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The modelling of supply in the shipping industry
OMEGA, The Int. J1 of Mgmt Sci., Vol. 4, No. 2, 1976. Pergamon Press. Printed in Great Britain.
The Modelling of Supply in the Shipping Industry AJ T A Y L O R (Recek'ed June 1975; in re~'isedform October 1975)
This paper considers the way in which certain variables in the shipping industry fluctuate. Factors such as supply and demand for cargo carrying capacity, freight rates, laid-up tonnage, are shown to form a number of interacting feedback loops, and it is demonstrated that it is possible to construct a dynamic model of the system.
INTRODUCTION WITHIN THE shipping industry there exists a great deal of fluctuation in various factors such as freight rates and the amount of unemployed and laid-up shipping. Such fluctuations can be extremely important in the operations of shipping and chartering companies. Consider, for example, the situation at the present time in the area of oil-tanker employment. Demand for oil tankers is low, freight rates are low and so the amount of tonnage being laid-up is escalating. However, to lay-up a ship is not to reduce costs to zero because certain costs are, necessarily, still incurred. A recently quoted figure [1] for the costs in lay-up for a very large crude carrier (VLCC) is $2300-$2600 per day, or almost $1M per year. I f a company could know what combinations of market conditions would lead to such large sweeps in important variables then some planning in advance would be possible. A number of authors [2, 3 for example] have examined certain relationships in the market for shipping services from the static point of view. N o dynamic analysis has been attempted in this field and it is the purpose of this paper to describe the approach being used by the author in the construction of a dynamic model.
A N A P P R O A C H TO THE M O D E L L I N G OF SUPPLY On examination the shipping industry, or that part of it concerned with the transportation of goods within the international shipping markets, comprises a number of interacting feedback loops. 175
Taylor--Supply in the Shipping Industry The basic loop in such systems is a negative feedback loop which may be described as a self-regulating, or goal-seeking, mechanism. Such a mechanism consists of a 'level' variable, (L), such as the number of ships in service at any time, and a 'rate' variable (R), such as the rate of delivery of new ships over a particular time period. These variables, L and R are related in a manner which may be described in the following way: 2
L2 = LI 4- ~"Rdt 1 R =f(L, and other factors), where the subscripts 1 and 2 relate to two consecutive points in time. This means that the input rate R depends upon L, which in turn depends upon R. It will be seen that an increase in R leads to an increase in L which, in a negative feedback loops, subsequently has the effect of decreasing the rate R. Hence the self regulation inherent in such a mechanism. In a managed system the input rate R could be a decision--or a policy--for the management of the system. Complications exist in real systems due to problems of identit}'ing the 'other factors' and in the delayed effect of changes in R being felt by L. How can this be applied to the problem of modelling a sector or sectors of the shipping industry? Firstly by identifying the various circular cause-effect relationship which exists. As an example of such circular causality consider the following extract from the report of a recent commission on shipping [4]. "In the longer term the course of freight rates has (also) been affected by bursts of shipbuilding orders placed in response to what may only be short term increases in rates". The next stage is to examine such relationships in order to provide a quantitative basis for the construction of the state equations. To take a systematic approach to the description of the various feedback processes operating within the industry, let us consider the system to comprise several interdependent sectors: Shipbuild Orders and Deliveries, Scrappings, Lay-Ups, Change of Trade, Freight Rate Formation. Further, in order to be brief, let us describe the modelling approach as applied to only two of these sectors.
SHIPBUILD
ORDERS
AND
DELIVERIES
With regard to the ship owners' decision to order a new vessel there are many factors to be considered, some of which are: I. Expectations regarding (a) Over-supply in future time-period; (b) profitability of particular vessels and markets. 176
Omega, Iiol. 4, No. 2 2. Existing prices at shipyards. 3. Backlog of orders at shipyards, and subsequent delivery delay. 4. Possibilities of obtaining finance. As to the question of which of these factors are most important in determining the size of orders placed at any time consider the data illustrated in Fig. 1. 3
.
/
~
7 5OO
_
400
.~
300
.o
"
\ A
-
"-./1
0
f,'"
o
/,'" I
1971
-I
-1 1
I
1972
1973
Orders
l-Jo 1974
Freight rate index
....
FIG. 1. Fluctuations in orders and freight rates (Dry cargo).
Here there is a clear relationship between the size of orders and the spot charter (single voyage) freight rates• Similar patterns of variation have occurred at other periods of time and, in fact, for the period of Fig. 1 the statisticalCapacity aquisi't'ion
.-k~
Capacity, C
Delivery
+
delay,D ~
,
{+
-
-
~
/
Order backlog,B
S'tart rate r
l+
;+
Order r a t e , 0 Freight ~ - ~ - - S u p p l y rates j F S
O=
+ ~
Delivery r a t e , S
f(F)
B :fOldt
O
--frld¢
: B/C
d.c . f ( O ) de"
5 ~ r delayed by D and 7" S ~ J ' 5 . d f - - Scrappings~ lay-ups~ trade changes
FTG. 2• Relationships in the order-build process•
177
~
Build time T
Taylor--Supply in the Shipping Industry correlation coefficient is 0.76 for a lag of 2 months in the freight rate data. The effect of a rise in freight rates is to induce owners to order vessels earlier than they would otherwise have done. It would appear that the most important determinant of the size of orders is the profitability at that time. The interrelationships between some of the factors which help to produce the dynamics of the system are shown in Fig. 2. This sector of the industry has a very low response time to changes in demand. The change in supply of new vessels is not immediate upon the occurrence of changes in demand, and the very large delays inherent in the system help to produce the, sometimes extreme, fluctuations which do occur. This is not to say that there are not other factors which also assist in this process. The policies used, for example, in deciding how much tonnage to order appear to be based upon the level of freight rates at any time and the ship-owners seem to have no memory of past periods when large influxes of orders served to depress the market some years later when the vessels were leaving the shipyards. This kind of situation exists at the present time in the tanker market where there is a gross over-supply of tonnage because of over-ordering in the profitable years of the early 1970's.
CHANGE OF TRADE The two important trade divisions within the industry are the tanker and dry cargo (bulk carrier) sectors, whose markets are fairly well defined. Uneconomic operation in a particular market, will lead an owner to seek more profitable employment in another market, if this is a feasible proposition. It often happens, in fact, that tankers move into the grain trade when oil-transportation rates are low, and 'combined carriers', having the ability to carry ore, oil and/or other bulk cargo, have a great flexibility in being able to change trades fairly easily. 5.0
5O
4.0
I"~ /7 !!i I v/ ',
40
30 7:
30 c --
E o u
20
20
J
/,:\ ,,/ #
1.0
"6 2 "~
~0
l
p
1971 _
F~G. 3.
_
r
I
1972 e/,
. . . .
1973
I 1974
Ratio
Fraction of combined fleet trading in dry cargo compared with the ratio of dry cargo--oil tanker freight rates.
178
Omega, Vol. 4, No. 2 The relative profitability of one market to another may be measured in terms of the ratio Dry Cargo Freight Rates/Tanker Freight Rates (Tanker freight rates are indexed on a scale known as Worldscale.) Figure 3 illusuates the variation in this ratio over a number of years, together with a comparison of the proportion of the total combined carrier fleet operating in the dry cargo market. A statistical correlation of 0.84 is obtained for a lag of one month in the ratio. Thus, as the freight rates vary the combined-carrier tonnage in the dry cargo sector varies, this having the effect of altering the dry cargo and tanker freight rates. A perpetual fluctuation is set in motion and as long as the indastry behaves in the same manner the fluctuation will not cease.
THE MODEL AS A WHOLE Only two sectors of the model have been described, albeit briefly, but the interdependence of some factors on others is clearly visible. When all the, previously defined, sectors are considered a network of cause-effect relationships is obtained, with the form of the example shown in Fig. 2. These relationships have been analysed and quantified so as to provide the equations for a computer simulation of the behaviour of the dry cargo market. Certain variables are, at this time, exogenous, these being the demand for cargo-carrying capacity and the values of the tanker freight rates. An example of the output of the model is shown in Fig. 4. The demand in this case has been kept constant. -- 8 O O
17.5--
~
I
0
J'"
"",.
,.,
~o
,~0- -~:,01-sL\\ 125
--
-- 600
/-..,
" ",.
o°°
~
o rl b-
50 --
0
I0
20
30
40
5'3
60
70
90
90
' '~
MonThs " !nocfive
tennrage -- -- Freight
r o t -~ i n d e x
.....
Deliveries
FIG. 4. An example o/model output,
FUTURE
DEVELOPMENTS
The present model is a simplified, but not unrealistic, representation of the real system under study. Developments to the model will include a disaggregation of the variable 'tonnage in service', a more refined approach to the modelling 179
Taylor--Supply in the Shipping Industry of various 'delays' in the system, and the treatment of the variable 'laid-up tonnage' to allow it to act as a buffer between ships in service and the scrapyard.
CONCLUSIONS It has been shown that it is possible to approach the modelling of the dynamics of supply in the shipping industry by use of the concept of feedback. With the assistance of such an approach it should be possible to predict the behaviour of ocean freight rates, quantity of laid-up tonnage, and other factors, given the possibility of alternative trends in shipping demand. Also, it should be possible to provide answers to specific policy questions such as what type of ship will be most profitably employed under certain future market conditions.
REFERENCES 1. Sunday Times (1975) 18 May. 2. THORBURN T (1960) Supply and Demand of Water Transport. The Business Research Institute at the Stockholm School of Economics, Stockholm. 3. ZANNETOZ Z (1966) The Theory ofOil Tankship Rates. M.I.T. Press. 4. HMSO (1970) Report of the Committee of Inquiry into Shipping, para. 524.
ADDRESS FOR CORRESPONDENCE: AJ Taylor, Department of 2~Iathematics, Liverpool Poly-
technic, Byrom Street, Liverpool, UK.
180
The Modelling of Supply in the Shipping Industry AJ T A Y L O R (Recek'ed June 1975; in re~'isedform October 1975)
This paper considers the way in which certain variables in the shipping industry fluctuate. Factors such as supply and demand for cargo carrying capacity, freight rates, laid-up tonnage, are shown to form a number of interacting feedback loops, and it is demonstrated that it is possible to construct a dynamic model of the system.
INTRODUCTION WITHIN THE shipping industry there exists a great deal of fluctuation in various factors such as freight rates and the amount of unemployed and laid-up shipping. Such fluctuations can be extremely important in the operations of shipping and chartering companies. Consider, for example, the situation at the present time in the area of oil-tanker employment. Demand for oil tankers is low, freight rates are low and so the amount of tonnage being laid-up is escalating. However, to lay-up a ship is not to reduce costs to zero because certain costs are, necessarily, still incurred. A recently quoted figure [1] for the costs in lay-up for a very large crude carrier (VLCC) is $2300-$2600 per day, or almost $1M per year. I f a company could know what combinations of market conditions would lead to such large sweeps in important variables then some planning in advance would be possible. A number of authors [2, 3 for example] have examined certain relationships in the market for shipping services from the static point of view. N o dynamic analysis has been attempted in this field and it is the purpose of this paper to describe the approach being used by the author in the construction of a dynamic model.
A N A P P R O A C H TO THE M O D E L L I N G OF SUPPLY On examination the shipping industry, or that part of it concerned with the transportation of goods within the international shipping markets, comprises a number of interacting feedback loops. 175
Taylor--Supply in the Shipping Industry The basic loop in such systems is a negative feedback loop which may be described as a self-regulating, or goal-seeking, mechanism. Such a mechanism consists of a 'level' variable, (L), such as the number of ships in service at any time, and a 'rate' variable (R), such as the rate of delivery of new ships over a particular time period. These variables, L and R are related in a manner which may be described in the following way: 2
L2 = LI 4- ~"Rdt 1 R =f(L, and other factors), where the subscripts 1 and 2 relate to two consecutive points in time. This means that the input rate R depends upon L, which in turn depends upon R. It will be seen that an increase in R leads to an increase in L which, in a negative feedback loops, subsequently has the effect of decreasing the rate R. Hence the self regulation inherent in such a mechanism. In a managed system the input rate R could be a decision--or a policy--for the management of the system. Complications exist in real systems due to problems of identit}'ing the 'other factors' and in the delayed effect of changes in R being felt by L. How can this be applied to the problem of modelling a sector or sectors of the shipping industry? Firstly by identifying the various circular cause-effect relationship which exists. As an example of such circular causality consider the following extract from the report of a recent commission on shipping [4]. "In the longer term the course of freight rates has (also) been affected by bursts of shipbuilding orders placed in response to what may only be short term increases in rates". The next stage is to examine such relationships in order to provide a quantitative basis for the construction of the state equations. To take a systematic approach to the description of the various feedback processes operating within the industry, let us consider the system to comprise several interdependent sectors: Shipbuild Orders and Deliveries, Scrappings, Lay-Ups, Change of Trade, Freight Rate Formation. Further, in order to be brief, let us describe the modelling approach as applied to only two of these sectors.
SHIPBUILD
ORDERS
AND
DELIVERIES
With regard to the ship owners' decision to order a new vessel there are many factors to be considered, some of which are: I. Expectations regarding (a) Over-supply in future time-period; (b) profitability of particular vessels and markets. 176
Omega, Iiol. 4, No. 2 2. Existing prices at shipyards. 3. Backlog of orders at shipyards, and subsequent delivery delay. 4. Possibilities of obtaining finance. As to the question of which of these factors are most important in determining the size of orders placed at any time consider the data illustrated in Fig. 1. 3
.
/
~
7 5OO
_
400
.~
300
.o
"
\ A
-
"-./1
0
f,'"
o
/,'" I
1971
-I
-1 1
I
1972
1973
Orders
l-Jo 1974
Freight rate index
....
FIG. 1. Fluctuations in orders and freight rates (Dry cargo).
Here there is a clear relationship between the size of orders and the spot charter (single voyage) freight rates• Similar patterns of variation have occurred at other periods of time and, in fact, for the period of Fig. 1 the statisticalCapacity aquisi't'ion
.-k~
Capacity, C
Delivery
+
delay,D ~
,
{+
-
-
~
/
Order backlog,B
S'tart rate r
l+
;+
Order r a t e , 0 Freight ~ - ~ - - S u p p l y rates j F S
O=
+ ~
Delivery r a t e , S
f(F)
B :fOldt
O
--frld¢
: B/C
d.c . f ( O ) de"
5 ~ r delayed by D and 7" S ~ J ' 5 . d f - - Scrappings~ lay-ups~ trade changes
FTG. 2• Relationships in the order-build process•
177
~
Build time T
Taylor--Supply in the Shipping Industry correlation coefficient is 0.76 for a lag of 2 months in the freight rate data. The effect of a rise in freight rates is to induce owners to order vessels earlier than they would otherwise have done. It would appear that the most important determinant of the size of orders is the profitability at that time. The interrelationships between some of the factors which help to produce the dynamics of the system are shown in Fig. 2. This sector of the industry has a very low response time to changes in demand. The change in supply of new vessels is not immediate upon the occurrence of changes in demand, and the very large delays inherent in the system help to produce the, sometimes extreme, fluctuations which do occur. This is not to say that there are not other factors which also assist in this process. The policies used, for example, in deciding how much tonnage to order appear to be based upon the level of freight rates at any time and the ship-owners seem to have no memory of past periods when large influxes of orders served to depress the market some years later when the vessels were leaving the shipyards. This kind of situation exists at the present time in the tanker market where there is a gross over-supply of tonnage because of over-ordering in the profitable years of the early 1970's.
CHANGE OF TRADE The two important trade divisions within the industry are the tanker and dry cargo (bulk carrier) sectors, whose markets are fairly well defined. Uneconomic operation in a particular market, will lead an owner to seek more profitable employment in another market, if this is a feasible proposition. It often happens, in fact, that tankers move into the grain trade when oil-transportation rates are low, and 'combined carriers', having the ability to carry ore, oil and/or other bulk cargo, have a great flexibility in being able to change trades fairly easily. 5.0
5O
4.0
I"~ /7 !!i I v/ ',
40
30 7:
30 c --
E o u
20
20
J
/,:\ ,,/ #
1.0
"6 2 "~
~0
l
p
1971 _
F~G. 3.
_
r
I
1972 e/,
. . . .
1973
I 1974
Ratio
Fraction of combined fleet trading in dry cargo compared with the ratio of dry cargo--oil tanker freight rates.
178
Omega, Vol. 4, No. 2 The relative profitability of one market to another may be measured in terms of the ratio Dry Cargo Freight Rates/Tanker Freight Rates (Tanker freight rates are indexed on a scale known as Worldscale.) Figure 3 illusuates the variation in this ratio over a number of years, together with a comparison of the proportion of the total combined carrier fleet operating in the dry cargo market. A statistical correlation of 0.84 is obtained for a lag of one month in the ratio. Thus, as the freight rates vary the combined-carrier tonnage in the dry cargo sector varies, this having the effect of altering the dry cargo and tanker freight rates. A perpetual fluctuation is set in motion and as long as the indastry behaves in the same manner the fluctuation will not cease.
THE MODEL AS A WHOLE Only two sectors of the model have been described, albeit briefly, but the interdependence of some factors on others is clearly visible. When all the, previously defined, sectors are considered a network of cause-effect relationships is obtained, with the form of the example shown in Fig. 2. These relationships have been analysed and quantified so as to provide the equations for a computer simulation of the behaviour of the dry cargo market. Certain variables are, at this time, exogenous, these being the demand for cargo-carrying capacity and the values of the tanker freight rates. An example of the output of the model is shown in Fig. 4. The demand in this case has been kept constant. -- 8 O O
17.5--
~
I
0
J'"
"",.
,.,
~o
,~0- -~:,01-sL\\ 125
--
-- 600
/-..,
" ",.
o°°
~
o rl b-
50 --
0
I0
20
30
40
5'3
60
70
90
90
' '~
MonThs " !nocfive
tennrage -- -- Freight
r o t -~ i n d e x
.....
Deliveries
FIG. 4. An example o/model output,
FUTURE
DEVELOPMENTS
The present model is a simplified, but not unrealistic, representation of the real system under study. Developments to the model will include a disaggregation of the variable 'tonnage in service', a more refined approach to the modelling 179
Taylor--Supply in the Shipping Industry of various 'delays' in the system, and the treatment of the variable 'laid-up tonnage' to allow it to act as a buffer between ships in service and the scrapyard.
CONCLUSIONS It has been shown that it is possible to approach the modelling of the dynamics of supply in the shipping industry by use of the concept of feedback. With the assistance of such an approach it should be possible to predict the behaviour of ocean freight rates, quantity of laid-up tonnage, and other factors, given the possibility of alternative trends in shipping demand. Also, it should be possible to provide answers to specific policy questions such as what type of ship will be most profitably employed under certain future market conditions.
REFERENCES 1. Sunday Times (1975) 18 May. 2. THORBURN T (1960) Supply and Demand of Water Transport. The Business Research Institute at the Stockholm School of Economics, Stockholm. 3. ZANNETOZ Z (1966) The Theory ofOil Tankship Rates. M.I.T. Press. 4. HMSO (1970) Report of the Committee of Inquiry into Shipping, para. 524.
ADDRESS FOR CORRESPONDENCE: AJ Taylor, Department of 2~Iathematics, Liverpool Poly-
technic, Byrom Street, Liverpool, UK.
180