experience.
This paper does not propose a change in the traditional
roles of the businessman and the engineer as related to
ocean transport systems, nor does it develop any new innova-
tions into either of their professional areas. It does,
however, attempt to define explicitly the formal relation-
ships between the parties involved in the design process and
to indicate how these relationships can be used in actual10
ship design. The approach taken is not traditional. The
result is not a new relationship, but rather a more defined
and process oriented approach where there can be a better
agreement as to each parties role with the result of improv-
ing their joint effort.
In an attempt to demonstrate this philosophy, the the-
sis presents a sample problem. With this problem, a method
of solution is then pursued. The important aspects of this
problem are identified in the context developed earlier in
the paper which defines the roles of the participants. The
problem is approached in an objective manner and the outputs
are identified which would prove useful to a decision maker.
The paper presents the results with caution. First, because
the solution addresses only the problem outlined in the
scenario. Secondly, the design model has not yet been veri-
fied by present design practice. Finally, the optimization
method may not in itself identify the overall best alter-
native to a real life problem. For this reason, no attempt
is made to identify such a result.
One of the easiest ways to present a problem is to re-
late a scenario. From this, the assumptions and simplifi-
cations made in the analysis become more palatable and the
solution is not regarded as simply a mass of assumptions
presented for the convenience of the solution technique. The
11
scenario also identifies a clearer division of roles of the
businessman (referred to as the customer) and the engineer
(referred to as the designer) in the scenario. By restrict-
ing the problem as stated in the scenario, the real life
complications and ambiguities are minimized. However, these
will not be ignored in the development of the design process.
The information flows of the design methodology guided the
development of the design program. This program utilized
the capabilities of the computer and the solution technique.
Before the design methodology is outlined or the scenario
developed, it is important to identify the approach of the
paper.
This paper uses a systems analysis format for presenta-
tion. By this it is meant that the first issues covered
involve the problem definition and objectives of the study.
Following the problem definition, the paper proceeds to
identify criteria and measures of effectiveness for the
problem solution. This is then followed by an outline of
the different types of alternatives available. From this
position, a decision model is developed. Tools known as
optimization techniques are applied to this model. The re-
sults and the analysis are accomplished by the application
of a Sequential Unconstrained Minimisation Technique re-
ferred to as STMT. The results are then studied and pre-
sented so that a decision can be made. This decision may
12
not cover the problems originally raised in the scenario,
but should at least pave the way for the next design itera-
tion. As such, the paper demonstrates the computer's capa-
bilities. This, in turn, will demonstrate the possible role
of a computer in a computer aided design.
Definitions are imperative for a proper understanding
of any study. A list of model variables have been collected
with their definition in Table lk found in Appendix A. Their
use in context should not prove difficult for the reader.
There is one definitbn, however, that deserves explanation
before we begin. This relates to the use of the terms
'closed form' or 'explicit' as qualifiers of expressions in
the mathematical model. These will be used interchangeably
in the paper. By an explicit expression, it is meant that
the relationships between the variables involved can be
found in terms of an algebraic expression. In particular,
we will be interested in the relationships involving the de-
cision variables.
The complexity of real life design problems made it
difficult to identify and assess all the implications of
the proposed design methodology. The results of the design
model were useful in identifying the usefulness in a con-
tainer ship design. This paper should serve as a basis
from which to reanalyze the existing methods used in the
design of ship systems.
13
CHAPTER I.
OCEAN TRANSFORTATION SYSTEMS
Much has been written about transportation systems.
The important features of any transportation system are its
collection, warehousing, transport and distribution subsys-
tems as well as the associated management and human subsys-
tems. In today's economy, some transportation systems are
so large that neither a single individual nor a single cor-
poration can control and direct the action of all the ele-
ments. This is especially true of the ocean transportation
systems. Y/e will limit our discussion to the actual trans-
port by the ocean vehicle. The character of this ocean
transport subsystem which distinguishes it from other modes
of travel is the need to have a transporting vessel capable
of transisting an ocean. In this transit, a ship will ex-
perience a hostile environment. The advantage of ocean
transport as opposed to other transport methods is the abil-
ity of an ocean transport system to carry larger loads,
either in bulk or weight.
1. 1 Elements
From the following figure, the ocean transportation sys-
tem can be divided into three basic parts. The first is the
mode of ocean transport by ship. At each end of the ocean
transport is a port and terminal system. At these terminal
14
u.
EHCO>HW
oHEH
EH
OPMC/i
2!
2
oo
u
•H
facilities, the cargo is handled so that another mode of
travel can he utilized. This constitutes the second ele-
ment. In the last element, we will lump all of the remain-
ing parts of a general transportation system. These will
include the various distribution and intermediate transpor-
tation systems.
1.2 Subsystem Interactions
We want to look now at the interactions between the
three parts. As described, the elements of the transpor-
tation system function in series, thus the capacity and the
related efficiency of the total system can be affected by a
single element. Any system design will attempt to size each
of the elements so that there will be no disparity in capa-
city between single units because of the resulting ineffi-
ciencies. An exception would be the planning of excess
capacity to be utilized during a future period of growth.
Conceptually this model should prove useful and as more
ports and shipping routes are opened, the same principle
can be used to describe the larger total system. This sim-
ple model ignores the management problem of capacity utili-
zation in large networks, but the interactions should be more
easily understood.
The major purpose of the ship is to act as a mode of
containment and transportation between ports. The terminal
also serves as a location to inventory cargo so that loading
16
and unloading of the ship can be achieved without delay.
Many methods have been proposed for reducing the cargo han-
dling at the terminals and thus increasing their capacity
and efficiency. One such attempt is the containerizaticn
of cargo. Instead of handling the different cargoes indivi-
dually, containers are used, thus simplifying the loading
problems and reducing breakage and loss of cargo. Over the
last few years this method has become even more popular,
especially with customers that transport small, high value
items, such as electronic equipment. For large bulk cargoes
ship barge systems have been developed.
The interaction between the ship and terminal has many
different facets. They can be related to a time delay in
port. When a ship arrives, it awaits space next to the ter-
minal, Once along side, the crane will continuously handle
containers during the loading operation. The duration of
this evolution depends directly upon the reach, carrying
capacity and speed of the crane. After the incoming cargo
is off loaded and the outgoing cargo is on loaded, the ship
may have to v/ait for favorable navigation conditions such as
slack water at high tide so that the ship can maneuver out
of port safely. The interaction is completed in the same
way that it started, with the ship at sea proceeding between
ports at its operating speed.
The interactions betv/een the port terminal and the rest
17
of the transportation system can be defined along similar
lines. It becomes evident that there is a large management
function at the terminals. The skill developed in these
functions and the capacities of each of the elements deter-
mines the volume of cargo flow in the total system. To say
that the transportation system is capacity limited by a sin-
gle element should require that the element is operating
with maximum efficiency. Otherwise, capacity can be in-
creased without additional capital investment. The complex
problem of capcity determination will play an important role
in the total transportation system design. It should be ob-
vious that when the total system is operating at capacity,
subsystems with excess capacity are not desirable unless
there are future plans for expansion. This points out the
requirement that the design cover the whole of the transpor-
tation system. Many papers have addressed themselves to
the overall capcity balancing problem. The reader is re-
ferred to Erichsen and Hancock^.
Independent of the overall transportation system design,
there will be a stage in the total design when the capabili-
ties and costs are desired of a ship that can interact with
a given terminal configuration. This may be for an addition
of shipping capacity on an already existing route or for an
entirely new transportation system. We are interested in
this interaction between the customer and the designer.
18
CHAPTER II.
SHIP DESIGN PROCESS
2.1 General
The ship design process is that set of actions involved
from the initial desire to build a ship until the final deli-
very of the product. In some circumstances, one or both of
these events may be difficult to determine. The process
involves two groups. One is the owner or user group and the
other is the designer or builder group. The traditional pro-
cess (see Figure 2) involves the determination of the owner's
expectations and his statement as to the capabilities desired
in the ship design. Many times this v/ould be the first for-
mal step in the process. The need for the ship may result
from intuitive feelings based upon years of experience as a
ship operator. Whatever the source, a gap is identified be-
tween supply and demand for services. The owner's require-
ments have traditionally been quite explicit — the speed,
endurance, and payload of the design being specified. This
statement provides the means by which the design passed to
the engineer from the owner. As depicted in the block dia-
gram, the designer then proceeds to implement a design pro-
cedure that results in a feasible design which meets the
owner's requirements. At that point, the owner would decide
19
SHIP DESIGN PROCESS
PresentSystem
CapabilitiesGap
Analysis
Demand for Services,Opportunities in the
I'larket Flace
DesiredSystem
TerminalDesign
PotentialProfits
OtherSubsystems
r<>
x /V
Ship DesignDesign V >
Owner's Requirements
Constraintsof Nature
Constraintsof
RegulatoryAgencies
Design
Procedure
Estimatesof Profitsand Risks
FeasibleDesign
Cost Estimates
FastDesign
Experience
OWNER
DESIGNER
Figure 2
20
if the ship design should continue to a building phase.
The steps listed in Figure 2 are representative of the
process. They may either be found explicitly or implicitly
in the design effort. There are two factors which disting-
uish the process. In general, it is a single pass system.
Inside each phase there may be iteration, but there is no
provision of changing the inputs to any phase. The second
characteristic is the parallel design feature of the
other elements of the system. The decision to build does
not necessarily provide for a system wide evaluation after
the owner's requirements are fixed. Before criticizing this
form, let us investigate the nature of the system,
2.2 Normative Design Process
From the ship design process, the decisions that must be
made are identified. They are in turn associated with a
level of decision making. The following conceptual model
exemplifies the hierarchy of decision making that makes up
the ship design process (See Figure 3)« According to
M. D. Mesarovic, et. al., there is no single best model for
describing the multilevel, hierarchial system. However,
the essential characteristics are a "...vertical arrangement
of subsystems, and [a^ dependence of the higher level sub-
Li.
systems upon the actual performance of the lower levels."
In the Figure, there is no significance to the number
of levels drawn. They are used only to show possible
21
INFORMATION FLOWSIN A NORMATIVE DESIGN PROCESS
DECISION MAKER
OWNER
OWNER
NEED
±DECISION
LEVEL #1
DECISION
LEVEL #2
CRITERIA
QUALITATIVE
CRITERIA
QUALITATIVE
CRITERIA
DESIGNER DECISION
LEVEL #3
QUANTITATIVE
CRITERIA
DESIGNERDESIGN
PROCEDURE
SOLUTION
Figure 3
22
relationships. The input to the process is the result of an
analysis which identifies a need. The output of the process
is a solution (design) which hopefully meets this need to
the satisfaction of the owner. At the higher levels, the
owner plays a major role. At the lower levels, the designer
accomplishes the design procedure. From each level, require-
ments and guidelines are passed down to the next lower level,
and from each lower level the current results and unresolved
decisions are passed up for action. The levels of decision
making have been identified as different stages at which
tradeoffs between criteria are accomplished. Associated
with each level is a set of criteria which are related to
the decisions being made. The decisions concerning certain
criteria can be delegated to lower stages in the design. In
this model of the design process, the owner has responsibil-
ity over all decision levels. Those involving quantitative
critieria such as cost have been identified with the lower
stages in the process. This assumes that the owner's pre-
ferences have been identified.
In the current design practice, the designer receives
the owner's requirements and stops as soon as a good solu-
tion is reached. This means that the last two stages of
the design process are in equilibrium with each other, but
not with the rest of the system. That is, the output of the
designer is a feasible solution which satisfies the original
23
owner's requirements. The traditional process terminates
here. If, instead of the last stages being conducted inde-
pendent of the rest of the system, continuous feedback and
adjustment were possible, a more desired result may be ob-
tained. This would require more coordination of effort
between the owner and the designer throughout the design.
By setting up a formal system to handle the various
levels of decision making, the owner will help control the
whole design process by giving better direction to lower
level management. This would be most important in the de-
sign of new ship types where the final desired solution is
not obvious to the owner.
This suggests that one of the first steps in the design
process is the determination of a set of criteria and order-
ing them in a way which reflects their importance to the
owner. In the normative process, some of these criteria
are assigned to lower levels of decision making. Usually
the criteria can be categorized as either quantifiable or
non-quantifiable. The quantifiable criteria can be easily
delegated to lower levels of decision making due to the
straightforward procedures involved in the tradeoffs. This
does not prevent some or all of the nonquantif iable criteria
from also being assigned. The owner can never comfortably
remove himself from the tradeoffs required by the nonquanti-
fiable criteria. He may, however, quantify his preferences
so that lower levels can perform tradeoffs similar to those
accomplished for quantifiable criteria in the decision pro-
cess. An example of such a delegation is in the economic
criteria which identifies the owner's preferences for
changes in the timing of cash flows. By identifying a dis-
count factor consistant with the owner's time value of
money, the designer can proceed with the economic evaluation
as if the criteria were entirely quantifiable. This relieves
the owner of the need to make tradeoffs of a large number
of cases but still allows him to influence the process. An
example of this influence would be a change in the discount
rate after several iterations. This method of manipulating
the economic criteria would reflect uncertainty of the owner
in his actual preferences.
For an individual as the owner, the decision process
presents few conflicts of interest. As the number and
diversity of those in the decision group grows, internal
conflicts arise when preferences are expressed. This be-
comes a significant problem when the owner is as large as
the government. The socio-political environment may then
prevent an explicit definition of the preferences due to
the nature of the system being designed. The problems of
decision making involved in this environment are felt most
strongly by those who act as representatives for the govern-
ment. The decisions based on preferences will produce focal
25
points for conflicting interest groups. This tends to re-
duce the area in which explicit decisions are made to those
in which mutual agreement on the method of quantifying the
criteria can be achieved. This often results in the quali-
tative criteria being either ignored or being considered in-
formally.
This multilevel, hierarchial system is compatible with
the ship design process. It has the advantages of isolating
the decision maker and setting responsibilities. This then
leads to reliable subsystems. In particular, the multilevel
system offers an improvement over other systems in the uti-
lization of resources when solving large scale complex prob-
lems. It also provides more flexibility and in general can
be expected to produce better system output. This does not
suggest that the system is ideal. Some of the disadvantages
are its complex operation or behavior. As such, it is diffi-
cult to analyze or comprehend. It also is difficult for one
to control or influence its progress. However, the multi-
level, hierarchial system has proven that it's general quali-
ties are better than other systems designed to handle large
programs
.
2.3 Proposed Design Process
Any proposed system must provide a method for the flow
of information from higher authority, performance of its
design task, and the reporting of results using the developed
26
criteria to the next higher level of decision making. The
upward flow of information will be used to determine if there
is need for further iteration to achieve a better overall
design. This is done by investigating tradeoffs between
various criteria and their associated costs. The informa-
tion that would be necessary to accomplish this task would
include first, the values of the decision variable and an
estimate of the confidence limits for these values. Secon-
dly, the information should include a sensitivity analysis
that would show the decision maker the resulting effect on
the criteria measures for changes in the values of selected
variables. The proposed design process (Figure H-) attempts
to incorporate these requirements.
The best way to understand the major features of the
proposed change is to contrast this design process with the
traditional process covered earlier. First, the proposed
design process, being iterative, takes more time and effort.
Where the designers objectives are fairly clear in the
traditional process, the guidelines now provide for much
more leeway in the actual design. This in turn requires
additional effort. The process requires increased interac-
tion between the owner and designers so that the designer
can determine the preferences of the owner. The owner's
identification of the criteria and measures of effectiveness
should be given substantial attention so that this
27
MODEL OF THE PROPOSED
SHIP DESIGN PROCESS
PresentSystem
CapabilitiesDemand for Services,Opportunities in the
Market PlaceGap
Analysis
|~ Other V-iSystems'
DesiredSystem
PotentialFrofits Other
SystemsGaps
M.O.E. forShip
HardConstraints
SoftConstraints
OWNERDESIGNER
.j Otheri
^Systems 1
OWNER_DESIGNER
i Other Systemi
! Constraints [\
DESIGN
: RCCEDURE
Sensitivity
PastExperience
Figure 4
28
interaction is effective.
In both systems the owner has the responsibility of
making his desires known and making the final decision to
build the ship. In the traditional process, the owner would
use a previous ship design to communicate his desires. When
this luxury no longer exists, it becomes necessary to for-
malize the method by which such preferences were made. This
is especially true for large systems when there is no one
single decision maker who can perform the vital integration
function.
One way to rationalize the prevalence of the tradi-
tional system is to study the time history of ship design.
Over the years the design process identified successful ship
types. This meant that the individual design efforts did
not require formal iteration to achieve good designs. Ey
perpetuation and extrapolation of the ship features that
had proven themselves in actual service, sufficient success
in the ship deisng effort could be achieved. This identi-
fies a situation in which the traditional approach may be
preferred. When the changes in the need as percieved by
the owner are fairly constant over time, newer ship designs
can be based on the more successful existing ships. A
change in the traditional method would thus require that
new requirements be placed on the ocean transportation
system. These would be similar to the needs generated which
29
caused the building of liquid natural gas (LKG) ships where
no similar ship type previously existed.
In order that the additional "benefits identified by the
normative model may be incorporated in the ship design pro-
cess, a new method was proposed. The major differences were
first, the iterative nature of the process? secondly, the
change in the form of the owner's requirements entering the
design procedure. This means that the designer will no
longer identify merely a feasible solution. In turn, this
requires a change in the perspective of the designer and
the owner. No change was made in the actual design proce-
dures. The next chapter identifes a sample program which
will be used to demonstrate the proposed design process.
30
CHAPTER III.
PROBLEM STATEMENT
3.1 Scenario
A large U. S. owner, an operator of containerships,
desires to expand operations between San Diego, California,
and Yokohama, Japan. The company is interested in purchas-
ing a single ship to increase the shipping capacity of this
route. The company presently has no available ships to
transport the increased demand for cotton and leather goods
in Japan, If present rates prevail, it is assumed that each
ton of cargo transported will generate $100 in revenues for
the company. At the present time, there are no arrangements
anticipated for the backhaul of cargo. The company usually
does not consider the backhaul when making their capital in-
vestment decisions because the quantity of cargo handled on
the return voyage is so small that almost any reasonably
sized ship would be capable of providing the capacity. Each
alternative would then generate the same backhaul revenues,
and thus would not affect the decision to be made.
The trade route imposes some restrictions on the alter-
natives. First, the terminal facilities are such that a
single loading sequence will not be able to provide more
than 1200 containers without excessive delays. Secondly,
31
the pierside cranes maximum reach restricts the ships beam
to 110 feet. Finally, the harbor channel restricts the
ship's draft to be less than 37'. The ports have an average
charge associated with the pilotage and tug fees which is
incurred upon entering or departing a port. Past experience
estimates these to average $1,000 per port call, While in
port, there are additional wharfage and port fees which are
determined by the number of days in port. The port delay
times have historically averaged two days per port call.
While in port, there are additional wharfage and port fees
which are determined by the number of days in port. The
port delay times have historically averaged two days per
port call.
The container size in use is a 20' X 8' X 8' container
which meets the American Standards Association requirements.
Each full container has been estimated to v/eigh 16.7 tons.
This restricts the stacking of containers, one on top of
another without an intervening, supporting deck.
In order that all costs and prices be consistant, the
base year of 1969 was selected. The prevailing economic
conditions in the U.S. in 1969 were such that the operator
could be assured of obtaining a 55 per cent building sub-
sidy from the Maritime Administration upon request.-5 In
addition, the company was anticipating financing three quar-
ters of the unsubsidized costs by incurring a 25 year loan
32
at ten per cent v/hich would be insured by the government.
Other alternative routes have been generating a yield on
the companies original investment after tax of about twenty
per cent. The company feels that any new route should
generate a similar yield. In addition to the subsidy, the
company will be able to take a seven per cent investment
tax credit, "or comparisons between alternatives, this will
be translated into a reduction of initial otit-of -pocket
costs.
3. 2 Design Problem
The above scenario presents several questions to be
answered. Here we will attempt to identify the characteris-
tics of the design v/hich would be obtained during a preli-
minary design stage. This effort will require that design
constraints be translated so that non-feasible alternatives
can be eliminated from consideration. After a choice is
made of the ship's characteristics, its confidence must be
evaluated taking into account possible variations due to
uncertainty in the information available in the design.
This will help to measure the uniqueness of the design.
Nov/ the problem of selecting a good design must be
addressed. In the next chapter, measures will be developed
that will help to insure consistancy in our selection as
well as providing a reference from which to base our deci-
sions.
33
CHAPTER IV.
SHIP DESIGN CRITERIA
The existance of different commercial ship designs to
accomplish similar tasks can be explained by the environ-
ment and experience level of those involved in the design.
The design selection process is greatly affected by these
factors because the real-world environment will influence
individually each decision maker. Insight as to what deter-
mines the merit of a ship design thus requires investigation
of the decision maker's preferences.
The objectives of the ship system which are to be
satisfied by the decision maker's choice of alternatives
are complex, however, a simple statement would list the
commercial ship as primarily a means of improving the eco-
nomic welfare of its owners by providing a marketable service.
h.l Criteria
The difference between the worth of ships is based on
a number of criteria from which the merit of a ship is deter-
mined. Conceptually there is a single list of criteria whose
various orderings reflect the preferences of the decision
maker. The following figure attempts to give a sample cata-
log of criteria. The determination of the relative impor-
tance of these criteria is a function of the decision maker.
3^
Table 1
CATALOGUE OF CRITERIARef. [3,6,7,9,27,36,37,39]
I
.
ECONOMIC
ProfitsDurabilityAsset LifeObsolescenceSalvage Value
II. MISSION RELATED CAPABILITIES
Transport Mission
SpeedEndurance, RangeCapacity, Payload, Cargo Type
Patrol Mission
SearchInvestigatePlant and RetrieveSecure
Interaction Mission
EngagementStation-keepingAvoidance, Defense
III. OVERALL SYSTEM CAPABILITIES
MobilityViabilityFlexibilitySurvivabilityOperatabilityEffectiveness
IV. MARKETABLE QUALITIES
Aesthetic Value, Style, ColorQualityPrestigePersonal Satisfaction
V. RISKS AND UNCERTAINTIES
Investment RisksFuture UncertaintiesReliabililityMaintainabilityAvailability
The commercial ship owner, on one hand, is ultimately in-
terested in economic criteria and in particular profits,
whereas a warship's merit will be a strong function of the
ship's mission capabilities. Where the ability of providing
defense from attack may be important in the warship, this
criteria is ignored in commercial ship design. Also, the
economic criteria loses its eminence for a warship design
because profits are no longer meaningful.
Another difference between designs is reflected in the
variation of risks involved in the design and the risk pre-
ferences of the decision maker. The term 'risk' refers to
the possible outcomes associated with uncertain future events.
For a commercial ship this may be in the form of unexpected
breakdowns resulting in expenditure of funds and delays in
operation. A risk associated with warship design may be
represented by possible threats such as a surprise enemy
attack. The risk preferences relate to the utility function
of the decision maker. From this it is possible to determine
the mechanism by which the decision maker assigns weights to
criteria, taking into account the values and risks involved
for each alternative. The process of determining a decision
maker's utility function uses successive lottery choices
where the decision maker is asked to determine his preference
between only two events. It is important to note that the
decision maker is not always consistant in these choices.
36
The risks of the design are measured by many of the listed
criteria.
The multiattributed analysis of Keeney and many
others could be applicable in helping to quantify the owners
preferences. For an example, if an owner of a commercial
ship experiences a situation where a breakdown only occurred
once during the life of the ship which required assistance
to get into port, the risks may be acceptable. On the other
hand, a single weapon impact on a warship may result in a
total loss of the vessel and perhaps result in the loss of
other units which it may have been defending. The risks are
high and even though the event may be very unlikely, the
resulting risk preferences of the decision maker may cause
changes in the ordering of the design criteria.
4.2 Measures of Effectiveness
To be useful in a modeling context, each of the above
criteria must have an associated measure. For those criteria
which are basically quantitative this presents no problem.
The economic criteria can be easily measured by dollars. The
others, however, present a real problem, both to the designer
and to the owner. This becomes most evident when it is nec-
essary to make a decision based on tradeoffs between two
qualitative criteria. It is not uncommon to assign measures
to these qualifiers. The regulatory bodies have taken the
liberty to associate floodable length with the safety of the
37
7ship at sea. This is satisfactory if the proper response is
obtained by use of such indirect measures.
It is not the purpose of this paper to propose measures
for the criteria. This is a function of the individual deci-
sion maker. For the remainder of the paper, we will handle
only the more accepted measures. We will use dollars as a
measure of the economic criteria and as the measure of effec-
tiveness for judging the ship design. Other quantitative
criteria will be introduced as constraints, giving minimum
standards for the design to satisfy, the freeboard requirement
is such a constraint.
4.3 Measure of Economic Criteria
When making a capital investment decision it is impor-
tant to identify all of the interactions that can affect the
economic returns to the decision maker over the life of the
decision. These interactions may be related indirectly as
would be the case when the reputation of a ship affects
the willingness of customers to do business. For this paper,
we are restricting our interests to the direct economic
effects.
4.3.1. General
In the context of the normative process, the decision
maker attempts to tradeoff different criteria in terms of
the possible changes in profit and other qualitative aspects.
38
Once the tradeoffs are made and the owner's requirements are
identified, one economic measure of the goodness of a design
is its ability to provide profit to the owner. In ship de-
sign, this measure is subject to uncertainty because of the
lack of information about revenues over the life of the
ship. The measures in the literature assume that the reve-
nues are unknown because a good forecast cannot be obtained,
the result being that measures typically involve costs only.
For the ship design, the costs can be predicted with a fair
degree of certainty.
If one assumes that the ship will be built and we are
merely interested in determining the best designs out of
the various alternatives, then the simplified problem can
be analyzed by including revenues. A marketing study could
provide an estimate of the income expected from the cargo
transported. This would help indicate the relative earning
ability of each design. The freight rate that would be
obtained will be used to drive the solution technique in
the sample problem.
The owner's requirement for a desired cargo flow rate
would be calculated as shown in the following figure which
depicts estimates of revenues and costs for shipping a
different cargo transfer rates. The owner would select a
value of the payload transported per year that would maxi-
mize his profits. Along with this point estimate, he would
also have an estimate of costs involved if the design
39
s>toa:
oo
STAPLE CAPITAL DECISION MODEL
(SINGLE SHIP)
PROPnS
fy, (oTT. RfiuJ «ATT "\ V,C^KC»0 FLOW R4t£ (w«rrs/ye,^
Figure 5
40
fluctuates from this estimate. This cost can he associated
with a penalty cost to the designer for deviating from the
owner's original requirement. Given the flow rate of cargo
required, the owner is interested in the design that mini-
mizes the cost of this service, subject to restrictions
placed on the design. The owner would easily change his re-
quirement on the flow rate of cargo if in so doing he would
permit a design that could increase his profits. This gives
the owner two options. First, he could direct the designer
to design for a certain speed and cargo capacity, as is the
present practice, or the designer could perform the evalua-
tion to determine the new requirements. In this case the
designer would need the criteria for setting up a decision
model. This should require less work of the owner than to
determine the owner's requirements, and it would reduce the
number of iterations of the proposed design process because
the owner would not have to wait until the designer proposed
each modification to the requirements.
For the sample problem, the decision model is formulated
in terms of economic criteria. By defining the general form
of the revenue schedule, the cash flows can be determined
by the designer. The model assumes a fixed freight rate for
material transported between two specified locations. The
designer would then be able to perform the tradeoffs in the
design procedure concerned with the economic criteria once
the owner's preferences are identified. One way for the
owner to project his desires is to identify the parameters
for the calculation of the net present value of a design
alternative.
b.3.2. Net Present Value
The Net Fresent Value (NPV) calculation takes a series
of cash flows and determines an equivalent lump sum value at
a specified point in time. It is based on the premise that
there is a time value of money. The assumption is that a
person will be indifferent to receiving one dollar today or
one plus X dollars at some later time. This value is in-
ferred from the fact that the one dollar can be invested to-
day and have earned X additional dollars by the end of the
period. We define the value of X as the discount factor. In
general, the cash flows can be continuous or discrete, but
for a continuous cash flow there will be an instantaneous
discount rate. The cash flows may either be positive or
negative. Also the discount factor may be a function of
time.
For ease of computation and also because of limitations
on the projection of future cash flows, we will restrict the
discussion to discrete cash flows and a constant discount
rate. See Figure 6. Since data is available on an annual
basis, we will use annual costs directly. The horizon of
our calculations will be the expected lifetime of a ship.
K2
,i
\
o x
l'
5 4 r Y£A
^ ANNUAL CASH FLOWS
- INITIAL -OUT OF POCKET COST
1
NPV I * C (i + O - i
t(l + t)25
sv(i*0
25"
I 5
C =
sv=-
Initial Investment
Annual Cash rlows(Assumed constant)
Annual Discount ?actor
Salvage Value
Figure 6
^3
It has been standard practice to use a twenty-five year life
for ships. This has been substantiated by studies conducted
by John McMullen Associated, Inc. for the U. S. Navy in 1967.
At the end of the twenty-five years, the vessel will have a
scrap value. This is usually a fraction of the initial cost
and will be an input to the model.
Looking at the operating costs when performing our
present value calculation, we can make some important gener-
alities. First, the operating level of the ship can be
assumed constant for the duration of its life. This indicates
that the crew hours and the fuel usage per year will be cons-
tant. We can then calculate annual operating costs if the
wages and the price of fuel are known. If a current market
price is assumed, then the discount factor could adjust for
the effects of inflation. This may not be adequate if there
is a restriction in the supply of fuel oil that causes it to
increase in price faster than other expenses. One solution
would be to utilize two discount rates, one for each different
cash flow but for this problem we will assume only a single
discount factor.
Until now we have not included the maintenance and over-
haul costs. These are significant when taken over the life
of the ship. They should be estimated and included in the
NPV calculation. These costs are dependent on the policies
of the owner and data is not readily available. They will
4/+
be treated in this model as an annual cost whose value will
be a fraction of the initial ship cost.
The following list gives the major restrictions and
limitations of our use of NFV.
(1) Cash flows must be on an after tax basis.
(2) Does not account for uncertainty in cash flows.
(3) Assumes that there is no capital rationing.
(4) Gives a poor measure for liquidity or timing
preferences.
Depending on the form of the capital rationing, modifi-
cations to the straight NFV calculation can be made so that
comparisons between designs are more valid. One method in-
volves varying the discount factor and noting whether or not
the relative merit of competing designs change. Another
would impose a variable discount factor. This could model
a temporary cut-off rate. For a strict capital rationing
which limits the initial cost of the investment, the addi-
tion of cost constraints to the design model would be another
method of accounting for the rationing of capital.
The other limitations of the net present value method
indicates that it will not always serve as a good single
measure of economic worth of the different design alterna-
tives. In order to compare the results from this measure
of effectiveness or objective with some others which are
commonly used, the model calculates independently the values
45
of the capital recovery factor and the required freight rate
for each alternative. This leaves open the option of selec-
ting the objective to be used.
Jf.3.3 Capital Recovery Factor
The Capital Recovery Factor (See Figure 7 for Defini-
tion) is the resultant of dividing the value of the annual
cash flow by the initial investment. This can be used to
find an implied or yield rate. If the cash flows and the
investment base is the same as for the N.F.V. calculation,
and the annual cash flows assumed are assumed constant, the
results will be compatable with the M.P.V. measure. The
capital recovery factor calculated is based on the total in-
vestment and as such is not consistant with the net present
value measure.
.
*t.3.4 Required Freight Rate
The Required Freight Rate (See Figure 7 for Definition)
is that cost that must be charged to break even with the
costs of operation, including depreciation or some return
on the original investment. This calculation does not re-
quire knowledge about revenues and is insensitive to change
in tax rates.
k6
CRF = I.- (2. + 3. +5.)
6.
RFR (*/T0N ) = 2. + 3. + 4.
7.
Where
:
I. - Annual gross revenue
<- - Annual operating cost
O. - Annual loan payments
4. - Annual depreciation allowance
O. - Annual tax payment
6. - Gut of pocket investment
1. - Fayload weight in tons
^igure 7
*7
CHAPTER V.
ALTERNATIVES
5. 1 Decision Variables
The decision variables were selected to simplify the
determination of the objective surface used by the optimi-
zation technique. The model must incorporate variables that
would first identify the physical form of the ship; second,
identify the loaded condition, and finally identify the oper-
ational capabilities. By using the linear dimensions and
the coefficients of form, the geometry was determined. The
specification of the draft and the displacement determined -
full load condition. The only ship performance investigated
was the speed of a transit. Thus the ship's speed was used.
The following is a list of the decision variables.
X. ....... . Displacement (A )
X2
Length (L)
X3
Beam (B)
X^ Draft (T)
X5
Depth (D)
X/;. ...... .Prismatic° Coefficient (CP)
X?
Speed (V)
Table 2
Note that the midship coefficient is a dependent varia-
ble. CM = CB/ CP.
^8
5. 2 Design Alternatives
The various alternatives that will be investigated can
be identified as a set of the design variables. For each
alternative, other parameters are held constant except when
sensitivity to changes of these parameters were tested.
This method of alternative identification was selected to
maintain simplicity in the design model and to facilitate
its understanding. Also areas of scarce information played
a role in the final set of variables.
The ship capabilities which have a major effect on the
ship owner are the load capacity, speed, and endurance of
the vessel. Prior to evaluating any design these must be
known. Each contains a continuous range of possible values.
For this problem, the endurance will be treated as a fixed
quantity. The speed and load capacity of a given size and
shape ship are now related. After the propulsion plant con-
figuration is determined, it is possible to evaluate the
available space and weight for cargo. The size of the pro-
pulsion plant is a strong function of speed for any given
ship geometry. It should be obvious that the alternatives
can be identified by the decision variables listed earlier.
In the search for the better alternative designs, the
feasible space must be identified. The following areas are
discussed to identify the limitations of possible alternatives
studied by the design model.
2*9
[,, ^*—^ arrangements of„ the
The various basxc space
englne reom a. or amidships <~£ZZL*~ - -
engine space vary are ^^ ls not
«—"" reaS°n. n
"p .—* ^ capability. »unique.for any given P «
dlfferenoes in the lccat.cn—*
payioad
;rr,ncU» »—
—
the
of engine spaces are^ ^^ ^ ^^ the
preliminary deslgn. Unle _the proble» of trim in
wi*m "hv introducing xne pi
scope of the problem by » ^ ^Uicaticns.
the benefits of a -ore ^^^ rf optimiza-
prcve useful. It ^ iooawon Qf the engine
tlon which would identifyof this
• .„ alternative design. The c
separate procedure may «This
. norease
tude as the cost of the rest of the P ^ ^^ta costs was treated as unreasone«.. ^^„ is not the intent to «*-"^
deslgn altematives
be built, but rather to^Alternatives are restricted
in a preliminary pnase. Thu
s„a <voace located aft.
by having their -*-J^^ location. the propul-
In Edition to
" on the number of
aion Plant configuration
50
propellers and shafts in the design. In the model either
a single or doable screw arrangement may be selected. These
restrictions are imposed by the program user. The model
only adjusts the number of engines and the associated opera-
ting levels and does not handle the actual engine arrange-
ment. The differences in the weights of units other than
the engines are not considered significant for the differ-
ent configurations. There is, however, an adjustment made
for the differences in appendage drag.
5.2.2. Ballast
As used in this paper, ballast is not considered part
of the payload. An upper limit on payload for each alter-
native would occur when no ballast is being transported by
a proposed design. There may be a configuration where bal-
last is transported. Of course, this is not an intuitively
appealing situation, but there may be a configuration where
ballast may be advantageous. This may occur if the ship is
stability limited. If by carrying extra ballast an addi-
tional container is transported, the benefits could out-
weigh the costs. Even though ballast may be 'off limits"
to most designers and operators, the only direct cost asso-
ciated with the ballast in a design with a fixed displace-
ment is in the initial installation. The inclusion of bal-
last impacts on the payload carried at the specified speed
and endurance. For the purpose of this study, the cost of
installed ballast will be taken as $1,000 per ton. This51
is higher than the real costs experienced, thus should help
to minimize ballast wherever possible.
5.2.3 Full load Condition
It is realized that designing to the fuel load condi-
tion does not reflect all of the possible operating condi-
tions which exist. The program does not address directly
the backhaul or other ballasted conditions. Through inter-
action with the program, however, it may be possible to
develop a design model that could incorporate such a ballast
transit. This would require that the designer interact with
the program and the results be carefully interpreted. The
design model could in this way serve as a small part of an
overall system design optimization.
5.2A Volume
Using a similar argument as that for disregarding en-
gine space location, the volume constraints of the problem
were ignored. Except for the obvious case of determining
the container configuration, the volumes were not tested.
A final hand calculation of volumes was accomplished for
the final results. From these hands calculations, it was
found that the designer may wish to be more careful in the
handling of the volume constraints. First, it was thought
the ship may be only weight limited for all but the container
configuration. That would mean that the space not used by
52
the container configuration would be ample for the volume
of any other weight group such as fuel.
5.2.5. Containers
The variation in container sizes has been standardized
since 196l. The American Standards Association standard
container dimensions are given in Table 2 . In this study,
only the 20• X 8' X 8 r non-refrigerator containers were
used. It was assumed that they would possess the strength
necessary to stack the containers six high. This standard
of the ASA is not accepted internationally, the International
Organization for Standards (I.S.O.) calls for the stacking
9of only four high,
5.2.6, Terminal - Interaction
The various interactions with the terminal were
treated as parameters in the design. It was assumed that
the ship relied on pierside handling and the average port
delay time was not sensitive in the range of the loading
capacity of the ship. This could have been modeled but
again this level of detail was beyond the scope of the
problem. There was one factor of the interaction that was
incorporated. The model is constrained to a maximum number
of containers per trip. This relates to the capacity of
the terminal facilities.
53
000) I—
1
rH
m o
to (0 (0 CO CO
i s c c c Go o o O ou -p -p P -pO -P.c; • W) hO WJ hO
3 -rH
u c tlo o d Ou a) rH r-< rH rHh ji
n o ITN o • o(1 2 m CM CM r-ip
,v!
hO•tH
><u
'd.
E!
< £ * » -
to
'
b o-i|^?i
s vdO 0O|r-l b no[5 O "roteK -p + i + 1 + _ t +' I
o X! ~E
•H iaO o o b bto •Hvl (U i 1 i i
0) wi
:
» ^ » »
H CO CO- CO COnJh
<U
c•rH
CO+->
aou : = kOO oo|rH O OOlrH O 0O|H O noirH•d .n + i + 1 4- 1 + 1
Sh p r 1 E K
CU 'd O o o o'd •Hel 2 ' 1 1 1
t\<
HCO co CO CO CO
•
«3j
en
< b rolco b TnUi- O OOlrH+ 1 + i + 1
b oofcO UTS lr\ IfN
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WJ o rH d ONC rH rH<U 1
J 1 1 1
b - - _
-* ONOJ
—
ONrH
ON
5*
5.2.7. Propeller Alternatives
It was decided to handle single or double shafts se-
parately. However, the effects on the overall propulsive
efficiency due to different propeller designs were ignored.
The problems associated with the propeller design could have
been incorporated at the expense of simplicity. Instead, it
was decided to test the sensitivity of the overall results
to changes in an arbitrary propulsive coefficient. This
would then indicate if more detail would be necessary.
55
CHAPTER VI.
DECISION MODEL
The objective of the optimization model will he to
maximize the net present value of cash flows to the ship
owners due to the initial cost and annual cash flows.
Each alternative generated will be subject to restric-
tions from rules imposed by the regulatory agencies, the
restrictions due to navigational considerations, and restric-
tions due to either data limitations or owners requirements.
The following is a simplified mathematical model of the
problem. The expressions are given in a simplified form.
The decision variables were covered in Chapter V.
6.1 Objective "Function
As determined earlier, the net present value measure
for the capital decision problem could be one of the cri-
teria used in making choices among alternative designs. Our
decision model determined the net present value of the cash
flows to the owner by calculating the initial building and
subsequent annual costs. The objective of the program will
be to maximize the net present value of the design. The
objective function is not expressed solely as closed form
equations, because some of the data is extracted from known
56
tables.
6. 2 Constraints
During the design process, there are several con-
straints that must be observed. These can be defined as
either soft or hard constraints of the problem. They help
determine the feasible set of design alternatives. The
hard constraints refer to the constraints imposed by tech-
nology and the laws of nature. These would include the maxi-
mum draft limitation due to the channel depth and the limi-
tations on geometry of the ship due to strength limitations.
The exact value of the hard constraints are sometimes diffi-
cult to determine. For example, the limit of strength is
not well defined. In these cases, rules of thumb have been
developed. These are the result of attempts by the regula-
tory agencies to quantify the factors involved.
The soft constraints, on the other hand, have no phy-
sical significance. They result, not from ship design
alternative, but from requirements of the owner or designer.
These could be imposed in order to insure compatibility with
other elements in the total design of the ocean transporta-
tion system. The maximum constraint on containers permitted
per trip is an example of such a soft constraint. It could
also be a limit indicating the range of data or experience.
The limit is obvious in the powering calculation. The soft
constraints thus limits the set of feasible design
57
alternatives. Even though there may be good alternatives
outside the experience of a designer he may not have con-
fidence in its potential. For this problem, we have im-
posed soft constraints due to the availability of data.
If these become tight constraints during the final itera-
tions of the design then a direction will at least be iden-
tified for further investigations.
For this problem, we have segregated the constraints
into four areas t Those due to the requirements of regula-
tory bodies, navigational restrictions, interaction restric-
tions, and data restrictions. (See Figure 8)
58
MATHEMATICAL STATEMENT OF THECONTAINERSHIP DESIGN PROBLEM
Maxim i2£ © NiPv of casm flows
r^T«yf/-i VA*l/4/l(_^S X<L<3 Mfl) %pf>)
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RESTRICTION
WITH TE/?A1f/i/AtS
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LEAJG-TH
beam
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Taylor s&? ( ps (§)
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& REFER- TO DETAILED CALXUL.ATIOM IN /IPPtAJDix. E
3 /w-rc-G-eye V/*xi/f-BL.e5 cXf>p, Xrs , Xco )
Figure 8
59
CHAPTER VII.
OPTIMIZATION TECHNIQUES
The optimization problem as stated in the last chapter
is a mixed integer, non-linear, mathematical problem with
some expressions not given in closed form. The relation-
ships used to determine the powering requirements of the
ship are a combination of working graphs and tables. The
relationships between several decision variables are in-
volved and any simplifying assumption necessary to obtain
a closed form expression would introduce unacceptable errors.
Without such a closed form solution, analytical solution
techniques cannot be incorporated. For a survey of the
approaches applied to this problem, see Appendix to
Reference 51.
One method of determining the powering requirements for
design alternatives has been tabulated in working graphs.
The Taylor Standard Series of model tests is an example which
presents the powering requirement as a function of five varia-
bles. (Displacement, beam to draft ratio, volumetric co-
efficient, and speed to the square root of length ratio).
There have been attempts at determining the analytic form
of the relationship, hov/ever, one or more of the independent
variables are usually set equal to constant values. These
60
variables selected are indicative of a special type ship. Be-
cause the relationships are not available for containerships
in general, these analytic forms were viewed as being too
restrictive. The solution methodology used must be compati-
ble with the data in its available format of graphs and ta-
bles. The identification of an objective surface is possible
using the available information. Also the constraints can
be readily evaluated. This situation suggests that some form
of search routine will be able to locate the location of the
optimal objective value which meets the constraints.
7.1 BASIC SEARCH ROUTINES
7.1.1 Random Search
The Random Seach Technique applied to the ship design
process is covered by Kandel and Leopold. The method in-
volves searching each variable sequentially, each time sam-
pling at random from the acceptable range of the variable.
As the procedure progresses, the search is concentrated
around the more attractive solutions. This results in the
determination of a solution for the first stage. The pro-
cess is iterative, it is started over many times, with the
best solution of previous iterations being retained. How-
ever, there are drawbacks to its use. First, there is
the large amount of computational effort required. Secondly,
there is difficulty in identifying the feasible range for
61
each of the variables searched. It maps out the surface dur-
ing the process which provides additional information to the
designer. Unfortunately, its randomness makes it difficult
for the designer to interact with the program. The random
nature does, however, help to insure adequate coverage given
enough iterations.
7.1.2 Climbing; Techniques
The Hill Climbing Techniques employ the information
gained from the gradient of the surface to determine the di-
rection for the next move. This technique is often used in
conjunction with other techniques which determine the dis-
tance to jump. The methods require an initial point and the
derivatives at that point, The process is usually slow to
converge due to possibility of rapid oscillation in the move-
ment vector as the solution is approached. Problems due to
special surface forms have been handled by variations of the
technique. Many of these include systematic rotation of the
coordinate axis.-^ The major difficulty with this technique
for our application is the problem of keeping the search
within the feasible region.
One method of insuring that the search remains in the
feasible region is to impose severe penalties for violating
the constraints. The Sequential Unconstrained method uses
this barrier technique successfully as discussed in the next
section.
62
7.2 SEQUENTIAL UNCONSTRAINED MINIMIZATION TECHNIQUE (SUMT)
Ref [15]
7.2.1. General
The name of this technique is very descriptive. It is a
process which transforms the constrained problem into a se-
quence of more easily managed problems without constraints.
The set of solutions to these problems possibly converge to
the solution of the original, constrained problem. There is
no single method of determining the sub-problems nor the
associated solution method. Presented here is one method
that has proven useful.
The SUMT is designed to solve the optimization problemi
Minimize +(x)
SuBxec-r to: *£(5c) > o L*l,2-,3, ,
•*»
Whcrc X - (x, ,Xi ,X3 ..., XK )
Tis e\ r\-T>\rlz«j h ,o*J column vfctok.
The technique applies a minimization method to a modified
objective function P(x,r), where r is a given parameter.
P(x r) = fOt) - rt^fP) + Z LW*tf/r
From the function F(x,r) one can associate the additional
terms to a penalty. Depending on the value of "r", the pen-
alty takes different forms as illustrated in Figure 8 .
In the limit as "r" approaches zero, both penalty terms
63
NPV (* 10 *)
2LU
>-
b<LUa.
oUJZD_J
LE NGT H
•
-I. -*
INEQUALITY CONSTRAINT
2ccLU
>
<z.LUQ.
LU
_J<>
NPV O'o')
Y«-|: (CB-^5-C,)ASSUME Cf=.6
SSS"
EQUALITY CONSTRAINTFigure 9
64
represent barriers. The systematic reduction of the value
of the parameter "r" and the solution of the associated
modified objective functions, under suitable conditions,
will result in a sequence of minimums approaching the
solution of the original problem.
mm. P(x.r) = X'(r)
UM. X'(r) -- X"*
LlM. f LX'C03 = flt'l - Vy- -* o
VvH^RF >^' IS TmF «-PTia-\4C SCLUTto/V TO T^F ^oBi-EM.
12The suitable conditions are as follows:
(1) The feasible region is non-empty.
(2) fo^ a™ $fc) , J- >,*, ••. »i are convex and
continuous and ^jC*"), j - m-n
, m-vz., m+r
are linear function.
(3) "or some constant K , "the set £x| f<J) - K;
is bounded. (This prevents a "minimum
at infinity")
(4) P($T,r) is strictly convex for all r> ° *
65
The objective surface of interest is not necessarily
convex. This means that the results of the technique may
be local optimums as opposed to a global solution. It must
be emphasized that there is no guarantee of finding the
problem solution in a single iteration. Additional runs
with various starting positions would be necessary so that
the characteristics of the surface could be fully explored.
Only then would confidence in a single solution be justified.
In this thesis, the application of the technique to a non-
convex surface will be successfully demonstrated.
There are a variety of ways to implement the SUMT
method. The one utilized here can be described as follows.
Given a starting point, the method determines if the point
is feasible. If not, the technique is applied to find such
a point by using an objective function in the first phase
which measures the degree of non-feasibility. After a
feasible point is found, the value of the modified objec-
tive function P(x,r) the first, and the second derivatives
with respect to the decision variables are determined at
that point. The direction for the next move is calculated
using the Newton-Raphson Method. If it is not possible to
determine the inverse of the Hessian Matrix (See I age 69),
the matrix of second partials is perturbed and a move is
determined when the matrix inverse is able to be calculated.
This results in an "Crthoginal Move" as identified in the
66
program. Once given the direction of the move, the Golden
Section Search is employed to find an improved point in the
move direction. This process is continued until the mini-
mum of the program is found. This completes the first sub-
program. Next the value of "r" is reduced and the process
is repeated. This continues until the sequence of solutions
converges. The result is the solution of the original prob-
lem with constraints.
In the next sections, the Newton-Raphson Method and
Golden Section Search is discussed in more detail.
7.2.2 Newton Raohson Method Ref [52]
This method is used to identify the move vector. It is
an indirect method for solving simultaneous non-linear equa-
tions. It utilizes the necessary conditbn for a point x
to minimize a function Y(x). All the partial derivatives
must disappear at that point.
yj(*Vo }= '.*. --.*
The Newton-Raphson Method then solves the system of
equations by using the derivative to estimate the functional
value in the neighborhood of a point. This is done by per-
forming for each equation a Taylor Series expansion of
\\i) about i . If the higher order terms are ignored,
the following equations are obtained.
67
The determination of x= K+I requires the solution of
these simultaneous equations. If we define the Hessian Ma-
trix of second partial derivatives}
H(xR) 5 HK ^
Y* Y",11
HiY,
Y'
v' V" "- v"'hi '*« Inn
WHERE
THEN;
XK~ = X
k
-H;''(vY^))T
WHfRt H K H k- 1 , THF /-C^MTiTV MATRIX
68
For the determination of the move vector, we are inter-
ested in the direction along which to search for a better
solution. The direction vector is defined by -j-j. (vYCT 1
^)
for each step. The next step involves calculating the dis-
tance to move. The procedure is then repeated until the
functional values of ^(x 1"') become small. This process may
not converge to a unique solution as seen by the graphic
example given by Wilde and Beightler 1 3 in Figure 10. Assu-
ming the system of equations has only one member, then this
curve could represent the functional value of an equation.
The roots or values of the independent variable X for which
the function goes to zero is represented by the intersection
of the curve and the X axis. In this case, there would be
two possible solutions at points a & c. Depending on the
starting position for the Newton-Raphson Method, the con-
vergence to a root (solution) takes on different character-
istics. The zones of definite, possible, or non-convergence
are identified. The program using this technique identi-
fies the non-convergence condition when it occurs.
7.2.3 Golden Section Search Ref [52]
The Golden Section Search is a method for determining
the optimum of an objective function by successfully elimi-
nating regions for investigation. This method is used to
search along the direction determined by the Newton-Raphson
Method to find the best solution. This new solution
69
QWooKOh
o
I
oCM
0)
0)
PS
•HCl
70
point is then used as the starting point for the next itera-
tion in the minimization of the objective. This method was
originally designed to search a set interval. The SUMT pro-
gram determines this interval in each case by searching
along the vector until a functional value larger than the
initial one is found. This defines the search interval.
The upper bound f^ is determined by looking at successive
points until a larger value than the initial one is found.
The distance between successive points is taken as Ou. .
e; t ^ biS)L
L^O
then
h • f (*° + e« s ) - fo)
where 0^ is defined with the smallest non-
negative integer which satisfies the above
equation and S is the unit vector in the
move direction.
SEARCH INTERVAL
Pi
e*tt
1 1
<.
X D "\
Iaj rriAup£>l«T uppee
Bou/o*
"Figure 11
71
After the interval is defined, the search proceeds to
determine the optimum value. This is accomplished by divi-
ding the intervals into two parts and looking at the deri-
vative at the intermediate position. This would indicate
in which section the optimum v/ould most likely occur. The
process v/ould continue until the optimum is found. The
method which minimizes the number of iterations without
additional information can be shown to be a method of
partition which divides the remaining interval into sections
of the ratio t (1 .618033989) . This technique converges to
a unique solution provided the objective function is strictly14
unimodal as defined by Wilde and Beightler.
IF *, < X^ < *
THENy. < Yt < y*
AS, IP X* < X, <Xe
TH-FM y* > y, >y*
y
(comowe
)
(CO-UTIMUOUS} (ATOiTftMX)
'igure 12 UNHIODAL FUNCTIONS
72
7.3 SUNT COMPUTER PROGRAM
The optimization technique previously described has
been programmed by the Research Analysis Corporation as out-
lined in Reference 16 . This program requires that the user
provide four subroutines. These include first a subroutine
that reads in values as needed by the user in the other
supplied subroutines; secondly, a subroutine which defines
the value of the objective function and constraint func-
tions; thirdly, a subroutine which determines the partial
derivatives, and finally a subroutine which provides the
second partial derivatives of the objective and constant
functions.
The program was written with the capability of linear
interpolating for the required first and second derivatives.
This required that the objective function be developed from
the design model. Such a routine would provide the required
objective value for any value of the input variables. This
routine thus describes the objective surface upon which the
optimization technique v/ould search and is used in the in-
terpolation of derivatives.
The development of any objective routine must insure
that for each combination of the input variables, there is
defined only a single objective value. The program used
defines several surfaces, one for each set of input para-
meters. The tabular .inputs for powering calculations were
73
easily handled in this method. Simplified expressions for
these would lead to the use of closed form expressions which
could then be handled in other optimization techniques, one
of which would be geometric programming as used in Refer-
ence 10. The model developed in the next chapter attempts
to incorporate sufficient detail during a preliminary de-
sign stage so that the full capability of the STMT optimiza-
tion technique can be explored.
The program requires the selection of an initial
starting point and various control parameters. The author's
experience with these and other features are covered in the
concluding chapter. The reader is directed to the user's
manual, Reference 4-3. A complete explanation of this appli-
cation of SUI.iT with input, set-up, and a sample run is
covered in the Appendix.
7^
CHAPTER VIII.
DEFINITION OF THE OBJECTIVE SURFACE
8. 1 General
The strength of the search technique depends upon the
explicit nature of the objective surface. The selection of
the decision variables and design relationships has focused
on the need to determine an explicit, single valued objec-
tive as a function of the decision variables. The general
application of an optimization technique as described ear-
lier in this paper requires the determination of such a sur-
face. The actual surface defined is intended to be repre-
sentative of an actual decision, however, the main interest
here is in obtaining a model with which to test the optimi-
zation technique.
In this chapter, the containership design model which
is used to determine the objective surface will be described.
The actual relationships and other data used has been com-
piled in the Appendix. The methodology used to construct
this model may assist in the understanding of its final form.
The first step involved defining a tentative set of
variables. The decision variables introduced in Chapter V
represent the primary, independent variables chosen. It
would be possible to define the surface in terms of only
these variables, but the comnlexity of the expressions would'
75
lend the model awkward. Instead of following the usual pro-
cedure of Introducing these new variables which are depen-
dent upon the primary variables and then structuring the
objective function in terms of these secondary variables, a
more convenient method was used. This also helped to mini-
mize the number of secondary variables defined. The trans-
formation defining secondary variables were viewed as "black
boxes" or subproblems. Often explicit relationships between
the output and inputs were available. At other times, the
relationships were given in terms of tables or graphs.
The construction of the model started at the end where
the output objective was desired. Using the subproblem
technique, the model was built up from the objective end.
This systems approach facilitated the model construction.
As subproblems were defined, their inputs became outputs of
the next generation of subproblems. The goal in defining
the subprograms was to determine the inputs necessary and
the relationships required to obtain a simple and single
valued relationship with the required output. It was found
efficient to make extra subproblems whenever the relation-
ships between the variables could not be expressed in a
simple, single, closed form algebraic expression. This
would provide the definition of new variables. Another ad-
vantage of proceeding in this manner would be the capability
of having several groups working simultaneously on the
76
model after the first few steps. The assignment of subprob-
lerns should prove to be manageable in a real design effort.
The following black box exemplifies the subproblem tech-
nique.
NPUTSMODEL
t
APW=A-Zwi
i=l
w,
W? .APW
. >•
Wt ,
OUTPUTS
The process culminates when inputs to all the subroutines
are either the primary decision variables or outputs from
other subroutine. Only as the process is near completion can
the final set of decision variables be identified.
The following block diagram depicts a single design iter-
ation. The diagram represents only a small part of the total
computerized program. It shows the development of the ob-
jective surface in terms of the design variables. The output
of the program is then used in conjunction with the SUKT to
obtain new solution points as shown diagramaticly by the feed-
back loop. Evei though the Net Present Value objective was
selected, it would be a simple matter to change to some other
objective for the problem. See Appendix A for definitions.
The relationships that are used in the black boxes can be
found in Appendix E by their assigned number. The program was
designed so that the user could substitute other relationships.
77
o-\
u
I 1 1 l J oj i
•
!
I_J CD h- Q O >
78
®o
o —
•
<u.tr3 H(f> cr
<TUJ O>V-oUJ—>COO
3u.
P.
vn
a>
u3W>•Hfx,
o o 80
I
cc > u_L_ CL crCC 2 o
-?-
X>' occCLno <
Q.
i
H-UJ
C9 Z) OCO ^
2<
\- cr^> CD
Z) oCO
q_
i
O Ld
O COO CL
_cx»
oouj
LJ UJ
Li_ -^
u
H
<
81
There are three blocks in the flow graph that require exten-
sive calculations and additional explanation. These are the
blocks which determine the required propulsive power, the
power plant selection, and the container configuration.
8. 2 Required Propulsive Power
Given a specific ship's form, methods have been devel-
oped to predict the required propulsive power to drive the
vessel at different speeds. The process involves the use of
model tests and correlations involving past design experience,
The best approximation requires that a separate model be
tested for each design alternative investigated. This is too
expensive a procedure to follow when there are several differ-
ent alternative geometries. Over the years, systematic stu-
dies of the resistance properties of ships have been conduc-
ted. These have resulted in several hull forms being tested
and the results compiled in working graphs. Each of these
series of tests typically limited the number of independent
variables by fixing the value of one or more shape coeffi-
cients. It should be obvious that the use of any one series
to determine the power requirement for an alternative would
be only an approximation if the geometry of the design does
not match that of the model series.
In the program developed, the Taylor Standard Series
was used. In this series, the relationship between two of
82
the decision variables is fixed. For the Taylor Standard
Series, the block coefficient is related to the prismatic
coefficient as follows:
It was found necessary to impose this as a restriction in
the mathematical model because of the strong relationship
between the block form and the revenues generated by the
design. When this constraint was not imposed, the program
would select a box shaped midship section to house the con-
tainers. The resulting changes in powering requirements
could not be calculated using the series data. Even if ano-
ther series were used instead of the Taylor Standard Series,
the program would experience similar difficulties with other
pairs of decision variables. This constraint reduced the
number of decision variables by one.
8. 3 Discrete Fower Plant Selection
This model assumes that given a required SHP, a pre-
ferred engine configuration can be identified. The problem
of discrete power plants experienced with gas turbines has
been incorporated into the program. Because the speed and
distance values remain constant for the selection, the gas
turbine engine alternatives are ordered according to their
initial cost and specific fuel consumption. An engine con-
figuration is identified by the number of gas turbines in-
stalled. In this problem the GE built L.M. 2500 is used.
As the SHP increases, there may be discontinuities83
in costs. Because the gas turbine is available only in dis-
crete sizes, there exists many situations in which the in-
stalled turbines may not be operating at maximum rated power.
The following decision rule is proposed for the selection of
the number of gas turbines for installation.
It is assumed that the initial cost of the power plant
monotonically increases with the SHP required (See Figure 21 ),
The variables cost for fuel varies proportionally to SFC for
a fixed required SHP (See Figure 22). Because of the nature
of gas turbines, their SFC decreases monotonically as the
power output is increased. It is, therefore, desirable to
install turbines that operate near full power. It is assumed
for this model that the best engine configuration is the one
that is just able to meet the SHP requirement. Any combina-
tion calling for fewer engines cannot provide the power re-
quired and is thus non-feasible. A combination that operates
extra engines will run at lighter loads and thus at a higher
SFC. The desire of minimizing initial fuel costs associated
with the power plant selection is consistant with this deci-
sion rule. This ignores the change in maintenance costs with
the variation in engine loading.
Past history has demonstrated the reliability of gas
turbines and it compares with other types of propulsion units.
Typically more units have been designed into the plant as
reserve power sources. This increases the reliability of the
84
total system at an increase in cost. This model permits the
designer to require additional standby units as desired.
8.^ Payload Configuration
There are two steps in determining the configuration of
the containers carried on board a ship, The first determines
the available space and weight available for the payload. The
second determines the loading so as to meet the weight and
stability requirements. This reduced the number of constraint
programs.
The space is determined by obtaining the maximum dimen-
sions of the available space for the containers, then divi-
ding the ships into decks. The weight available for the pay-
load is determined by incorporating Archimedes Principle. The
payload and ballast weights must equal the difference between
the displacement weight and the sum of the other weights pre-
viously determined. The program then loads each deck sequen-
tially until one of the constraints is met. The number of
containers per deck is calculated as follows. The containers
carried on decks below the waterline were treated together and
assumed to have a shape factor relating directly to the ship
block coefficient. For those containers carried above the
waterline and above the main deck, each level was considered
to have a shape factor equal to the coefficient of the water
plane area. The program assumes that the coefficient of the
85
water plane area can be expressed as a function of the pris-
matic coefficient, The shape factor is used to determine
space for containers on each level by multiplying the shape
factor by the dimensions of the cargo space.
The model test for the stability constraint uses a cal-
culation of the available weighted moment at the designed
displacement. The program starts by placing all of the
available weight as ballast in the double bottom of the ship
without regard to space limitations. This automatically in-
sures that the weight requirement is met. If this results
in a feasible solution, that is, if the non-linear stability
constraint is not violated, then small increments of weight
are removed from the ballast location and placed in the form
of containers in the cargo hold. The only change in the
weighted moment would then be due to the movement of the
weight in the form of ballast in the double bottom to a
position at some higher position that would correspond to
the position of a container. This process is continued se-
quentially until the actual full load GK is reduced to 5 per
cent of the beam or one of the restrictions is encountered
resulting from stacking the containers, "or ease of calcu-
lation, the model groups the containers. Each deck is filled
one tenth at a time. The program starts with the lowerst
possible level and fills each deck sequentially. The model
v/ill stack containers external to the main deck. The
86
designer can limit the number of levels in this configura-
tion. The sample problem assumes that the maximum number of
containers that can be stacked is six. This is consistant
with the ASA requirements for this size container. Also,
the number of levels above the main deck was limited to two.
8.5 Input Parameters
Associated with many of the subproblems shown in the
flow chart are parameters that must be provided to complete
the calculations. These constants may be supplied by the
program user. The input parameters are listed in Table k.
The adjustment of these parameters permit the designer to
approach the real design problem and to introduce the
effects of other criteria expressed by the ship owner.
The ship availability refers to the per cent of time
that the ship will be operational. The design and cost
weighting factors are provided to permit the user to modify
the equations used in the computer program.
87
PROGRAM
Table b
INPUT PARAMETERS
PARAMETER SYMBOL.....
VALUE
DESl&M PaiWMGTERS
PAOPU LS IfC COEFFlClGAJT PCEHDUHAKtCt £
Dist/Wc<? QETidGrv Ports DBPsntT> awl/iBk-itv AVAlLwaMbt^ op shahs MSMAFT
"MlN. No. of Eu(riAjeb* NsveuW(9. OF VPARF EWG-l^fS A/GXTR*
HA-/-. pAVcOAb va^~. WWHlw. PaYloAD WT. WPMIAJMAX. COa/TAIaAFW SlACKlMfr KIX)
f^TA-x. stackia/6- ABdx/F X>k. IHT)•
AVSZAGF dO/JiftwZH *JT. wcBfFecnu& COajT. LFA;&T71 ELENtrT
ewcmi/e coajt. wi-d-th £WI"DTH
SrFECPue <?<WT. "DfTTtf Et>EPTW
DouBlf Bottom H£t6Hr "OouPjUG
B/ULAbT V/eifrf+T K6-. K^rB
MAX. 5»fP Fo* Sw6<.e 6«& S|4PM
S6/q 5PtfT) F/»CT o a? Ber4 1
5PC FACTO* BeT/t£
H(SC. \A/ei(rH7 wxxMISC.. U^FlG-HT KG-. X.K6-X
E>F5I<9/«J W/t(&-<4TW6- FACTOKS
Factor fo« OwTPrr u/r. y/Wo
FACTOR FOR STFFC \ajt. wwsFACTOR FOfi. \AAc\MAJeRi Wl V/WM
* fje^A-ri^t- vacw<? fA»t>ic4T65
88?>/«0PUt-Si©/O
PROGRAM
Table 5
INPUT PARAMETERS
PARAMETER
.
SYMBOL VALUE
NAVIGATION CoUttRAiVTS
MAX. LEM6TH LE^&TM
MAX. BEAM BEAMMMAX. D«AFT BRflFTM
ECONOMY WMMETfcRS
FRPIG-HT RAT£ FRPO^T QALL F££ PcfPA-iLY "f>oAT F££ D?FprtlCt or Fufl PR|C<^
AWVUAl k>Sc<R/WC€ RATE AIRASSET Uf£ NNSALVAGh S/ALUG SV
DISCOUNT FACTOR DP' SubsW Kat& SUSIDR
p&AGJE'JT FlHANC&b PFIMTFRE5T RATt RAreCortT. Tax R^t? CTR
INV£3TMEA/T T4X CtftTMT A^TC.
COST Wer(0rHT/A'G- FACTORS
F/KTO/e Fofi OJTFil COST CCo
F7K.TOA- fox 5TteC CjO^T CCSFactor Fo/2. MAc^we*** c, £C.M
PR06KAM PARAMETERSOBj^CTlt/c 5fC£<-T(OA/ Itffo?
COMSrAAjAJT 5£ajS (Til/ ITY DFLtAC^
89
CHAPTER IX
ANALYSIS
Responding to the needs of the owner as outlined earlier,
the optimization techniques are applied to the ship design
model. The results of the investigation are presented to de-
monstrate the capabilities of the computer programs. Prior
to discussing the actual problem solution, an attempt was
made to validate the design program by comparing the program
results with three containership designs.
9. 1 Program Validation
The design program was used to develop details of three
separate preliminary containership designs. The first design
was developed by George G. Sharp, Company, during the evalua-
tion of gas turbine "-power plants. The remaining two designs
are products of the Maritime Administration CMX Project. The
designs were developed separately by Bath Iron Works and the
Newport News Shipbuilding and Dry Dock Company. The follow-
ing tables indicate the similarity in results. In each case
the design program was given the principle dimensions of the
ship. The input parameters used in each of the designs corres-
ponded to the values obtained from the respective preliminary
designs.
90
MODELTable 6
VALIDATION
VARIABLESG.G Sharp MODEL
bisPL/ictMewr JOfe^ ZoGS-'r
Length 75-3. isr*
REAM 93 <?3
DR4FT ^1.3 =0.3
DfPFH 5-S".o rs".
PtfiSMAT/c doer. .4,i_
.65"
©Lock Coff. ,5T>t ,60
VOLUMt CotP, .OO^S" OO^f
Vt^oCITY /tS". 8 2S\1
Fuel wt. Iflo jc?3r
MA-ch. wT. II 23> /I Zf
OC/TFfT WT. 1 fe.r'f /5TfeO
ST&EL WT. 9o30 d*i/i>
M.lS<L~ WT At? 3oo
Ballast wt. O /38fc
T^YLoATi WT, 15" 3 «? f '^637
fi-M |.">3 e. 1
Mo. Q-owrAi^t^S 75"' ll^\
Top? ffc>s M 3
IStLow "fee* N/\ 6
No . Sh-zift^ X 3
TPY K)A nsShF Rfq 5SS"oo b"5~6tO
CdstI 25 .5-8 ^O.tJ
Aod- 2.S"* '.'.If *
RFR NA \o.S~
CJRF MA .To
FR W A S~0.
NPy AJ/5 n.rs
1 1
1-1 Fun e*jTE>ic\ i-j erneo*
91
MODELTable 6
VALIDATION
VARIABLES
NFWPoy?i
News hottc
B^TH1 So//
no'ia
DiSPUceMw 3A2oo 3^Joo 3ll7o 311T0
Len&tH 696 6«?t 64<T &4<r
Beam I 03 /03 86 84
DRAFT a<?.J XHS 3f.S 31. J
DE"PTH 6o Go STA.8 54.7
PRISMATIC t. S4 8 5*8 .63? •439
bLoCk COEF. .S32 •S"32 .£2t .($24
VOLUM. CoSF. .0033 .0033 .DOH .OC=f-
Velocity ^3.3 A3.
3
3.0.H 2c4
Fuel wr. 33oo. 34*5" 3S~io 31i?
MACH- V/T. (((2. !2?2 MA 10732
Out Frr WT. /gS-3. /6 3o MA 3oo2
STFtL WT- ^US, 8 s? 4T MA (>& 59
HiSC. WT. *A3. 3oo HA 3oo
i5/}LL/4srwr. 367. l5rg>o ^3(,oo ° 5"°°o
PAY^o/T^ \vt. /6 0^0 I5"03g NA lo(,lo
&M -2.<f 6.^i~ MA 4.37
f\/o. CoAJT^ive/Ci i3S~o '268 <?22 ^33
TO?>S(T>f -x 3 2 3
bcccw "Deoc 7 ^ 6 6
Mo. 5rtAFTS [ 1 1 /
TPY ^4 /r-8f MA n.3«
S rt-P Rts
.
3 5~oo a 35"fo JMooo Z<t Voo
CCSTI W4 I8.1 AM 22.*
/foe M 4.1 wA ASRPR AM V.H AOA 37.93
CRF A//f.5"! WA ,14
F« AM SO WA 5"0.
MPv AM /7.t NA 4.9
2 t * 3 3
* LI«icTc*)
(J) -^,/HJ-A^T u enciw-r fox; sno/er<.-< ue7Kio-i
92
9.
2
Program Inputs
The application of the decision model to the scenario
requires several input parameters. Unless otherwise stated,
these parameters were used for each of the designs analized.
The parameters are categorized as either design, economic
or financial. The design parameters include the assumptions
necessary to determine the ship design as well as several of
the constraint values. The economic parameters cover the
various costs and revenues generated by the design. The fi-
nancial parameters relate to other economic aspects that in-
directly relate to cost by indicating the owner's preferences.
Table 18 gives the values of the coefficients used in the sam-
ple problem.
9.
3
Procedure
The application of the minimization technique requires
the identification of a starting position from which to
search the objective surface. The primary concern is to start
each search with a feasible solution to the problem. From
this point, the STMT Frogram will take over the procedure and
then locate a local optimum. Because the objective surface
is not always convex over the feasible domain, other starting
points or solutions may result in the search culminating at
different local optimums. The concern is then to start the
93
program a sufficient number of times, at different locations
so that the surface characteristics can be deduced and the
best local optimum can be taken as a solution to the prob-
lem at hand.
The procedure was to select four starting solutions,
each different, so that the total search would encompass
most of the feasible surface. The first starting point,
which is labeled Alternative 2 on the next page, represents
a modification of a design used by George G. Sharp Company.
This alternative has similar characteristics of the actual
design which is • shown as Alternative 1. The major differ-
ence is in the number of shafts in the design.
The second starting solution was chosen with a higher
displacement. Alternative 3 was used for a starting point
even though it had been an output of a previous optimization.
The third and fourth starting points, double and single
shaft arrangement for a smaller ship. They are shown as
Alternatives 5 and 7,
The remaining alternatives show the results obtained.
Not shown are two attempts to start the program at non-
feasible initial positions on the surface. This resulted
in an unsuccessful attempt by the program to find a feasi-
ble starting point. "or the nonfeasible alternatives, the
measure of effectiveness was most easily minimized by re-
ducing the size o^ the design. No revenues were generated to
94
IDENTIFICATION OF ALTERNATIVES
^ALTERNATIVE\\N
V/HRlABlFSX ©. © © ©DISPLACEMENT 30>5<i. 30,fe£9. 31,tsf. HS^lo.
Length iro. 1iO. 133,. 7fcl.
BEAM <?3. S3. <IH.I ^8.S
DRAFT 5*7.3 J1.3 J*.2 3-i.f
DEPTH 5t>. »5. 5"8. 7 yt.t
PflisM/vne Co. .61" -4«T .(,<? .ts
BLock CoeF. .5k ,st .43 • t3
Yolum. CoeF. .002.6" .002.S • oo3fe .0034
VELOCITY ^r.T as".*? ax. 8 a.3.^7
Fuet wt 4U<;.3 "7I"W.< S^bO.7. 7 dlj.l
MAC-tf. wt. lo7o.3 1 1 HI,
3
^fe^.T 1 ia?. T)
OUTFIT WT. S-330.2 5^33o.7 ^1 2.1 ."? S-^Tf./
STEEL WT. $ 7 is -7 SliS-.*! gUC 3 ?r?v
H'SC WT 'boo. 3oo. JOo. 3oo
QALLA5T WT. 23.6 IHJ-.V a.fcs'.i 3.0^M,9
?A\LOfKt> wt fS-5-J.fe 7,? <tu *» J 8(
S"«,1 v**-
&M IT.S lt,.l 4.8t 8,o<f
Ko. Cewr.4i.ve*s 5"<8 47 s ( I25-
1 (7o
ToPST>t O Z 2
BeLOuj ]>£<:* s <f 6 fe
Wo. -5H4FTS 1 a 2 Z.
Mo. Faj&iw?5 3 4- 2. +
Shp rfq. 57,231. 6r, 63m. h-jT.377. rt,j"o
CO JT 1 31.2b 31..U, M.38 '
3t.fefe
/}©G (o.fV iz..2a 9.18 IZ.il
KFR 82. ST /oo-fes" i.8.33 Y3.70
Cf^F .13 ©+.7*1 .57
FR /oo. 100. lOO, /oo.
MPY lO.H? 0" 78. OS S"Oo
Pko&rak NA. IWPuT ouTTvr/,»«,"T OmtPWT
4 (_1 imncATes NAC.rn/f value
Table 7
95
IDENTIFICATION OF ALTERNATIVES
X ALTERNATIVE
s.
VARIABLE^ ©. © © ©Displacement /5",ooo. 11,111. If.ooo, £8,38*.
LENGTH too. 4*?f. feOO. 67o.
BEAM to. 7 8.2 50. 7?.Z
DRAFT Z5.0 28.t 25\o 32.4
DEPTH HS. 45". **s. *?.«
PRISMATIC to. .bo .40 .40 .62
Block coef. .t* •53 .1-4- .57
\jOLUn. COEF. .002.4- .002fc .002.4 .0033
VELOCITY 2.0. o 20.0 2o.o 20.5"
FU?L WT. l,?5"8.-7 2,375.8 2.,?0O.f-
MACd. WT. 843. t ssr.j ?To.8
OUTFIT WT, 2.,13H.3 3, fos. i 3.<iHt,.S
STEEL Wr 5>M>.*t i.cni.t 6,H"2S".o
Mist. WT 3oo. 3oo. 30O.D
b/ALLAsr wr. 28/7 1.4 2, Uv.^
P/VfLo/TD WT 3,tl>8.3 ?, 65-?.f> /Z, Zi^.U
• GrM IHS 5". 4 ff.f 6
K|0. CONT/(W#S 2.IO 5gr 74 C?
LEV/. ToPSi"De 1 2
Lev. Bev*^ £>fck 3 5" rMo. SMAFT3 2 £ 1 i
Mo. FajG-I^es L 2. Z* 2*
Sh? «cq. '3. W). '4,?/7 2/jOoo.
COST 4. lo.o x2 2.oZ 2H.yi
AOt S.Z 5". Co 4.5-r
RFRCRFFR too. loo loo. loo.
WPV <E> //.'Ti- © 21. 9
PRofcM^ \uVuT ourPjr lAJ-puT G urfpuT
* USEP> Fo«cet> £xtRa FAjbiA/e For Reci/qsiciTY.
Table 7 (cont.
)
96
counteract this tendency. Suggestions for future modifica-
tions are covered in the concluding chapter.
9.4 SUKT Trajectories
The following tables show the trajectories followed
during the search by the SUKT program. The starting point
and program optimum alternatives are given in terms of the
decision variables. The intermediate solutions are shown by
the incremental differences resulting in the changes between
successive steps. The tables also indicate which constraints
are constraining the solutions. These intermediate solutions
represent the solution for each of the subproblems associated
with the successively decreasing value of the program para-
meter 'r'
.
Most of the improvements in the objective seem to occur
in the first few iterations. This indicates that the process
could be streamlined by imposing looser convergence criteria.
This would permit the program to terminate its search earlier.
It would not be necessary for the penalty terms introduced
in the modified problem to be diminished by an even further
reduction in the parameter *r*. The execution times for the
optimization procedure are given for each of the problems.
The comparison between results is not possible here. The
differences in the objective function result from various
freight rates used. The final table of comparisons account
97
SOLUTION TRAJECTORY /LTERNATIVE^^^
DESIGN
VARIABLESSTARTINGPOINT
CHANGSUB
1
1 IN
PROBLE2*
MLUEM NO.
3
IN
4
FINALPOSITION
Displacement 50^57, f e.iio. -s. 39,«H|
LENGTH ISO. -if. -8. ^ZJ.
BEAM 93. +i. fr.l 9^.i
DRAFT 2-7.3 +*. + .9 32}
DEPTH ss\ +3. -f .1 5-8.1
PRISM. CoFF. • fcS" •+.0T — .492
VELOCITY 2?.n -2.* -.1 22.
g
CONSTRAINTVALUES
TlMe
I.OIO 12.390 If.CJ'o If.oS
FREET504RD UnKjl
STAEN&TH (L/d-^)
Max. LEng-th(9oo)
Max. Beam (ho.)
Max. draft (37)
Max. V/c (1.2)
MW. V/VT (•?)
M4k. £P (.70) Tlfa+CT TltrHT T 16-HT
MM- CP (48)
MAX.B/r (3V5-)
M/a/. Vr (2-W)
MAX. CV (.oefe)
M|A|. Cv (.ooi)
CB - .^25 CP TltrHT T|(r«T TlirHT
OBT£CT(VS 4
( KJPV Xio'V35-. 8 8 + 890 t ST. 129.88
*. SouxmoN c*«ve*freb at -rv,e sa>%
OP 5>/f»P«ogLf/rt 2..
(.—
)
IU^lt*T«T M% CM<l(,f
Table 8
98
SOLUTION TRAJECTORY ALTERNATIVE^-*^
DESIGN
VARIABLESSTARTINGPOINT
CHANGSUB
1
I IN
PROBLE2
y/ALUE
U NO.
3
IN
4
FINALPOSITION
Displacement 3*? 6H0. + 5 tfcO—
•» 10. *+5",3io
LENGTH "»23,o + 38.- 1u,
BEAM 9*f.| +«tt M ns
DRAFT 32.2 + i.ac— - —
33.H
DEPTH 5-«.7 + .J?4— — — sys
PRISM. CoEF. .492— — — —
,(,?2
VELOCITY 22.8 + .«?— — — 27.1
CONSTRAINTVALUES
TlMt.960 +.460 5^0 6.4^0 e.zio 8.2.7o
FREEBOARD (iFfcJ
STRENGTH ( %-^M4X. Leng-th(9oo)
Max. Beam (no.)
MAK DRAFT (37j
Max. Vsc (1.2)
MW. V/vTT (•*)
M**. CP (.70) TlOrWT TltM-T TlfrK-T TI&kT TltHT TIC7-H.-T
MW- CP (48)
M/tt.B/r (375)
M/M. B/r (*W)
MAX. cv (.oofe)
M|A/. Cv (.001)
CB - .925 CP T16-HT TlfrH-T TiOt+T TlfrWT t'Ch-t Tifrttl
OBTECTiVS *
(wpv Xio'cJ
/I2t.2 + 11. H + 0. + 0. -» 0. 131.4,
Table 9
99
SOLUTION TRAJECTORYALTERNATIVE(5>(6)
DESIGN
VARIABLESSTARTINGPOINT
CHANGSUB
1
E IN
PROBLE.
2
VALUEM NO
3
IN
4
FINALPOSITION
Displacement i5;ooo. +•7,14,0, -18fcO. + 2,t8o. -4. IZ, ***)(.
LENGTH bOO. 0. + 1, + 7°. —fc****.
BEAM fro, 4- O -1.9 + .t—
78.2
DRAFT £5. -*s\z -1.8 O —28.<<
DEPTH 1£ + + * O — H5
PRISM. CoEF, -to _ - - —.to
VELOCITY 2o.o — — - —-2o.o
CONSTRAINTVALUES
T/MC
,?fio 7.620 10. UO IZSoo /3.37o 13-770
FREEBOARD UfO Ti&mT "rifru 1
STREN&TH (L/D -^) TI&MT TlCrHT
Max. lemg-th(9oo)
Max. Beam (ho.)
Max. draft (37J
Max.v4c (\,z)
MlM. %T (-5)
MA*. CP (.70)
MlM- CP (40)
MAX.B/r (3-75-)
M/a/. Vr (2.W)
MAX- ^v (.oofe)
MlM. Cv f.001)
CB - ,9£5CP
ObTECT(V£ *
( KJPV X IO"CJ
3.5T4 +2*7.1 4 l.t + 5-.Z 4 0. "J1.H
* FR^ZOO./ton
Table 10100
SOLUTION TRAJECTORY ALTERNATIVE©"*®
DESIGN
VARIABLESSTARTINGPOINT
CHANGSUB
1
E IN
PROBLE2 *
VALUEM NO
3
IN
4
FINALPOSITION
Displacement 15, 000. + 13.38*.— 20,384-,
LENGTH bOO. +7o,—
670.
BEAM So. -i.—
79.
DRAFT IS 47,fe— 32.6
DEPTH ts 44.7—
^9.7
PRISM. CoFF. .4 -f 08*-
.68
VELOCITY 20.0 + ,5— 20.4'
CONSTRAINTVALUES
FREETi04RD (£FB»d
STPvEN&TH (L/D^l?)
MAX. LEN G-TH (9oo)
Max. Beam (no.)
Max. draft (3vJ
Max.v4t (1.2)
Ml* V/SC W
Max. CP (.70)
MlM- CP (48)
MAX. ^f ^•75')
M/a/. B/r (2A5)
MAX. CV (.oofe)
MIA/. CV (.001)
CB - ,925 CP Tlfc-*T •TIG- (41
OBTECTIV6 t
( K/PV X io"t
>)L.bS + r7.<>t + .0 5«.32
F* •*«• /ro*
iwe?«o-Bi-rM ** Table 11
(,— ) iXfciCA.'cS VO <M*V6-r
101
for these differences and presents the results based on a
freight rate of $100/ton.
9.5 Ranking the Alternatives
After conducting the individual optimization problems
with the various starting points, a comparison of results was
desired so that the best design could be identified. The
various alternatives were compared using three measures of the
economic worth of the designs. The following table gives the
Net Present Value of the design based upon $100/ton received
in revenues. Also the Capital Recovery Factor based upon
the total investment and the Required Freight Rate are listed.
The RFR depicts the rate that must be charged by the opera-
tion of the ship so that the revenues would just cover his
costs which include depreciation charges.
The matrix shows that no single ship is preferred using
all these criteria. It also shows the improvement obtained
in the measure of effectiveness using the SUMT Program. Al-
ternatives 3 and k switch position in relative ranking as the
objective is switched from NFV to CRF or RFR. The solution
to the scenario with the given assumptions would be Alterna-
tive h. Other scenarios may result in one of the other de-
signs being a solution. Each of the designs carry a different
payload. The differences in worth per ton transported is not
.so great which indicates that two smaller ships may be
102
RANKING OF ALTERNATIVES
BY VARIOUS CRITERIA
f_) |/OblcATSS fJSGAllije VALUE
Table 12
ALTERNATIVE NPV (^ o\f B KFR */T\ A- 30fo59.
\J_y L Shaft10.^8 b .13 B 82-37 5
>s3/ 2. SHAFTS (-) a (-) I0D.&5" S/Z\ A= 3964-1.& z shafts < 48.08 S ,7f 35.35 m(a) A -4-5-3/0.W 2. SHAFTS P-i'^ m .57 B 43.70 s^3J 2 5wm K-) a (-) a 1Z3.4? 7
/£\ A ^ 22i
77 '- b -37 H 47?£ Bfj\ A = \5,ooo.
Viy J_ Shaft (-) a (-) a — D(q\ A -28,38*.^—/ 1 Shaft
27.10 b .^8 E 4-2.80 1]
103
preferred over one larger ship. The increased flexibility-
available to the owner may make a number of small ships an
attractive proposition.
9.6 Discontinuities
During the design of the various alternatives, discon-
tinuities were observed in the objective surface. These were
the direct result of the discrete characteristics of the en-
gine and installed cargo. The following graphs show the
effects of the discrete factors in the design and additionally
show the performance of the search routine in the neighborhood
of the discontinuity. In order to demonstrate these factors,
the ship hull design associated with design Alternative k
was held constant as the design speed was varied from nine-
teen to twenty-seven knots. This provided a profile of the
objective surface along a single dimension. A similar graph
is also developed for Alternative Number 3.
The effects of the discrete power plants are evident as
the speed is increased. The graphs note the speeds at which
additional engines are required. The cost function reflects
the additional costs involved in the transition. In the graph
for Alternative b, the quantum drop in the objective function
just before twenty-four knots is due to the cargo capacity
lost when the engine box was enlarged. The same integer num-
ber of containers could no longer fit in the length available
104
OBJECTIVE SURFACE PROFILE
FOR DESIGN ALTERNATIVE FOUR
SHIPGEOMETRY
A 4-5,3/0. to«5
L 761.'
B 98.4'
T 33.4-'
D 59-1='
CP • 6?
2 SHAFTSFR^200./ T0Ay
w38-
37-
"b 36-
2S 35-
8 »H<
31-
30
6?
21 .o
(2) e^&i/ves
Q"
NPV
C0ST1o —
- H .
C 3
.£>
20 21 2e
.72 X .80
2AO—I
3f.l
(4) EN6-INE5
3-DQ- P
•6!.©-©-
23 2« 25"
.63 .87 .11
«H.S V.4 ^n
"(6)*
-130
-120,
lt-0
UO
-100
90
O
X
>
7 VBUOC (KT5)
% x its *v SHP (% t03
J
5TACKI»J<f--»f«— WEI6HT-
* cost of ballatt wt. KEMoweV
Figure 17105
OBJECTIVE SURFACE PROFILE
FOR DESIGN ALTERNATIVE THREE
SHIPGEOMETRY
A 39,64-/. tovs
L 723.'
B 94.1'
T 3Z.Z'
D 58.7'
CP .6?
2 SHAFTS
FR = Szoo./TOtJ
NPVIT Q"
oX
Hc/)
oo
fe) £WC.IME5
C0ST1-to G>-
2° 2l
.7^ •78
2i.f
a-
D-
22—
r
23
.82 86
-(4) EN&INE5
— ©'
-1
—
24- Z5
.M .13
to
-.©-
24
.*?7
2C.4- J2.3
STABILITYLmnrt
STABILITY
VTAC.Kl'Jt-
STABILITY
STACK !»*
'"WFldHf*
rai vta lOl.o
i.lMtT7T>
t cost of ballast wt, senovet>.
Figure 18
106
cp
£7
W
oX
>CL
Veloc (KTS)
illA
L
6HP (x lo3 )
and this resulted in a loss of about fifty containers. As
stated earlier, the length of the engine box was modeled
solely as a function of the required shaft horsepower. If
the engine box were modeled more accurately, the loss of cargo
may have occured at the same time that additional engines
were added. The graph of Alternative Number 3 shows a simi-
lar drop in the value of the objective function. This is
again associated with the engine box size. At the bottom of
each graph, the tight constraints are listed for the various
design speeds.
9.7 Sensitivity
The final segment of the analysis is concerned with
determining the sensitivity of the design solutions and the
associated objective values. Only a limited effort was pos-
sible in this area, but this section should help to re-enforce
confidence in the results of the previous sections. The re-
sults of this step will point out the critical assumptions
made in the design model and where additional effort may
prove rewarding.
In order to obtain a sensitivity analysis in a general
search routine, it is required that perturbations be made in
the values of the decision variables and the input parameters.
Here we will study the sensitivity of the design Alternative
/*• due to variations in discount factor, propulsion coefficient,
10?
midships coefficient, endurance, freight rate and the number
of extra engines that may be required for increased relia-
bility.
The procedure was to start with the best alternative
available, and determine the affect of changing one factor
at a time. The changes on the worth of Alternative k are
noted for each perturbation. In Column B of the table, the
NFV objective resulting from the change is recorded. This
design was used as a starting point for the SUKT Program.
Column C indicates the worth of the design resulting from
the optimization, A qualitative indication of the overall
changes are also given.
The most critical factor in the design was the assumed
value of the discount factor. A variation in this input
parameter caused the greatest change in the design. There
are several other elements that deserve explanation.
The sensitivity of the design to the assumption of P.C. may
be more important than indicated by a quick look at the fig-
ures. The reduction in the F.C. resulted in a design with a
higher block coefficient. This would cause an even further
decrease in the F.C. for the design. The other interesting
effects are noted on the table. The design incorporates
a severe cost on the design for ballast. When the ballast
is replaced by fuel, there is a sufficient increase in the
NFV of the design. This appears twice in the analysis.
108
Table 13
SENSITIVITY ANALYSIS
P
VALUFDF
p=p,
YflLUt-
or
P-P,AP
OBJECTIVE VALUE
B-CB-C
EFFECT ONDESI6-N
ReF£»>t»JCE"t> FWH
ASOLUTION
V P,
BSolution
Vw/ JJ,
c
«// P*
DF .20 .15 -.05 47.2 62.4 67.3 -^ ft. SHi?
DF J5T .10 -.05" 67.
3
87.1 78.3 -7.1 184.Scowe f<
SH-ip
PC ,fc5" .625 -025" 47.2 43-1 43, fc- ,5" 10.
SultrHTLYi+ife-H-cve
Block coep
Ol*'
.725" .950 t025~ 47.2 47 2 4fi" -Z..o -80.
SLLtrHTLY
SH-F?
wo.
2 4" *2 472 46.-53 44.37 -.04 -.OZ.
SLIGHTLYUO aJ fe c- ^
Ski?
£MT5l/7^t*Xr IZ.,SoO lb, 000 +2.500 47, a f5~,0 WS* -4.5- —
FR WO. ?o. -10 47 2. 38.9 59.0 -.1 .01
SU6-WTLV
1
.
Change which could cause a further decrease in FC2. Effect on powering not assessed3. Ballast replaced by fuelh
.
Two engines as on line spares5. Ballast replaced by fuel
109
CHAFTER X
CONCLUSIONS AND RECOMMENDATIONS
10.1 General
As the first iteration of the design procedure is cul-
minated for the sample problem, it is important to put the
discussion in context with the overall design philosophy.
The preliminary design was pursued in this problem with a
broader interpretation of the owner's requirements as was
made possible by the quantification of the owner's prefer-
ences. It was found that this approach resulted in a
streamlining of the design step which permitted a larger
range of alternatives to be evaluated. The results from the
sample problem would be presented. In the proposed design
process in Figure U-, the next step would involve an evalua-
tion of results of each system design by the owner. This
would be followed by a possible decision to iterate in the
design of the ship with modified criteria.
The ourput of the design step should provide useful in-
formation of the owner so that future iterations will con-
verge faster to the design selected. There will be many
occasions where the owner will want to have results of a
design based on the traditional requirements of speed and
payload capacity. This approach used should prove adapt-
able. The information on sensitivity would be obtained.
110
10.2 Optimization in the Design Process
We have seen that the computational efficiency of the
computer has permitted extensive parametric study of the ship
design. The interaction between the problem formulation and
the solution technique has been demonstrated. The application
of the Sequential Unconstrained Minimization Technique re-
sulted in a straightforward design sequence that could be
used to evaluate many design alternatives. The ship design
model was developed to provide the information necessary
to identify the objective surface for an optimization proce-
dure. In the sample problem, the surface was generated using
the net present value for measuring the cash flows expected
over the ship's lifetime.
The thesis has shown that partial optimization of a
ship design is possible if the problem can be structured. It
was also observed that interaction of the designer with the
program is needed to achieve the maximum benefit from the
programs.
10.3 Experience with SUTT
The experience with the SUMT program generated several
observations releveant to the design process. The first is
that a programmed search which requires derivatives of the
surface, could be employed using linear interpolation of the
111
derivatives and remain relatively efficient. The SUKT Pro-
gram used such a linear interpolation scheme to determine
the partial derivatives of the objective surface. This
efficiency was improved by deriving the design constraints
so that interpolation of their derivatives would not be
necessary. For those constraints which were not expressed
in closed form, they were handled internal to the design
model by insuring that the ship designs would satisfy these
constraints. The non-linear stability constraint was handled
this way because the change in stability could not be deter-
mined from the decision variables along, but must include
the effect of the container loading. The design model was
constructed to insure that all alternatives would meet the
stability constraint by controling the loading of containers.
A second observation dealing with data restrictions
should be imposed external to the design model. When they
were introduced internally, it was difficult to assign
appropriate penalties within the design model to keep the
design feasible. No matter what reasonable level of pen-
alty was assigned, the program would find alternatives that
did not satisfy these constraints.
The imposition of the equality constraints was not
found to be practical in this design application because
none of the intermediate designs were feasible. It was only
after the parameter "r" was sufficiently small that the
112
equality constraints imposed sufficient penalty to the modi-
fied objective function. It was preferred that the equality
be replaced by only a single one way constraint. If two
inequalities were imposed, the associated penalty in the ob-
jective function would be of infinite value and as such would
obscure the real driving factors in the problem. This
approach was used for the equality constraint of the block
coefficient in the sample problem. The nature of the prob-
lem caused the program to design ship alternatives with as
large a block coefficient as possible. The equality was
replaced by an upper bound.
There are two other observations on the application of
the program which should benefit future users. The first
deals with starting points for the program and the second
with the selection of the value of the parameter "r". With
the regard to the first, in the present form of the SUI-T
Program, it is recommended to start the search with a
feasible design. The program is capable of finding its own
feasible starting solution, however, the barrier penalty
technique used in the optimization program requires a sepa-
rate method for finding a feasible starting solution and
attempts to employ its use has resulted in unreasonable
alternatives. A feasible starting solution would prevent
the excessive costs experienced when this feature was tried.
Finally, it is recommended that the selected value for
"r" and for the associated reduction ratio which determines
113
the successive values of "r" be determined as follows. Look-
ing first at the modified objective function, it is impor-
tant to have the values of the constraint and objective
functions of the same magnitude during the first iteration.
This will insure that the program encounters both the affects
of the objective surface and the constraint penalties in the
initial phases of its search. If the value of the constraint
were larger than that of the objective function, the first
several iterations would produce solutions that did not ob-
serve the contour of the objective surface. If on the other
hand, the objective value were larger, the program may sat-
isfy the given convergence criteria prior to reaching a
local optimum on the surface.
In the sample problem this sizing was accomplished in
two ways. First, the objective value was expressed in
millions of dollars. This resulted in the objective value
being of the same order of magnitude as most of the penalty
values that were possible from the constraints. For this
reason, the value of "r" was set equal to one. Other com-
binations have worked as well. The selected value of the
reduction ratio depends on the convergence of the sequence
of subprogram solutions. Most of the improvements in the
sample problem optimizations were made in the first few
iterations. The remaining iterations were to decrease the
11^
penalty values so that the convergence criteria would be
satisfied. I would recommend using a higher ratio than
twenty which was used in the sample problem.
10. ^J- Areas for Additional Study
future applications of the design program could pro-
vide even more realistic results if the following improve-
ments were incorporated. They were not included in this
program due to the limited resources available. The follow-
ing comments cover most of the areas that could use addi-
tional effort.
Propulsive Coefficient
The sensitivity analysis showed that the solution is
sensitive to variations in the propulsive coefficient. As
the design alternatives develop blunt sterns, the efficiency
of the propulsor will decrease. The ship propeller inter-
action should be included. The determination of the actual
propeller would also prove helpful. One approach to deter-
mining propeller fit is covered in Reference ^5 .
Other Constraints
Additional constraints commonly handled, such as the
requirements on the period of roll should be included. This
would require only a slight change in the program. Also
the volume requirements were used only to determine feasible
container configurations. The addition to the model of
115
restrictions due to fuel and ballast volumes should be de-
veloped internal to the model. The volume requirements of
the engineering space should be more carefully defined, es-
pecially since the length of this compartment is used to cal-
culate the length available for containers.
Velocity in a Seaway
The additional resistance experienced in the seaway
causes a loss of speed. The program uses a simplified model
to predict this loss. A subprogram would prove useful in
determining the value more accurately.
Interaction with Terminal
The program presently uses a very simplified inter-
action measure. The model could be expanded for a specific
situation to determine the actual turnaround times and
charges. This would require information on the container
handling capabilities, both in terms of speed of operation
but also the inventory capacity.
Backhaul
Any actual study should investigate backhaul opportu-
nities and incorporate their effects.
Maintenance
Maintenance was assumed to impose an annual dollar
cost. If an overhaul policy is known, the cash flows should
be adjusted. The Net Present Value objective function is
the only measure which could handle the non-uniform cash flow.
116
Seakeeping
An effort should be made to determine the seakeeping
qualities of the design. At the least, limits of perform-
ance could be included in the constraints. One such limit
would be the deck wetness criteria of Reference 39.
Powering Prediction
This program used the Taylor Standard Series to predict
ship resistance. Other predictors such as the Series 60
could be easily employed. Of primary concern is the power-
ing predictions for designs with large block coefficients.
Another alteration would provide calculation of resistance
for the different ballast conditions.
10.5 Applications
The design model was developed for the preliminary de-
sign of a containership. There are other ship types which
could be studies with the existing program. For example, a
LASH or Barge Ship could be considered, also bulk carriers or
oil carriers could be designed. This would require an ad-
justment in the input parameters describing the size and
weights of the containers. The barge is a large container
and the analogy is obvious. The bulk carrier on the other
hand is loaded in a continuous way. By loading small
blocks of oil, the program could approximate the cargo
117
carried.
Another application of the program would call for its
use to test the effects of governmental policies on the
nation's merchant fleet composition. The effect of subsi-
dies has the effect of changing the economic preferences
of ship owner's for different ships. The model could show
the trends in the fleet population that were due to these
policies and regulations. Of more immediate concern is the
effect of oil prices on the design.
The last suggested application involves using the
programs as a teaching aid in a graduate course in ship
design. The following characteristics make this applica-
tion attractive. First, the student is required to provide
a feasible starting point for the design. This could be the
result of a hand calculation and as such provides an oppor-
tunity to understand the design methods. Secondly, the
design program could then be used to generate the data to
check the student's design accuracy for his selection of deci-
sion variables. Finally, the optimization program would pro-
vide other design alternatives so that the student could be
exposed to a higher level in the design process. As such,
this would provide an interactive tool to permit a more
complete design effort in the more advanced design courses.
118
1. Ref
.
16
2. Ref
.
11
3. Ref. 20
4. Ref. 38
5. Ref. 22
6. Ref. 29
7. Ref. 35
8. Ref. 5
9. Ref. 8
10. Ref. 3?
n. Ref. 42
12. Ref. 42
13. Ref. 52
14. Ref. 52
FOOTNOTES
P. 1-5
P. 34
P. 17
p. 46-50
P. 7
P. 3
P. 55
P. 219
119
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3. , "Measures of Merit for Ship Design," MarineTechnology, October, 1970. pp. 465-4-76.
4. . "Engineering Economy in Tanker Design,
"
S.N.A.M.E. Transactions, Vol. 65, 1957, pp. 775-838.
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11. R. J. Duff in and E. I. Peterson and C. Zener,Geometric Programming -
-
Theory and Application ,
John Wiley and Sons, Inc., New York, New York, 1967
12. S. Erichsen, "Optimum Capacity of Ships and PortTerminals, "University of Michigan, Department ofNava3 Architecture and Marine Engineering, Ann Arbor,Michigan, Report No. 123, April, 1971.
120
13. "Evaluation of Steam and Gas Turbine Fower Plants inContainership Ships, " George G. Sharp Company,New York, N. Y. , September, 1969.
Ik. J. H. Evans and Dan Khoushy, "Optimized Design ofMidship Section Structure,: S.N.A.M.E. Trans-actions, Vol. 71, 1963, pp. 144,
15. J. L. Everett, A. C. Hax, V. A. Lewinson, "Optimi-zation of a "fleet of large Tankers and 3ulkers:A linear Programming Approach, "Marine Technology,October, 1972.
16. A. V. ^iacco and G. P. Mac Cormic, Nonlinear Program-mine; Unconstrained Minimization Techniques, JohnWiley and Sons, Inc., New York, N.Y., 1970.
17. wranz A. F. ^risch, "Notes on Freight Analvsis",April, 1968.
18. J. S, Folkers, "Preliminary Fleet Design by Geo-metric Programming, 'International ShipbuildingProgress, October, 1969, PP« 308-326.
19. Gas Turbine Propulsion Machinery , Frait and WhitenyAircraft, June, 19-9.
20. Morton Gertler, "A Preanalysis of the Original Te stData for the Taylor Standard Series," DT.-"3
Report , No. 806, March 1954-.
21. Jan R. Getz, S. Erichsen, E. Heirung, "Design ofa Cargo liner in Light of the Development of aGeneral Cargo Transportation," Paper No. 6,Presented to the S.N.A.M.E. Annual Meeting,1968.
22. J. R. Hancock, "An Economic Planning Model of anIntegrated Ship, Terminal and Container System",M.I.T. Thesis, June, 1972.
23. Handbook of labor Statistics , U. S. Department ofLabor, 3ureau of labor statistics , U. S. Govern-ment Printing Office, i960 and 1969.
24-. R. I. Harrington, "Economic Considerations in Ship-board Design Tradeoff Studies: Marine Tech-nology, April, 1969.
121
25. J. J. Henry, "Containerships", S.N.A.M.E. Transactions,Vol. ?4, 1966, pp. 305-320.
26. W. C. Hewitt, "Ship Power Plant Selection, M.I.T.Thesis, June, 1972.
9 7. E. L. Holmboe, J. M, Sheehan, A. D. Evans, "A Guideto Assess the Operational Implications of NewShip Design Concepts", Operations Research TechnicalReport No. 667, Silver Sorings, Maryland, June 11,1971.
28. E. C. House, B. J. Wooden, "Numberical Methods and theOptimization Problems in Engineering Systems",S.N.A.M.E. New England Section Paper, 1959.
29. R. P. Johnson and H, F. Rumble, "Weight, Cost and DesignCharacteristics of Tankers and Dry Cargo Ships",Marine Technology, April 1965, pp. 148-173.
30. D. Kavlie, J, Kowalik, S, Lund, and J. Moe, "DesignOptimization Using a General Nonlinear ProgrammingMethod". European Shipbuilding, Vol 15, 19&5.
31. R. L, Keeney, "Multidimensional Utility Functions:Theory, Assessment, and Application", TechnicalReport No. ^3, M.I.T. O.R. Center, October, 1969.
32. LM-2500 Marine Gas Tubrine Installation Design Hand-book, General Electirc, Marine Industrial Department,Cincinnati, Ohio, MID-IDM-2500-2, April, 1970.
33. T. Lamb, "A Ship Design Procedure", Marine Technology,October, 1969.
3^. T. A. Louakis, "Computer Aided Prediction of SeakeepingPerformance in Ship Design", M.I.T. Report No. 70-3,Department of Naval Architecture and Marine Engineer-ing, August 1970.
35. P. Mandel, C, Chryssostiomidis, "A Design Methodologyfor Ship and Other Complex Systems", Royal Societyof London, Transactions, A. 273, 1972, pp. 85-98.
36. P. Mandel, "An Evaluation of General Cargo Ship Weightand Cost Data for Use in Ship System Studies",Cambridge, Mass. , June, 1967
.
37. . M.I.T. Subject 13. ;+1 Lecture Notes, 1973.
122
38. P- Mandel, "Some Hydrodynamic Aspects of AppendateDesign", S.N.A.M.E. Transactions, Vol. 61, 1953,pp. 464-515.
39. P. Mandel, R. Leopold, "Optimization Methods Appliedto Ship Design", S.N.A.M.E. Transactions, Vol. 74,1966.
40. M. D. Mesarovic, D. Macko, Y. Takah^.ra, Theory ofHierarchial , Multilevel Systems , Academic Press,New York, N. Y. , 1970.
41. R. D. Murphy, D. J. Sabat and R. J. Taylor, "leastCost Ship Characteristics by Computer Techniques",Marine Technology, April, 19-5, pp. 174-202.
42. D. S. Miller, "The Economics of the ContainershipSubsystem", University of Michigan Faper No. 033,October, 1968.
43. W. C. Mylander, R. I. Holmes, G. F. McCormick,"A Guide to SUMT-Version 4: The computer ProgramImplementing the Sequential Unconstrained Minimi-zation Technique for Nonlinear Programming", ResearchAnalysis Corporation, RAC-P-63, McLean, Va. , October,1972.
44. H. Nowacki, F. Brusis, F. M. Swift, "Tanker Prelimi-nary Design — An Optimization Problem with Con-straints", S.N.A.M.E. Annual Meeting Faper No. 9,November, 1970.
45. R. I. Newton, "Comouter Aided Marine Power PlantSelection", M.I.T. Thesis, Kay, 1973.
46. E. G. Pollack, E. G. Frankel, "Aspects of Ship Opera-tion Effectiveness", International ShipbuildingProgress, May, 19^7.
47. E. G. Pollack, G. N. Novaes, E. G. Prankel, "On theOptimization and Integration of Shipping Ventures",International Shipbuilding Progress, July, 1965.
48. W. R. Porter, Subject 13.43 Lecture Notes, 1972.
49. J. W. Schmidt, "Preliminary Ship Design with the Aidof a Comouter", S.N.A.M.E. New England SectionPaper, May, 1964.
123
50. R. J. Scott, "Containership Design", S.N.A.M.E., GreatLakes Section Paper, 1962.
51. G. R. Snaith, M, N, Farker, "Ship Design with ComputerAids", Transactions of the North East Coast Insti-tution of Engineers and Shipbuilders, Vol. 88,1972, pp. 151-172.
52. G. E. Wanddahl, "The External Penalty Function Optimi-zation Technique and its Application to Ship Design",University of Michigan Dept. of NA and ME. RenortNo. 129, June, 1972.
53. J. v. Weston and E. F, Brigham, Managerial Finance .
Holt, Rinehart, and Winstor, 3rd ed., New York, N. Y.1969.
5^-. D. J. Wilde and Charles S. Beightler, Foundations ofOptimization , Prentice-Hall, Inc., 1967.
12^
XIII. APPENDICES
125
Appendix A
VARIABLE DEFINITIONS
126
Table Ik
DEFINITION OP TERMSftD^Tv - AMNHAL A WIN Ami) 41 SC' W ~RAT I M!V Z OTS\i :. - \ \ i.uw i nt.Jkanj.. l ;o..i
AT 5 - <* J \MIA! l MSIJP lyM"? -Mil*ai. 3ha r w r
*_-"*'
^
l a JF. ini-'-ita c)-"
-iic T F\ir
AN'NJ ' - MvNH r R O r fiW'llN-'i l\JfS1'A|_ED I \) TH-_ SHI 3
AN'J V - M-1 PRESENT VA_J =
ao: = ammual o j£watimij :osrsAPT = AM JIJAL POHT CO iT
APV = AVAILABLE PAVI. )A0 WEI3HTAVAI.i - SHIP AVAILA'UI. 1 T f
ftV'M = AVAILABLE WEIGHTED M)M-:NT FOT ^A y_ JAO ANJ ^Ai'^ST3.D3 = ^EAM-DPA'T RATIO=*F = rrr ECTIvE HFAM 0" TH r
i S°ACE ON THE SHIP ~3* r')NTAlN-RS3FA^ = SHIP REAM3FA^ = "UXIM.UM BEAM3M = ^TACFNWIC HF1CHT AlOv/E THP CENTER OF R-JOYAsiCYCASH] r TvjiriAL COST T) 0rfNlE3"
CR = SHIP RL'KK COF r ICIE^rCC = ASJNlUAL. C^EW COSTSCM r SHIP MIDSHIP S-.CTI3M COE r ICIENTCOSri : IVJITTAL HUlLOlM'i :OST 3r THF SHU 3
rnsn = :o^>r or halastCOST 1 = ~OST 0^ MACHINERYrn = :o->r or outfitCP = SHIP PRISMATIC COMMENTCRCWlO) = ? r :>lD'.lAL RESISTANCE :OEF. FOP TSS DOWFSIM3 CaLCWL^TTONCS = COST or STEELCT? = CORPORATE TAX }AT r
i
CV = SHIP VOLUMETRIC COE r ICIEvjTCW 3 = SHIP WATEHPLANt C")E~ICI~MTOR 3 = II STANCE P-ETWF- M ^0-?TS0C r - STANDARD CORRECTION -"ttCTOR ^O 3 3 E->ISTANCE CorrlcIiNJTIF = -:
r:rECTW: DEPTH Tr> S^lACE OM THEl S-tl 3 FOR C-»NT AlNE -<S
0F 3 TH = SHIP DEPTHOF = OTSCOUNT FACTOR r OP A^ 3 V C AL C J.IA T I ONOIS°.l = SHIP DISPLACFM-NTOOJR.F = HEIGHT 0^ DOUBLE BOTTOM0P~ = OAILY PORT FFFSORA r T = SHIP D9A r T
OR&-TM = MAXIMUM OPAFT• - EN")URA\)CE ^ I ST ?v JC E 1
EDE P TH = --'F.rTW; OFPT-t 0-~iA COMTAlM'RELEN3T = ELECTIVE LENGTH OF X COMT A I \)E ?'
fWlOTH r ELECTIVE VIOTh 0-"i A CONTAINERFC = rUEL CONSUMPTI JNri^AM' = "T^ANCEOr R = r REI3HT RATE C^P~,E3 " }R TRAvJS^ORT 0OLLAR~> oER T JmPA4MA = SPECIFIC GPAVlfY ")F SEA WATE 3 '
mV :- &NMISMFVieffl&* ,n*n 127
GN J
<H
<m<g=,
<gx
LFLFNGTLF W T -1
L^LP
SfPC
NIP vMOMO r
MFMGml-:
NN=>C
3f r
3F
3RICE
5AT"OM*1AK
SFZ
RU^Si J
SI 3S<svTOtpvve_o:vflo:evf_o:sVL3VOL 1
WR
wcWFWl^JGTWM
CONVERSION FACIO} ^-OMCFMT'R : ' HUOYANCY
GRAVITY 0"
graviiy )r
SPAVHY :)"
grav I I v .)-"
grav I I v ):
<TS TD r P ;
C E N T - R
cent* <
- - Ni 1 ~R
O c 3MAST V~ISHFMACHINE ?Y rf* I .?Hf
^ J T ~T T rfEI^HI
;t-*:l whisht*ISC WFT3-W
c NGTH-REAM i? A I 1 >
_t" \JG1 H-D" PTH RAT 1 I~ rrF.CTIVE LENGTH }F
^HIP l.PMfiTH
<4AX.lM.lH LKNGTH_c"NGTH F SHIP_r\JGTH O r SHIPMAXIMUM MiJf-l'-iFP
M ri S°AC r
' DN i +1 1 SHI OP COMlATNFRS
SPACiimac -m ME *«Y
P->A<l T'^KS0-"C<S )
ri CONTAI -Jrpt>
DR rONTAl^r^S
S-tTP
OF SHIP
T A < P \J J >l RYT A<FM J D AY
AMMIJAL MAINT AO PE D M *' TOST S
MlJM*fER n r COMT'kl NJf^tJ ACRDSSMAXIMUM MJMHFR 0" INTEIIOR ::C<S "
MjM^Fp ,-) c CONTAINERS Vm 3
NJ'.HH r P OF TUPRTM'S' iMSfALFO I M j-\-
M.H^P 0" CONTAINERS L0M3ITUTI NiAJ-Y3--JI00 0- INTEREST "DP LOAM AM 11 _H r E^PJ^JLSIVL COF r ICTEMT3"WT PALL FFFS p ~ 1 ^DUNO TRI*^^-(CFMT 'iNANCiO^IC r O^" FUEL IN
ANNUAL REVENUESintepesi raif )M
*4AXlMiJM -MGHTl JG
5 3£CTFIC FUEL CONSUMPTIONSHAFT HORSE P0-JE3MAXImom CONTINJ'JJS S-)P OC A S I ^r; _r 3AS TJR-iI\|E
MAXIMUM SHP AVAl_A-<L-:i r PDM ^ PO^i I „lS I ON PL A\J I
^EJJI^EO Shp 11 ->3lV-:i SHIP AT *- J>MTY ViLJCANNUAL SUPPLY AN") STDCX COSTSVJ3S1TY
DO_.IA}S °FR T")M
_0A^'vlOMINT AVAI.lA^Li r0^ PAYL'JAO AND 3ALAST
TIMi IN 0AY5
= VJHM.7V i-.TE
- 'ALVi^E i/ALUF= AVERASE IMPORT OEiLftY
= -n.JNI T^IPS PF. v VIA*- SHI^ VELOCITY= -:\J)UPA\JCE VFLOClTir: ^HIP S°EEO MAO-: 3303= v/^LOCI ty-sojar:; •? do t
r ship oisplacFd vd.uh-:i
=3AL*ST VEIoHT= AVERAGE WEIGHT 0" A ZO^iTAlN"?' IM= r 'j:L WEIGHT= WIMG TAN< Sl/F (IMClJO'S ROTH T A >J
= V'I3HT DF MACHI 4l?Y 12Q
l\(i SEAWAY")-"' LFNGTH 3*ri>
I DNS
' s>
WO = V r I'HT O r OUTFIT*/P = MfLOA") WE I3HTWP<^ = 3T5HTlM(i WMF NT 1"l -MY.OAO^P^ak. : ^.vHum rft"I'»HT *WA 1 -<H .E F03 3 *YJ><0US = a'-:1>-ht 0" STFF_ww = -iA < I mi im ^FiciHT o- ^r'jAi pnMurOiWX : mSC ^IGHTyf: = ashuai. fjl'l ro->T
AND Rv L (\ST
129
Appendix B
EQUATION DEFINITION
Contents
Equation definition for design model.
Graph of speed reduction factor for speed madegood during transit.
Curve of machinery weight as a function of shafthorsepower.
Curve showing model for determining SPC for gasturbine power plant as a function of shaft horse-power.
S?C nlot for various gas turbines.
130
Empirical unci Other Equation* Utcd lor CargoShip Model
Tin- equation-, presented in this ap|te:idix tin;
taken from rvfen nee 1 1Iand form tin basis fur the
computations that are carried out in stvp '.'* of
each sampling ryrlc. These equations crnilil
undoubtedly l>i' presented in different fonii with
imprt>vv<l accuracy. The equations arc listed in
seven major groups: (I) Weights. II'. (2) Volumes,
V, (3) Freeboard. /•'.( I) Stability, A'. (.">> Cost. f.
(0) Power. /'. inn! (7) Miscellaneous. U.
I Weights (nil weights arc given in long toils),
'••-»'4 <"r,
r
w
(a) Approximation to oiiilit weight
X b) K,
UNI
A', m 0.080
Approxinmtion to steel (Wight
(c) . Approximation to wet machinery weight
W. - 7.18 SUP"" (311')
(rf) Weight o f iucI oil required to sail tnc
specified distance. £ plus ID percent allowance, at
a given speed, (!').
(Ill)
W,m (I.lllE) XSHPX Fit
22-10 X V11.491 X III-
"IE X SUP X FRS] (III')
am
(0110F, 2 4.21 + 3.50 -j^ +
(«) Approximate fuel rate
FR - 0.5SHP/(SIIP - *.->;>)
(/) Miscellaneous deadweight
W, - 300
(|) Actual payload weight
W, - A - II'. - It'. - H'„ - W, - W. (7110
where A « (sec Table 1).
2 Volumes (all volumes given in cubic feet),
(a) Approximate gross bale cubic of the ship.
This value applies to all dry-cargo ships except
where excessive sheer is used. This expression
includes machinery space volume and excludes
the double-bottom, settler, and peak tanks
CHC - ().873|Z, X U X D X C„\K, (1 n
RtF [39J Optimization Methods Applied to Ship D»ugn
<li) Approximate fuel oil eapaeilv ill the double
bottom. This equation i-. used ill coiljlllU'liou
withe<|U.ilioii (.". I'l todeleriiiine whether adequate
Volume exists to aeeoiiiinodate the fuel oil com-
puted by equation i III)
(Vol),. - [(A'» X /.) X H X (A', X D)
X (O.G'J C„) !
- 0.7N.SA', XGHC (21')
where
A', <= o.ll
t"» block coefficient al LVVL; factor till |kt-
ccnt is u correction for («) structure in
inner boi loin, and (//) correction to obtain
C» at the \VL height equal to tank top
height. Fuel-oil stowage factor is ;17.2
cu ft/ton
(c) Approximate fuel-oil settler-tank capacity
(Vol)A - 5000 cu ft (150 tons) (:M')
(rf) Approximate machinery space volume
(Vol). - 47,032 + 7.112 (SUP) (41')
(c) The actual payload volume is
Vol, - GBC - VoU»,„„ - [37.2 If,
-(Vol„-f-Vol /,)j (.jl')
(J) The towage factor is
sf - voi,/ir, (or)
3 Freeboard (all freeboard dimensions are in
inches).
(a) Available freeboard. Equation assumes
3-in. margin line and that the uppermost con-
tinuous deck is the freeboard deck. Equation will
differ for a shelter-deck ship
F. - 12 [D - (0.25 + T)] (If)
(b) Minimum permissible freeboard from
USCG Load Line Regulations.
For:i S 400ft:
71 (]¥»)' (2/-)
For: 400 ft S L S 7 50 ft
•, i - 77.07 + 42.5SL
100" ogo (4)'
fa* Li "wo-ft
oos (4)'
Fr fc .232* »l-
(.(/•)
131
4 Stiilitlily (mints which are Mated In cli>1lnrs liy a factor n(
(>/) A|ipin\iltialiiill In (III' transverse inertia between I and .M "
cnvllicieill <il llu ilvMxll Innl water plaiu'. n « l>i| • limit costs
trans. watcrpl.ine inertia//./)'
u - H.ltWlC, - IIJHJ:' (1.9)
(/') A|i|>rn\iiiialiiiii In (lie KG i if stni
ac. - a-
, DA, - 0.01 (25)
(c) Approximation In the AC of outfit
kg. - a, nA. « 1.011 (.15)
(rf) Approximation to tlic KG of payload
AC, - A-
, DA, « 0.03 (45)
For.O £ II'. S IIiki tons
C. - {1 1 (Ml - iiiii.'I II'. .f. (11.112 x I0-")IIV
- (11.1:12:1 x n> «)ii'. ,|ii'. (in
For: MINI < II'. < 2000 tiHIs
C. - 124.10 - I 02S II*, + ("722 X 10") II'.»
- (11.1191 X 10 •) ll'.'l H'. (20
For: II'. fc 2(1110 tons
C, - HIM II'. (3C)
(4) Approximation to steel cost
(e) Approximation to the KG of miscellaneous ft ~I21S.4 — 2l.-1.sl --- ^ 1
deadweight
" MB(iono)
,
-W ,*(Ss),
],r
'(4C)AG, - A", D
A. - 1.00 (35)
(/) Approximation to AC of fuel oil in settler
tanks
AC„ - AV> + 4.S0
A. - 0.11
(c) Approximation to machinery cost. (SHPis normal shaft horsepower.)
For: SHP £ 13,000
(65) C.-
(g) Approximation to KG of fuel oil in double
bottom Frr :•-:•"-' '*,:p- ,r"» •« •.!.-»,. •»« («!/.")
(tank top height)
AC* - 0.07 K,l) (75)
(A) Approximation to machinery AC, with
boilers full niul fur conventional arrangement for
steam-turbine plant
137.7 - zzSHP
75.32 + (SHP)
"iSF (3-K>.
SHP
For: SHP g; 13,000
C - SHP3.249 (SHP) - 173.05
ioo"
AC. - 55 D (S5)
(0 The available CM in the full-load condi-
tion uncorrected for free surface is approximatedby
(rf) Annual fuel cost
CM. - A,r +LB'
C, - KwRiWtV/EAw > 5205 for this study
A, - 3.09 cost pts/ton
SHP (00
(70
35 X A
-Kir. ac. + ii'.ac. + irjcc.
+ ("'/ - VV»)AG„ (95)
+ \V„ KG„ + II'. AC, + IP, KG, |/A
A, - 0.54
(7) The required CM is
GM, i 0.03 H
An explanation of A'K is given in section 8 of this
Appendix.
(e) Total annual cost. Cost
The yearly fuel cost {equation (7C) ] is included in
this cost which is computed as follows:
Cost - 0.0050 X (C. + C, + C) 4- C, (SO
where the fraction I KioO reduces the total initial
(105) building cost to a yearly cost usin^' the assump-
tions :
(This required (",M is also for th. /full-load condi-
tion, uncorrected for free surface. I »Th, term ens, p„i„„ i, used in HI to avoid dire*,o Costs (all costs are given ,,, terms of cost a>«nci;t<ion with dollars
Optimization Method. Applied to Ship Des/gn
132
.9
ooo .8oUJQ 7< • i
2
Q p;UJ ,pLlJ
Ol.
COh-
.5(T C/)
O 2U- <
ce
ccK-
.4oH- oo Z<u_ 5
3 .3
2 Qo~
.2oDQ1 i 1UJor: .1
VELOCSVELOC 2. - EXP (.0075X VELOC
)
10 20 30
CALM W^TER DESIGN SPEED (KTS.)
—
r
40
Figure 19
133
I
z.LUz<c
oCD
OrO
CLX oo
XIT)
CXI
rO
il
CD IT) sj" rO r\J O CD
'00SN01)
to
in
O
OrO
O
OoOO
OOX
o CCcr> LU
Oo n.00 Id
COnroX
o(O \-
U-<
n xur> to
otf-
orO
O00
1H9I3M AH3NIH3VW
Figure 20
134
I
oUJ
<c
X
XOJ
X
4-
o_XCO
X<sCD
O
rO C\h O CT> 00 CD
( 01 X$) AH3NIH0VW JO 1S009"
^igure 21
135
IT)
M
u.
o
o
oI- rO
O
O
OO
oCO
o
oCD
OID
o
orO
Oc\J
- O
OOo
X
crUJ
OClLjJ
COcro
u_<CO
EXPLANATION CF S^C I.:CD3I
The graph in Figure 22 shows the minimum
S?C as engines are added to the power plant to
achieve a given installed shaft horsepower.
The initial segment shows the S~C curve for a
single engine. "For the multiple engine install-
ations, the same minimum SFC is achieved at in-
stalled shaft horsepowers of multiples of 18,700
SKF. For the intermediate powers, all engines
are assumed to operate at equal levels.
136
om
s
orO
O(M
O O- oo
8 x
IT)
CDrO
aLdorCLXCO
X<
en i)
01UJ
co Q_UJCO
o cr^ o
X
CM
oLi-
CO
oCD
Oin
o
<m00
*1
orO
O
z
O 2
- o
en oo n- CD m rO C\J
OJS 'igure 22137
170
I to'
ISo
O
FT -<t^
esvr F^et. TwFcefi^vcf ["32.3
Ln- Z.5T30 /I
Wo -
l3o -
\to
l\o
FV .its-
\
\C-V5„A
CD \ \
\ \Q
V\^
lOO
'SHp't
—I
—
+0
—1
—
4o
-1
—
803o 50 70
°/o SHP
S?C CURVES FOR MARINE GAS TURBINES
Figure 23
138
<?o loo
Appendix C
INPUT FARAKETERS
139
N.N.S. DESIGN
PROGRAM INPUT PARAMETERS
PARAMETER SYMBOL VALUE
DPSi&M P/wwurrtRS
PftOPULSlWG COfFFlC/GAJT PC .*?£" (/WPUM6-6 '-03^
EHVUHAhlCt £ I^Soo
Dis-|/)aJc6 BrrueEA/ PoRrs DBP 5"ooo
StffP /h/4'L/lBl UTY AVA 1 L •98
wuMbt* op stt/vrr'b NSH^fT 1
MlK. NO. OF £-AjG-(/U<rS* N£AJGU (-3
|UO. OF SP/^RC EWW^^S /vexTR^ OMAX. pAV(.0/4b WT- ww -?0,000
Ml/v. ~?AYloAX> WT. wpmia; Omax. coa/t/)ia/(?^ st/kki^g- MD V
MA*. stacking- /4Bo^ X»k. MU ^
AV£ZACyF £OaJ7%iajE*1. *JT
.
WC H.8G
BfFBCTIOt COaJT. LFA/(^T7f ELENOtT 23-o
BliC-C-TlVG COWT. vvi"CTH E W lt>T H 8.75-
EFF&aiue QoArr> t>£PTtf EhZ-PTH 8.02
DouBlf Borrow TwickAteis t>oui$u£ a.r
B/ULAbr wei&^r k&-. K£rB 2.0
M/\x. 5hp fo* si*j6<.£ e>o& S|4?M N.A.
Sg* SPcfeU F/}ct o a? Bft/9 I .co^r
5fc factor BeTA2- •3tr
Misc. weKri-iT wxx o
MISC.. uyerfCrHT KG-. XK6-X
Df5K»aJ U/t((^4T7V6- F4CT<3«5-
F^CTo^ Fc5* OwTF(-r i~T- V/Wo i
R4CTOR Fop, stffc wr. WWS j
,
F^CTo/? Ffl/2 MAcHWe/^w VWM i
,
Table 15 1*4-0
N , N.S. («>»t)
PROGRAM INPUT PARAMETERS
PARAMETER. SYMBOL VALUE
NAV16ATIOM CoW5TRAi*JT5
MAX. LEKIGTH LE/v/tTM 9oo
M4X- SEAM T3EAMM Ho
MAX- DtfAFT DRflFTM 3^
ECONOMIC PA"AAMFT£K5
FRFlCrl-fT RAT£ FR So.
PO/^T GALL FEE PCF (OOO.
PA-iLY TtoftT F££ T>P F looo.
PftlCt OF' FUEL PR I c ET ife.S
AwWU/Il IvSUR/WC£ RAlt AIR .1
Asset UFt NM AS"\
SAiAMGk value SV cDiscount factor DF ,2o
'Submw Kate SUSI"DR .5S
pE/<2C£/<->JT FNA/VC^~b PF lb
interest rate RATE AO
Co<7>. Tax H/\tg CTR .ne
INVE3TMEA/T TA^ CtfttMT A/TC ,o7
Cost weight/ a; 6- factors
Factor Fo/<? outfit Cost CCo 1.
Fflrt-TOA FO* ste-fc Cost CCS 1.
Factor FO/e. ma^ia^/cy c, C-CM 1
PRoGR/lM PARAMETERSCBjFcn^c StcECT'OAy ItfftJ 1 (/J>u\
DtLTACil Ate C°
)
Table 15 (cont. )
141
B.I.W. DESIGN
PROGRAM NPUT PARAMETERS
PARAMETER SYMBOL VALUE
DESIGN P/w?AM<=TER5
FRCPU LSifCT COeFFlC|£A/r PC .70 (Af^FATMGe i.05)
EKiDUHAKftt £ 12,5-00.
Disr/Wce BETiJeFA^ PoRT*> DBP S^ooo
Si4i7> AVAtL/HSlurV AVAIL .9&
WUMBF* OF SHAFTS nsuaft 1
' tMti. NO. OF £AJ6-(Aje-S* NeAJfetJ c- >
HO- OF "STPARG ENb-WCS a/gxtr/i
HA/-. pAV<-0/4b ^T- WW io,ooo
Mia/. "P^VLo/qb WT. WPMIa^MAX. COa/7/1W<Ev\! S7/KK(^&- AJD 3
MAX. stacking- ABoi/f "Dk. M*) 6
AVCZAGF COAJiqi<uF>{ vJT. we 11.5"
BHC-CTlUt CoaJT. LFAJ&T71 ELENGT 33.0
£7FF<lTii/(F Co/uT. WyfDTH EWFDTH 8/JS-
ErFtCTWf QOaJT- "beVTif EbfPTU e.oz
DouBlf Bottom thick/u^s "D^aT^uf 4.5"
B/ULAbT V</fi6rMT kfr. K<^B A,r
MAX. 5f+P Foa? scufrce &u& S|4PM /sf.A .
Sea 5P<ffT) factoa> BET/? i .OOTS"
5 F C FA^TO/"? BftAE. ^feS"
M<sc w<fi6tW7 W)<X O
M(SC u;f<&-ht KG-. XK6-X
E>F5i<s*J u/t((344T?v6- FAcrartS
Factor fo# Out^ct <*n. \</Wo f.
FACTOR FoR STFFC wr. wws 1.
fa.cior Fofi. ^AMt4iAj£/a vn vwm 1.
1 2|>2Table 16
P>/« O PU«- Si OAJ.
B.I. W. (<o*n\
PROGRAM INPUT PARAMETERS
PARAMETER. SYMBOL VALUE
NAVIGATION Cow 57 RA ia/TS
MAX. LEM6TH LEA/&TM ?0O . FT.
M4X. BEAM T3EAMM 11© . FT.
MAX- CXAFT DRflFTM 3*7. FT.
ECOMOMlC P/OV\MET£R5
FRFlfrWT RAT£ FR 5*>.
PO^T CALL F££ PCF (6>CO.
PA-iLY "PoAT F££ "DP F lOO<?.
PKlCE OF FUEL PRICE Ife.5"
AHVUAl \\)SURA*JC£ RATE AIR .1
Asset lifS NH *S" '.
SALVAGE VALUE SV O
Discount FACTOR DF .Zo
"SuBSW tfATf SuSlftR .5"5"
pe>«(Le*/T Fltf/4/VC*T> PF .75"
IWTFREST RAT? RATE ./o
Coiflf?. Tax RATE CTR .**8
INV&3TM6/JT TA> C*tT>IT AlTC,
..on
COST WC'EHTl^G- F^CTO^S
FACTO* Pofi OUTFil COST CCo i.
Facto a. fo* Srcec Cd^t CCS I.
Fa<ctoi4. Fo/e. MAmi/je/ci t. C-C-M i.
PRobRAH PARAMETERS0"Bjfctwc Stctcrrfo-N/ IC>^>^ 1 (jJP\j)
D#-T*(tf -4U C<?^
Table 16 (cont.
)
1^3
GEORGE G. SHARP
PROGRAM INPUT
DESIGN
PARAMETERS
PARAMETER. .SYMBOL VALUE
NAVIGATION C.0W5TR/WWT3
MAX. LEM&TH L£a/&TM fs-o
M4X. BEAM T3HAMM X oo
MAX- DM FT DRfl FTT/M tfe
ECONOMIC PfyTKAtAkTERS
FRFIC-HT RATE FR So.
Po£T call fee ?CF ( OOo.
V>M Ly 7>oflT Ft E "DP F (OOO,
PRICE OF FUEL. PR ICE- 1/ *16.5
AMKIUAl. \\)SUR/\ajC£ RA-T& AX R .1
Assey Lif£ HH XS
SALVAGh VALUE SV o
Discou^ factor DP • 2o
SU'SSW ftATB SUSI"DR <SS
PF^CjFaJT finance PF •7r
INTEREST RATE RATE ie>
Co<P. Tax RATE CTR ,fS
INVFSTMPA/T T4* CtfeTMT AfT^ .o*7
Co ST W<?'G-HT/a;G- FACTORS
Factoa? Pofi. OUTFCT Cost ceo /
F/KSTOA PCA ST&fC Cd%t CCS 1
FA-CTOA FCA- MAQ+l-VP/tT' C. C-cM I
PROGRAM PARAMETERSOBj^CTXc/c SecEcnTOA/ lc?R>? 1 (wpu)
DELtA-C^ Ate Co)
fTMTCTKr^ '^ cUKOK
Table 17144
G. 6. S. (cowt )
PROGRAM NPUT PARAMETERS
PARAMETER SYMBOL VALUE
DFSl&W P/^AM<=T£R5
VkOVU LSlUiE CO£FFKM£AJT PC .7o (^^Pe^Tj/ice l.o?)
EAJDUHAMdt £ 5^ooo.
DiStAaJCS BeTuJeE^ Ports DBP- tv 8oo.
Si4fP AvWL4B(UTV AVAIL .98
WUMBe/4. OF SHAFTS MSH/\F7" 2
'
tf Itf . A/o. °F e'AjG-t-u^s* N£AJ&U 2
W(3. Or SP/ARt EUG-[AJGS AyexTR/i
HA/-. 'pA^LOAh wyr. ww ^OOOO.
Ml/J. PaVloAD WT. wphia;MAX. COa/TAia/<F^ STACK(^6- KiV 6
MA-x. ST/Kki/W- /4Bo^ "DK. MD 5
Ave^AC^F Coat^/a/cX vjt. wc ^0,5"
&W-ECTIU& COaJT. LtAlb-Tli ELEN&T 3§.o
EFItFdTiWF COWT. WfDTtt EWlt>TH e.ti
EFFECT! OF Q.OAJT. DtTTtf Eb&PTH 8.02
DouBLt Bottom th feloness "Dcja'BL-^ 3.r
B/lLLA^r W/f|fri4T KG-. K^B 2..0
MA/- 5H-P Foa? swg-cf e/uG S|4PM 1 S,*)^
Se^ 5P<FF?) F/Jctoa7 Bfta i .oo"?S"
5FC F4CTO* BetAE, •T^r
Misc. w<f»^wt WKXMisc. w/enG-HT- kg-. XKG-X
Dfsi&aJ \A/fe((^i4T?Ay6- factors
FACTOR Fc?*? OuTFcr i~t. VWo 1
Factor for stfec wr. wws i.
factor for MAcHwe/e^w wv/m 1.
* MPOATIiJt- V4LMI- |A)t)it^TB Stf^l T"U-<Ol^fc- ^^PUt-SiO/O,
Table 1? (cont. ) 145
SAMPLE PROBLEM
PROGRAM NPUT PARAMETERS
PARAMETER SYMBOL VALUE
DLrS(GM P/\rtAM<=TER5
PAOPULSlUE' C.OC-FFlClGA/T PC .65
EKJVURAMlb £ 12,500 WmT
DiSrAfJce i$eT<JoF*J Ports DBP 4,600 MM?
Sl+fi9 AVAlLABlUTY AVAIL .98
WUMB^* OP SHAFTS AJSH/\fT 2
ttltf. NO. OF EUCxikJC** NeAJ6f 2
W0. OF S"PAR(F e^W^G'S VEXTRA o
HA*. pAVcO*b WT> WW.
"^oxooo toa)5
HlA). PaVlo^D WT. wpmia;MAX. tO/s/TAi/v&t S1ACK[*J<t ^D <o
MAX. stacki/V6- ABo^ "DK. NV"b X
AvetfAGF CcW74ja/£X v*JT. wc I fc.5 TOa^s
BHFCTIU& COajT. L£"A/Gr7H ELENGrT 2-3. FT,
eWF«TH/e COAJT. WiVTH £W l"DT H 8 ,VS F7
EFFECTi oE <?<WT. DeTTM1 ET>EPTH 9,oZ FT
"DouB'-F Borrow TWick/oess ^DOUPoLf <t.S FT
B/ULAb~ VC£fi6-i4T kfr. K4-B *.:T FT
MAX- 5H-P Fo* s/<vG<* aix» S|4P^ ^7oo 5HP
S^a SPfFt) FActo a7 BFT4 i • 007F
5fc factor Beta 2,3fcy
M(SC WCT6-H7 wxx 0.
Mi St. wf<&-HT KG-. XK6rX 0.
E>F5<6aJ U/e(k(-fTW6- FA^TtftfS-
F/tcro^. fov 0"TPtr u/r. . y/Wo 1.
Factor for stffc wr. wws L
factor fa* Nvke+wtv^w VWh I .
Table lg6
^OPULSiO-M.
SAMPLE On)
PROGRAM INPUT PARAMETERS
PARAMETER. SYMBOL VALUE
NAVIGATION CowS'l RAtVl^
MAX. LEM6TM LEA/&TM 800, FT
_M4X. BEAM BEAMM IIO. FT
MAX- OtA FT BRflFTM 3*7. FT.
ECONOMIC P/mAMETtRS
FRFlEHT RAT£ FRPO#T QALL FEE PCF lOOO. / (Ml*.
PA-iLy >oAT F£E "DP F ^looq/tMy
PRlCt OF FUFL PRICE- •* 63-V/niAw^uAc |ajskR/wc£ RA-nt AIR .©I
AsseT ^-(Ft NM 25-. YeMS
S/lLV/IGt VALUE sv
discount factor DF .^0
SuBM~£>Y K/rre SuSiDR .ST5-
Pl-ACJEaJT F"|NA/Vd^"b PF 7S"
INTEREST RATE RATE .10
CoR*P. Tax rate CTR .H8
lNVF3TMfA/T tax c/eet>iT Aire,
.07
Cost w<F'feHT/^6- factors
Factor Fc?/« cutfct cost CCO /,
Fa<ltoA fo* 57CR. Cost CCS 1.
FA<CTOA FOA. MA*U-flA/e/C"f C-, C-C-M 1.
•
PROGRAM PARAMETERSOBOCCTt^c Sc <-Hc_t(Oa/ iota 3 1 (/J-pv )
DCt-TACt'j /ILL (O)
ftfFCfCTs ho<( Cu<«c^T T«eA^S ft FuFe "&*«* CTWfO? i<«,<i (.PuR.)
Table 18 (cont. ) 1/|?
Appendix D
USE OF SUMT FROG RAT'S
^
1^8
USE OF THE SUMT PROGRAMS
Two programs were developed to obtain the output used
during the analysis stage. The first utilizes the SUMT rou-
tine to develop attractive alternatives. These alternatives
are identified by the values of the decision variables and
the objective function. In addition, a second program is
available which gives a detailed breakdown of a single de-
sign alternative. This second program does not employ any
optimization technique. It merely identifies a design in
terms of its weights and costs. The inputs for each of
these programs are outlined in the next section.
Input ^ormat
The input deck for the SUMT program contains two
major elements. The first lists the parameters used by the
optimization technique and the second contains the data used
by the design model in defining the objective surface. The
cards are listed in the order of appearance for the input
deck of the SUMT program. (See Figure 25 ) The second pro-
gram uses only the design data as its input. See Figure 26.
CARD 1: Problem #1 Parameter Card (See Guide to SUMT)
1^9
CARD 2: Initial X Vector of Decision VariablesFormat (6E12.6)
Displacement j length? Beam; Draft j DepthPrismatic Coefficient.
CARD 3: Initial X Vector (Continued)format (6E12.6)
Velocity.
CARD 4 « First Design CardFormat (5F10.2,5X,I2)
Propulsive Coefficient j Endurance; DistanceBetween Ports; Maximum Shaft Horsepower of aSingle Engine; Average Fort Delay Time; Maxi-mum Stacking of Containers.
CARD 5: Second Design Data Cardformat (5F10.2.5X, 12)
Maximum Payload Weight; Average Weight of aContainer; Effective Container Length; Effec-tive Container Width; Effective ContainerDepth; Maximum Containers Stacked Above Deck.
CARD 6: Third Design Data CardFormat (5F10.2,5X f 12)
Port Call v ee; Daily Fort Fee; Freight Rate;Price of Fuel; Annual Insurance Rate; Indi-cator of Objective.
CARD 7: Fourth Design Data CardFormat (5F10. 2,5X,I2)
Percent Financed; Subsidy Rate; Interest Rateon Loan; Salvage Value of Ship; Discount Fac-tor; Asset Life.
CARD 8 j Fifth Design Data CardFormat (5F10.2, 5X f 12)
Investment Tax Credit.
CARD 9: Sixth Design Data CardFormat (5F10.2,5X,I2)
Maximum Ship Length; Maximum Ship Beam; Maxi-mum Ship Draft.
150
CARD 10:
CARD 11:
CARD 12:
CARD 13:
CARD m-t
CARD 15:
CARD 16:
CARD 17:
CARD 18:
Seventh Design Data CardFormat (5710. 2,5X, 12)
Double Bottom Thickness; Center of Gravityof Ballast Weight Above Keel; Ship Avail-ability; Annual Corporate Tax Rate.
Eighth Design Data Card, Sensitivity DataFormat (8? 8. 2)
Betal; Beta2; WWOf WWSi WWMi CCOj CCS; COM.
Ninth Design Data CardFormat (878.2) .
WXXj XKGX; WPMIN.
Tenth Design Data CardFormat (313)
NSHA7T; NENGU; NEXTRA.
Eleventh Design Data Card, Sensitivity DataFormat (14-F5.2)
(DELTA(I),I= 1,14)
First Option Card (See Guide to SUMT)
Tolerance Card (See Guide to SUMT)
Second Option Card (See Guide to SUMT)
Problem #2 Parameter Card for Next Program,Repeat Other Cards As Necessary.
151
/ //
'_ / /
S^OO^A} OPTION CA~i*X> \ /
TfLtA?,4XJCc CAhTD
OPTio/O CMt)
^es/fe^ >>AT-4 C4«i>S
Initial Xe v/tCTo< ca^>t
P*06u?/--i #£. PARMierez c^<d
StCO/0"b OPTlO/yJ C/Kb
Tote*Auct tyWt>
OPTIOaJ tA<b
De5i6Aj t>ATA C4rtt>S
IWrriAL Xo VeCrOrf CAiVb$
PROBLEM #1 PARAMETER CARb
1/
t-A^'D 1*1
CA<£T> tfc
CAftT> ,?
1/ CA<OJ 3- IH
CAftt^i.*- 2-
CAM) L
PRO&RAM PATA DECK .5TRUCTUR,fc
Figure 2k
152
SAKPI.E DATA CARDS ?0R SUIuT FRCGRAWc
c
c
IT < (\ — U— (V
c a Ifif C"
—
—
i
c • • • •
u (V a•
ccv
<) IT In cr cr
• r- r- cr <Jr • • « •
r c a Nl
i
c J>
u vt• r\
c .—
c a• • 1
—
a cr. cr
J c • c 1 • * • A »—• c m c r^ .—
1
Ca a rv *-. r~
c <j
cr
I
cr•
u cr• c —
*"~
. L1/
Lf LP
•
cr CO • 1 • • t • 1
•S *In c
c c c c1—
i
«J cr .- if\T •— vT c —r^ r •
L • c
L U u r-
• vT [»• c 1/ c c.
• 1
—
c c c s* r- cr c c« c c c c f\ c
c c c o c c«
—
t- c — • c •
r • rv c fv •
u r c c-3 r c
p igure 25
153
SAMPLE DATA CARDS TOR DESIGN MODEL
r• r-r •
a irrv
a<r if
ccv c <r
rv • • •
cr cr cr•
• a •— cr rv c• i_r • • c • c (V. • <rC LT i ^-t • ^ • #—< • *—i •v£ <J cr a » c
cr
c cr c.• • •
IT U" P c c cr criT «N . « .• c •
O • cr • -*> ^ cu"iS # <X —a s c cr
~ a cr ir r- - cr -j- cr(\ r- <t • n- • -o • •
o # c- a a "" c
• i~- #— c r- •-» cr
r*" • • f • oc c c • c • ••f—«cf\cr a c cr • c cr vf crecu- c • cr a Lr r- <j •
OLT • cr <t c- • crf r~
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Figure 26
154
Sample Output
Figure 2? shows the output to the program giving the
detailed design.
1. Values of the decision variables.
2. Weight break down of the design.
3. Container configuration.
k- , Cash flow statement.
5. Value of objective functions.
Figure 28 shows the output to the SUMT Frogram. The
following annotations apply:
1. The values of the SUMT parameters used for this prob-
problem.
2. The initial X vector of decision variables with the
associated objective value (F), Also an internal clock
is referenced. (Use of design alternative h)
3. The starting feasible point (same as #2 in this problem)
k. Recording of orthogonal moves made by the routine.
5. The solution to the first subproblem after 10 moves
r = 1.0.
6. The solution to the second subproblem after 12 moves
r = 1./20
7. Final solution of the first problem.
155
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160
Appendix E
SOURCE LISTING 0? CClvIFUTER PROGRAMS
161
FROGRAM MAIN
Routine that calls design model and
outputs a detailed ship design.
Calls subroutines?
RSADIN
RESTNT
162
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2 • C#-* «3 I- ** #—» »c • J z Ll «
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16^
SUBROUTINES USED IN SULIT FROGRAM
includes routines
READIN
RESTNT
GRAD1
MATRIX
Notes
Subroutine RESTNT Calls
Subroutine Object
165
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SHIP' DESIGN PROGRAMS
includes subroutines
OBJECT
SHPREQ
RESIS
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Subroutine object callssubroutine SHFRQ
Subroutine SHPRQ callssubroutine RESIS
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T»T^SEP74 DISPLAY
S 1 5 1 9
Thesis 153603F623 Fortson
Application of the se-
quential unconstrainedminimization techniquein a systematic contain-ership design.
lhesF623
Application of the sequential unconstrai
3 2768 001 95933 1
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