
22. Criterion functions for optimization of vessel’s characteristics for commercial order, other asset or the property complex of the marine company, based on application of the economic criteria and value
The financial investment in the real assets of the marine companies from the economic point of view is innovative activity, and the economic model of the evaluation and the economic efficiency estimation among comparable variants of innovative strategy is the basis of the investments planning.
The investments planning for the marine industrial activity includes the optimum choice of characteristics of the marine company’s real assets by the economic criteria and appropriate ones with view of financial or other limitations for optimum investment, in particular the determination of the optimum vessel characteristics by economic criteria for the contract commercial order.
The examples of the choice of the commercial vessel characteristics in the property complex the shipping company for the commercial order with the aim of replenishment and renovation of the commercial fleet are considered earlier (Chapter 19). The necessity to adhere to the systematic approach and concepts of comparability of evaluated variants of the vessel, that is very important in marine industrial activity, is explained, considering, that characteristics of the marine company assets are functionally interconnected substantially.
22.1. Systematic approach in elaboration of the criterion functions for optimization of a commercial vessel or property complex of the marine company characteristics
It should be noted, that the property complex of the marine company functionally is a single whole, its elements are in many respects interconnected technologically and structurally, as well as the developed ocean resources.
When the investments are estimated in compliance with the systematic approach concepts the functional integrity is among the methodological features of the marine company’s property complex in comparison with the investments estimation in other branches.
Object of the project optimization by economic criterion is the real asset (for example, a commercial vessel) which can be evaluated as the isolated property complex or the working company. And applicability of the project optimization methods by the economic criterion depends on how accurately the properties of optimized object can be correlated with the properties of the isolated property complex of working marine company. To put it otherwise it matters what properties of the optimized object are more important: economic, functional or technological.
Optimization of the project characteristics by economic criterion is the most effective approach for complex industrial objects for which, owing to the variety of properties – physical, technological and functional one property cannot be a generalized criterion, and the quantity of properties is transformed to economic quality which is a criterion.
The economic criteria serve as index of efficiency and are determined by mathematical operations on the basic economical indexes: the annual income I, operation costs C, investments – market value MV or other value – with one definition or another, for example the value of a new asset of the marine company, the costs for manufacture of a real asset in market prices – reproduction cost RC.
Unlike the annual income I and operation costs C which characterize distributed in time t economic flows of incomes, and expenses, and in economy are determined and summarized usually per a year, investments MV or RC have one–time or discrete character in time or can be transformed to an estimation of the present value index.
The basic economical indexes and value (I, C, MV or RC) in them–selves do not reflect critical judgments, suitable for the choice of optimum decisions at a stage of designing, and are not criteria of a choice in optimization, but they serve to formulate the criteria which mathematically are determined by correlation of the basic indexes.
It is impossible to determine, for example, if it is required or not to choose optimal characteristics of the marine company real asset by the criterion of minimization of the operation costs C taken separately from the indexes of: incomes I and investments MV or RC. With varied optimized characteristics it is required to analyze joint change of the basic economical indexes of the marine company asset.
Mathematical operations on the basic indexes in formalizing of the criterion functions reflect critical judgments which are necessary to provide the compromise of advantages and disadvantages when optimizing project characteristics of the marine company’s property complex asset.
The correlation between the applied economics and mathematics goes deep with the complexity of expert tasks. For wide consumption the estimation of serial objects can be carried out by the expert methods under the simplified adapted instructions.
The applied economics and some sections of mathematics, such as theory of numbers and sequences, theory of the differential equations, probability theory etc., practically merge in case of estimation of complex objects which include: the functional property complexes of the industrial enterprises with the account the system analysis in time and prospects forecasting; the investment projects, including evaluation of strategy and intangible asset which estimation requires preliminary working out of corresponding economic model of the separate assets, durable and proportional to the enterprise as a whole, for example, marine commercial vessels or batches of vessels for the commercial order, where investments into their manufacture are elements of innovative strategy, etc.
In process of globalization in the industry the convergence of mathematical and economic bases in an expert estimation will proceed.
Formation of global economy should be correlated with the development of the technological pattern of the world, considering, that the core of the pattern is digital technologies. According to the given criterion the formation of the global economy will come by the end by the moment of change of the pattern, that is, when possibilities of the core development will be exhausted, and the basic direction of development will be changed.
As digital technologies are aimed at the artificial intelligence modeling, probably the resource of the development directions will be exhausted and it is necessary to expect the change of the technological way when the intelligence will be technically sufficiently reproduced.
By this time it will be possible to consider the formation of global economy finished which will be carried out through a digital model of public intelligence. And, possibly, this process will not take a long time, as dynamical processes of formation change can be observed.
The greatest convergence of economy with mathematics will be implemented, when the control of digital processes in networks allows raising globally integration, and economic interaction will be carried out not pair wise, but integrally, that is, each enterprise will cooperate with all global set. The economy thus will become a mathematical model of global strategy, and monetary concepts will be displaced to consumption sphere.
In modern market conditions, typical for the developed states and prior to globalization, investors are separated. At the same time in investment activity it is required to use criteria which are mathematical transformations on the basic economical indexes and allow operating investments with global orientation which is in the fact that that the general concept of efficiency and optimality for all investors are introduced by mathematical transformations on the basic indexes.
Criteria of the optimality, allowing to separate the optimal project characteristics (or the range of the optimum solutions) from not optimum, are a way to use the economic criteria of efficiency which allow to arrange all compared project options in order of preference, that is, in other words the criterion of economic efficiency is a more general economic concept than the criterion of optimality, since it is not required to narrative all options by preference if there is a need to separate only optimum options. The criterion of optimality is a way to use of efficiency criterion.
On the other hand, if to arrange the options by the criterion, then, in case of a limited quantity of options or in case of a limited range of definition of variables the optimum variants will be found as well.
The criterion in the form of a criterion function f is defined depending on varied unknown characteristics of the marine company asset: variables X (that is a vector or a set of variables), parameters Y and data Z (constants).
The set of variants of the resulted project characteristics investigated for the optimality, means a set of values of variables X (namely, values of vector), and each option is characterized by a certain value of this vector.
The set of variables X is defined as a part of those independent values (that is, independent on each other, on parameters and constants) which substantially influence the criterion of the marine company’s property complex asset optimality.
For example, to optimize economically the commercial vessel project characteristics, a certain value of the vector of variables X corresponds to each option among the compared, and the structure of the vector can include vessel characteristics varied by optimization (in particular, the displacement of commercial vessel, the deadweight, the load–carrying capacity, the tonnage and the power of main engine or the velocity).
Working out of criterion function is inseparably linked and also is accompanied by classification of mathematical values in sets: variables X, parameters Y and data Z.
While working out the criterion function f it is supposed, that the metrics is defined, for example, in the form of algorithm according to the influence of an independent values (X, Y or Z) on the criterion, and it is taken into account, that the structure of the criterion function which is based on classification of entering values, is developed by successive approximations. The estimation of influence of any entering value on the economic criterion can be made at each step, and working out of criterion function structure comes to end concurrently with performance of optimizing subject and, as a matter of fact, it is solution of this task.
The set of parameters Y is introduced as a part of those independent values, where each of them separately does not influence substantially by the specified metrics on the optimality criterion in the form of criterion function f.
For example, the unlimited quantity of economically insignificant for optimization of a commercial vessel design characteristics can be included into set of parameters, except those which are concern to variables X.
For practical purposes the parameters can be taken structurally, let us assume, according to a technological prototype and can be considered invariable when making project optimization of variables by the economic criterion.
According to system–based principles of project optimization by economic criteria the real asset as part of the marine company’s property complex methodologically should be defined as a single whole consisting of the parts. And when connecting the parts in the whole the dialectic principle of «quantity transition into quality» is carried out and the object as a single whole acquires new properties which were absent in parts. For example, if at stage of choice for the commercial order the cargo vessel optimized by economic criterion to consider as a set of two parts – a hull characterized by cargo capacity and a main engine (more exactly, a propulsive complex – a vessel’s «running gear») characterized by power, then, when connecting these two parts there appears a new property of the cargo vessel, in particular, carrying capacity which was absent in separate parts.
It is an additional property arising in process of connection of parts of the real asset or the marine company’s property complex in a single whole that is a subject of the project optimization by economic criterion, instead of a set of the properties which are in the parts of the asset taken separately.
It should be added, that determination of a complete object as a complex of parts in case of project optimization by economic criterion has a methodological rather the mechanical sense.
Continuing an example concerning cargo vessel, the parts in methodological sense it should be defined more exactly as not a hull and an engine (and so on, with the account inexhaustibility of division), and not separate parts of the hull – a fore, an aft, sides, decks, bottom, bulkheads, details etc., but in each case as all the vessel as a whole, considered from the point of view of one part of methodology or another, that is, from the point of view of separate seaworthy properties and operational characteristics.
In particular, with due account of design methodology the following characteristics can be considered as parts of commercial vessel: buoyancy, that is a commercial vessel as a whole from the point of view of useful physical property of buoyancy (seaworthy property), stability – all vessel from the point of view of physical property of stability, and further: unsinkability, controllability, marine propulsion, life time, manufacturability, etc.
In other words, with due consideration of the systematic approach for the project optimization by economic criterion, the separate functional or technological properties referred for the asset as a whole should be considered as parts of real asset or marine company’s property complex.
Since the optimized object is defined as a single whole of parts and its divisibility into parts is inexhaustible, there is a concept of a more general object, part of which is optimized object, and also there is a concept of inexhaustibility of induction, that is, methodological generalizations of optimized objects, by analogy to inexhaustibility of deduction – methodological divisions of objects into parts.
For example, the shipping, the shipbuilding industry, the marine engineering, the marine industrial fishery etc. would be a more general object in project optimization by economic criterion, than a commercial vessel, in methodological sense.
It should be noted, that representation of the marine company real asset optimized by economic criterion, as a whole of parts for dialectic definition of the objects properties absent in separate parts and appeared when connecting the parts, leads to definition of hierarchy of the economic models used for project optimization.
Except the economic model of optimized object there supposed to be the models with more general objects, that is, the models of «top levels», as well as economic models of separate parts of the optimized object, more exactly – the separate properties referred to an object as a whole, – the models of the «bottom levels». And as a result of the decision of more general, so–called external subjects of optimization of «top levels» are defined the data set Z (constants) which in subjects of «top levels» were optimized variables X are defined.
It allows us to formulate the concept of options comparability in process of optimization of the project by the economic criterion, in other words, the concept of similarity of options compared when optimizing the real asset or the property complex of the marine company, that differ by characteristics X, and are similar by other characteristics.
The concept of options comparability, which is the options similarity, means, that at the variables X range – the combinations of optimized object characteristics compared by the economic criterion – the data Z, which are determined as variables X in a more general subject of optimization remain unchanged and similar.
It should be added, that in process of detailed elaboration of marine company’s property complex into parts and optimization of separate parts, that is in each case of the whole object considered from the point of view of a part of design methodology (the separate functional properties related to the object as a whole), variables X, which are determined in optimization of the whole object, become data Z in subjects of project optimization of «the bottom levels» for object’s parts.
And the structure of variables X in subsystems (that is for a commercial vessel or another asset, estimated from the point of view of separate functional property) for subjects of «the bottom levels» is defined among the set of independent characteristics which in optimization of the whole object were parameters Y and were taken expertly, for example, according to a prototype.
Thus, the criterion function f in project optimization of the marine company real asset by the economic criterion is defined depending on variables X, parameters Y and data Z. Thus the comparability of options compared by economic criterion that differ by the values of varied variables X is provided.
The criterion function is formalized as an economic model of optimized object which is a sequence of dependences between variables X, parameters Y and data Z, on the one hand, and the basic economical indexes: the income I, the operation costs Ñ and investments MV or RC, on the other hand.
And any of the economic criteria used in optimization in the form of the criterion function f, is based on the correlation of the basic economical indexes – the income I, the operation costs Ñ with the investments MV or RC.
It’s worth mentioning, that the criterion function f is a mathematical generalization over the income I, the operation costs Ñ and investments MV or RC and is defined depending on variables X, parameters Y and data Z of optimized object, since the basic economical indexes are defined depending on variables, parameters and data.
It is necessary to add, that besides the specified economic indexes: I, Ñ and MV or RC by which the economic criterion f depending on the values of vectors is defined: X, Y and Z, there are also generalized variables (intermediate values), dependent on X, Y and Z that are used in the structure of economic model during optimization.
For example, if in case of vessel optimization the displacement empty DP and deadweight DW are referred to a number of independent variables X, the cargo displacement, which is the sum of deadweight and displacement empty D = DP + DW, does not enter in the structure of independent variables and is a generalized variable.
It should be added, that for the applied purposes choose the set of independent variables X (vessel characteristics, other real asset or property complex of the marine company), varied in process of optimization by the economic criterion, it is reasonable to use practical recommendations in the form of the following properties of independent variable:
– It substantially influences on the economic criterion of optimality;
– It is not determined unequivocally by other characteristics which are independent variables;
– It is ranged changeable, that is, it differs for comparable variants;
– It has numerical measurement – it is expressed by a real number (that is, the discrete characteristics and non–numerical, as for example vessel class, shouldn’t be included in a set of the independent variables varied by optimization).
Usually, when the specified practical recommendations are observed, the criterion function is continuous in the range of definition, smooth in mathematical sense and convex.
The economic criterion functions which can be applied in optimization of vessel project characteristic, other real assets or marine company’s property complex are reviewed below without going into details. Besides, the examples of criterion functions practical use are shown in the form of graphs.
Test questions
1. Economic definition of the innovative marine industrial activity.
2. Subject of the investments planning when choosing of optimal characteristics the marine company real asset.
3. Object of optimization by the economic criterion.
4. Basic economic indexes.
5. Criteria of efficiency and the criterion of optimality.
6. Ways of economic criteria transformation to the value.
7. The criterion of an economic optimality as a way of general and comparative efficiency indicators application.
8. Criterion function and the economic model.
9. Definition of the structure (set) of variables for optimization.
10. Signs of the set of parameters.
11. Systematic approach and comparability of options in case of optimization by the economic criterion.
12. Definition of the data set (external data).
13. Practical recommendations for definition of the independent variables set.
22.2. Economic criteria of characteristics optimization of vessel or property complex of the marine company for the commercial order, based on costs minimization
The criterion of the discounted costs (the specific costs as discounting of operation costs and investments by the discounting rate i) with the assumption of set life time T of the marine company real asset in the form of criterion function is defined as . 
(22.1) 
And the economic model used in project optimization of the marine company real asset consists of dependences for determination of the basic indexes: , , , and also effect and from the dependence of one criterion or another in the form of the criterion function on the basic indexes.
The basic indexes in themselves: the income I, the operation costs C and investments MV (or RC), – do not reflect critical judgments, suitable for a choice of optimum results in investment planning. For example, it is impossible to determine, whether it is necessary to reduce the operation costs C or not, since much depends on how the index of the income I thus will change., 
(22.2) 
,  (22.3) 
Test questions
1. Practical recommendations for determination of the set of independent variables definition.
2. Criterion of the discounted costs (the formula derivation).
3. Advantages of cash flows discrete summation.
4. Transformation of the discounted costs criterion to the criterion of the resulted costs (the formula derivation).
5. Application of discounting by exponential function of the Euler’ number in economic criteria (the formula derivation).
6. Methodological assumptions in case of use the economic criteria for optimization of the vessel characteristics or other asset of the marine company.
7. Criterion of internal rate of return (the formula derivation).
8. Macroeconomic index of total risks according to the discounting rate and the real interest rate.
9. Relative property of commercial vessel economic life time or other asset of the marine company with the account payback and the macroeconomic index of commercial risks.
22.3. Optimality criteria of commercial vessel project characteristics, assets or property complex of the marine company, based on an estimation of profitability indexes
The criterion function of the internal rate of return IRR is defined as
, 
(22.4) 
, 
(22.5) 
, 
(22.6) 
For estimations when investing in the purchase at the second–hand market there is an expert problem of correlation of additional risks with planned indexes of efficiency, which for the second–hand market are substantially higher.
And efficiency of investments at the second–hand market increases (fig. 22.6) in the relative value owing to the depreciation of the vessels or other assets over the time, and risks of investing thus grow.
The estimation of growing risks balance and estimated indexes of efficiency is required. Apparently, in some cases it should be recommended to limit the efficiency with a view of decrease of investment risks.
At the same time, there are companies which bought not new vessels on regular basis, and this activity with the account the ability of their managers to strategic planning, generally gave the positive results.
It should be specified, that strategic planning usually is aimed at the reduction of risks in conditions when the basic branch activity involves commercial risks.
.
For example, if the source of income and profit is the purchase and use of not a new vessels before the decommission in the productive operation, the recommended object of innovative investment can be the development of shipbuilding, that, by the way, corresponds to the above mentioned example of Onassis’ activity, that is, the preferable object of investment is usually located in adjacent economic and branch space in relation to the basic industrial profile activity, to be exact, the preferable object of investment is an economic reflexion of branch activity.
, 
(22.7) 
, 
(22.8) 
or for the discounting by the exponential function of The Euler’ number
.
,  (22.9) 
, 
(22.10) 
, 
(22.11) 
, 
(22.12) 
Test questions
1. Criterion of the internal rate of return for optimization of the commercial vessel or other asset of the marine company for the commercial order (the formula derivation).
2. Criterion based on indexes of profit and capitalized costs with the account the limited life time of the commercial vessel.
3. Economic criterion of the net present value (the formula derivation).
4. Criterion of the net present value determined with the account the limited life time of the commercial vessel (the formula derivation).
5. Possibility of application of the criteria which is not expressed by economic indexes for estimation of efficiency and for comparison of variants of investment in marine industrial activity.