6.1 Selection of Alternatives

6.1.1 Analysis of present-worth
6.1.2 Point of equivalence
6.1.3 Optimization techniques

The aim of this chapter is to enable the selection of alternatives for which capital might be required during a period, such as engineering projects or general business dealings. It is essential to consider the effect time has on capital, as capital must always produce some yield. If time-value relationships are not adequately accounted for, the results of the economic studies will be inaccurate and could lead to incorrect decisions. Appendix B gives a concise review of financial equations, necessary to calculate interest and time value of money.

6.1 Selection of Alternatives

Despite the fact that experience, intuition and judgement are still the dominating factors in high-level decision-making and in the majority of decisions at the operational level, significant progress has been made in the use of quantitative techniques that help the decision-making process through the use of economic models. Direct testing of alternative operational procedures is usually costly and, in many cases, impossible. However, the decision models and the simulation process provide a suitable medium where the evaluator can obtain information from the operations under his control without disturbing the operations themselves. As a result, the simulation process is essentially one of indirect experimentation through which alternative courses of action are tested before being implemented.

The economic models are formulated to provide the analyst with a quantitative base for studying the operations under his control. The method consists of four steps:

The methodology applied in each case depends on its nature, and on a clear definition of the objective being pursued. Among the different methodologies available are:

Analysis of the present-worth and equivalence point will be discussed in this chapter, where a brief introduction to optimization techniques has also been included. Methods to calculate project profitability and break-even analysis will be discussed in the next chapter.

6.1.1 Analysis of present-worth

The decision-making criteria must incorporate an index, equivalence measure or base for comparison that summarizes significant differences between different proposals. The relationships and equations developed here are the necessary elements that allow comparisons to be made between two or more alternatives that have the same or different useful life. Data required include initial investment, uniform or irregular operating costs, salvage value and useful life.

The alternatives that can be obtained are the result of considering different sums of money in relation to different times, within the useful life of the alternatives. To enable the most appropriate selection to be made, these alternatives must be reduced to a common time base, that is, the comparison must be made at the same point on the time axis. The most common bases for comparison are:

Example 6.1 Selection of Alternatives with Equal Useful Life

Manual vs Mechanical Heading, Gutting and Labelling in Small Fish Canning Plants

Analyse the following proposal. Substitute machinery for labour in the heading, gutting and labelling operations in small fish canning plants in tropical countries. Production capacity is 10 000 cans of 125 g of sardines each, every 8 hours. Table 6.1 shows the investments and operating costs for each alternative. Ten % per year is adopted as the time value of the money. Working with these conditions, determine the most satisfactory decision that can be made from an economic point of view. Express the result as present-worth and annual uniform cost.

Table 6.1 Investment and Operating Costs for Alternatives A and B



Alternative A

Alternative B

Investment (US$)



Labour costs (US$/year)



Maintenance costs (US$/year)



Consumption of electricity (US$/year)

1 262


Insurance (US$/year)

1 596

1 398

Useful life (years)




Present-worth = PA10 = 172 930 + (42 408 + 7 965 + 1 262 + 1 596) x FAP 10%, 10 = 172 930 + 53 231 x 6.15 = US$ 500 300

Present-worth = PB10 = 154 006 + 81 076 x 6.15 = US$ 652 623

where FAP 10%, 10 is the value factor for an interest rate (i) equal to 10% for a 10 year (N) period (see Appendix B Table B.2).

Annual Uniform Costs = AA = PA10 x FAP 10%, 10 = 500 300 x 0. 163 = US$ 81 450

Annual Uniform Costs = AB = PB10 x FAP 10%, 10 = 652 623 x 0. 163 = US$ 106 377

where FAP10%, 10 is the recovery factor for i = 0. 10 (10 %) and n = 10 (FAP 10%, 10 = 1/ FAP 10%, 10) (see Appendix B, Table B.2).

The economic effect of the substitution of equipment by labour depends on the costs of the additional labour in relation to capital expenditure. From the preceding data, alternative B for intensive labour results in higher costs (30%). However, it could be considered that the social benefits arising from the increased employment will amply compensate for this economic disadvantage and tip the balance towards the adoption of labour intensive technology (Edwards, 1981).

Example 6.2 Selection of Alternatives with Different Useful Life. Natural and Mechanical Fish Drying

Analyse the natural or mechanical drying of small freshwater fish from an East African country (Waterman, 1977). Annual production is 53 t, with a yield of 32.5%, working at full capacity 12 hours/day, 250 days/year. The product is sold in bulk and not packaged. Mechanical drying is achieved in a small-scale drying chamber, indirectly heated by Diesel oil, with forced-air circulation and a 12-hour drying cycle. Its useful life is estimated as approximately 10 years. Consumption of fuel, electricity and labour will have to be taken into consideration.

Sun-drying is accomplished on frames built from wood and wire mesh, the useful life of which is one year. Just over 5 kg of fish can be spread out on 1 m2 of frame, and the drying cycle lasts 5 days. Double labour is used in this procedure. Table 6.2 gives all the values for investment and costs. Express the results as present value and annual uniform cost.

Table 6.2 Investment and Costs for Mechanical and Natural Drying


Alternative C

Alternative D

Investment (US$)



Labour costs (US$/year)



Maintenance expenses (US$/year)

1 200


Electricity consumption (US$/year)



Useful life (years)




PC10 = 9 000 + (1 200 + 4 440+375) x FAP 10%, 10 = US$ 45 992

PD1 = 720 + (750+360) x FAP 10%, 1 = US$ 1 729

where FAP 10%, 10 is the present value factor for i = 0. 10 (10 %) and a period of one year (n = 1).

It would not be equitable to compare the present-worth of the cost of 10 years service for alternative C with the present-worth of the costs of one year's service for Alternative D. Application of the following equation allows for conversion of the present-worth of an alternative with a useful life of (n) to its equivalent present-worth for any other useful life (k):

PK = PN x (FAP 10%, n / FAP 10%, k)                                 (6.1)

where FAP 10%, n is the capital-recovery factor over n periods and FAP 10%, k is the capital-recovery factor over k periods.

Equation (6. 1) was developed by Jelen (1970). In this case, the present-worth of the costs of alternative D for a period of 10 years is:

PD10 = 1 729 x  1.1 / 0.163 = US$ 11 668

Expressed in annual terms, (see P to A equation in Table B. 2, Appendix B) the values are:

AC = US$ 7 492 and AD = US$ 1 901

The economic comparison shows that natural drying has still a favourable annual difference of US$ 5 591 when compared with mechanical drying, even when calculations are adjusted for difference in useful life. Moreover, in practice, each comparison contains intangible elements. In this case, to obtain good production of naturally dried products in tropical climates, the following must be considered: temperature and humidity of the air, lean or fatty raw material, duration of rainy season, market characteristics and conditions where fish is marketed, etc. If monetary values could be assigned to all of these elements, they could be included in the quantitative analysis and thus substantially modify the result.

Nevertheless, with regard to fish drying, the economic difference in favour of natural drying continues to be very great in many practical situations, and this is basically why more technologically advanced drying methods have not been adopted in developing countries, despite the effort of developing agencies (national and international). It is worth mentioning that natural fish drying is still used in Japan and some Scandinavian countries.

6.1.2 Point of equivalence

In a situation where costs can be expressed as a function of a common decision variable (number of units of production, duration of operation, etc.) these alternatives can be analytically or graphically evaluated by applying the following criteria: Point of equivalence: is the value of the common decision variable for which the costs of both alternatives are equal.

For instance it is feasible to apply this decision model to the following options:

  1. With the prospect of a new frozen fishery product, it is necessary to assess the volume of production at which the costs of expanding the existing refrigeration capacity will be equivalent to the costs of using nearby refrigeration services; viz., whether refrigeration services should be rented or constructed;

  2. When the request of a client makes it necessary to acquire a new machine, the monthly operation time must be known in order to determine whether it would be more profitable to buy the machine instead of renting it.

Example 6.3  Determination of Equivalence Point Local vs Imported Mackerel for the Canning Fishery Industry

Analyse the costs of production for canned fish using local or imported raw material. Determine the price (expressed in US$1can) of the national raw material, which will be equivalent to the price paid for the imported raw material. The example corresponds to the situation which occurred in Argentina in 1986, when imports of H&G mackerel from Ecuador increased, as an alternative to canning. It should also be stated that there is a coastal fleet in Mar del Plata which engages seasonally in the capture of this species.

Data common to both alternatives:

Fresh mackerel (whole); local

H&G frozen mackerel; imported


Costs of equivalent production will be calculated (present-worth, with zero time at 15 November) for each of the possible raw materials. This will depend on factors such as: yield of raw material, value of import dollar, value of monthly interest rate. Those factors that differ in each alternative will be considered, since there are certain inputs (quantity of cans, consumption of vegetable oil as filling, income from sales, costs of direct labour, costs of indirect labour) that are equal for the same level of production (in quantity and duration).

Two production alternatives are considered using a simplified model. Such production plans are limited to a two month period. In a detailed analysis, however, an annual production programme would have to be examined, together with the sales forecast. Moreover, the opportunity costs of the working capital would have to be considered; that is, financial costs of packaging, raw material, labour and 30 days of finished product would have to be included (Parin and Zugarramurdi, 1986b). To achieve the desired production level using a national supply of mackerel, raw material must be purchased once a month. For imported mackerel, one purchase is made and the mackerel is kept frozen. Cold storage should be paid every 30 days, at a rate of US$ 1/t/day.

Local mackerel:

Raw material

1000 000 cans x 0.38 kg/can x (1-0.2) / 0.38  = 800 000 kg fish/2 months

20 000 boxes are therefore needed every two months (1 box = 40 kg).

Costs of Raw Material (Ci) : Prices between US$ 10 and US$ 20/box will be considered.

TCi = 10 000 boxes x Ci x (1 + 0.01)-0.5 + 10 000 boxes x Ci x (1 + 0.01) -1.5

TCi = 10 000 boxes x Ci x [(1 + 0.01)-0.5 +(1 + 0.01) -1.5

TCi = 10 000 boxes x Ci x (0.99504 + 0.98518)

TCi = 19 822.5 boxes x Ci                                                                     (6.2)

TC(1) = US$ 198 225.0 with C(1) = US$ 10/box

TC(2) = US$ 237 626.4 with C(2) = US$ 12/box

TC(3) = US$ 277 230.8 with C(3) = US$ 14/box

TC(4) = US$ 316 835.2 with C(4) = US$ 16/box

TC(5) = US$ 356 439.6 with C(5) = US$ 18/box

TC(6) = US$ 396 044.0 with C(6) = US$ 20/box

Imported mackerel:

Raw material

1 000 000 x 0.38 x (1-0.2) / 067 = 453 731 kg/2 months = 226 865.6 kg/month

FOB costs = US$ 390/t x 453.7 t = US$ 176 943

Importation costs = US$ 210/t x 453.7 t = US$ 95 277

Cold storage costs

For this calculation an average quantity of mackerel to be kept during the month should be estimated. Seven and a half tons are processed per day which implies a consumption of 225 t in 30 days. If, at the beginning of the first month, the quantity stored in the freezer was 453.7 t, the average quantity will be 339.35 t/day. The cost will be:

339.35 t x (US$ 1 / (t/day)) x 30 days = US$ 10 180.5

The average amount stored for the second month of production will be 117.4 t/day. Thus at the end of the month, US$ 3 522 will have to be paid. The present equivalent value for all costs (average interest rate 1 % per month, i = 0. 0 1) is:

TC = 95 277 + 10 180.5 x (1 + 0.0l)-1 + 3 522 x (1 + 0.01)-2 + 176 943 x (1 + 0.0l)-3

TC = US$ 280 531 (imported) (6.3)

The point of equivalence is defined in this case as the intersection of equations (6.2) and (6.3). This means that the following equation should be solved:

TC(x) = 19 822.5 x C(x) (US $)

TC(x) = 280 531 (US $)

The point of equivalence will be:

TC(x) = TC

from where:

C(x) =280531/ 19822.5 = 14.152 US$/box

This result indicates that the point of equivalence is reached at a cost of US$ 14.15/box of local mackerel. Costs of local raw material above this figure may induce local canneries to import raw material; below this figure, canneries will certainly buy mackerel from local fishermen. It may be useful to find the point of equivalence graphically (TC vs Ci, or TC per can vs Ci) in particular if there is an additional variable to study, for instance real interest rate (i). In Figure 6. 1, the case discussed here is solved graphically and, in addition, the cases of i = 0 and i = 0.03 are added for comparison.

Figure 6.1 Points of Equivalence for Two Different Alternatives of Raw Material (imported and local mackerel) at Various Real Interest Rates

In this example, it is clear that the higher the real interest rate, the lower the price (US$/box) local fishermen should sell their fish to compete with imported raw material.

Example 6.4 Selection of Equipment. Fish Filleting Machines

Analyse the different technological alternatives for the mechanical processing of hake fillets.


Annual equivalent costs were calculated for 12 mechanical lines resulting from a combination of the equipment used in industrial plants (heading, filleting and skinning machines) and refrigeration equipment in Mar del Plata (Argentina). Possibilities include local and imported equipment. Two broad groups emerge from analysis of the results; one with a type A filleting machine with less capacity and not performing the V cut, and the other with a type B filleting machine, greater capacity and speed, that performs the V cut.

The following differences are observed: yield (greater with type A filleting machine), labour utilization (greater with type A filleting machine) and investment (greater with type B filleting machine).

The values shown in Table 6.3 are for a capacity of 20 t of product daily. It is assumed that there is no variation in the overall yield of the operation. They were expressed as a function of the price of labour, which is the factor that changes most in the different countries. For example, it is observed that the price of labour in developing countries could be as much as 20 times lower than that in developed countries.

Table 6.3 Investment and Production Costs for Lines with Type A and B Filleting Machines  



Filleting Machines



Type A

Type B

Investment (US$) 

475 750

659 174

Labour costs (US$/year) 

530 690 CL(US$/h)

484 600 CL

Maintenance expenses (US$/year)

238 680


Fixed costs (US$/year) 

777 060


Useful life (years)10 




The annual equivalent costs for the line with the type A filleting machine will be:

AA = 475 750 x FPA + 530 690 x CL + 238 680 + 777 060

where FPA (10 %, 10 years) = 0. 1627 (FPA, capital-recovery factor, see Appendix B Table B. 2)

AA = 475 750 x 0. 1627 + 530 690 x CL + 238 680 + 777 060

AA = 1 093 144 x 530 690 x CL

AB = 659 174 x FPA + 484 600 x CL + 208 980 + 911 520

AB = 1 227 747 + 484 600 x CL

The point of equivalence is determined by equating the annual equivalent costs:


1 093 144 + 530 690 x CL = 1 227 747 + 484 600 x CL ..CL = US$ 2.92/h

The cost functions and the point of equivalence are shown in Figure 6.2.

Figure 6.2 Point of Equivalence for Selection of Equipment. Hake Filleting Machines (total installed capacity 20 t raw material/day)

For labour costs higher than US$ 2.92/h (without social charges), the alternative of using the line with type B filleting machine will be the most economical; but the line with type A filleting machine will be the most convenient for labour costs lower than US$ 2.92/11.

This example shows that the installation of a mechanized fish processing line can be a function of labour costs. The drive towards more sophisticated and automated fish and shrimp processing lines in northern Europe is a result of it. However, the need for this type of studies can arise in developing countries, for instance, when insufficient qualified manpower is available or when a given level of quality or safety should be attained and kept.

6.1.3 Optimization techniques

An important characteristic of the industrial world is the continuous improvement of its operations. Optimization is the mathematical representation of this idea. Any problem in design, operation and analysis of manufacturing plants and industrial processes can be reduced, in the final analysis, to the problem of determining the maximum value of a function of different variables.

Many methods have been introduced to determine optimum processes or policies. Optimization methods provide efficient and systematic means for choosing from among infinite solutions, occurring in problems with a large number of decision variables.

Optimization techniques can encompass analytical and numerical methods, which be chosen as a function of the nature of the objective function, and the restrictions which define the model. In order to resolve the most common problems in the fishery industry, two techniques are widely used:

  1. Linear Programming (LP) is a mathematical tool that finds the optimum solution for the efficient use or allocation of limited resources in linear systems. It is the technique most widely used for economic analysis. The results obtained through LP can also be acquired by determining the optimum combination of resources outlined in the micro-economic treatment of production. In this case, production requirements from a set of restrictions similar to those which define the isoquants, and the prices of the inputs are represented by the isocost lines. Other applications of LP, such as problems of inventory control, transport, product formulation, etc., may also be mentioned.

  2. Dynamic Programming (DP) is a strategy which is especially applicable to the solution of problems with multiple stages. It allows complex problems to be broken down into a sequence of simpler sub-optimization problems. Some applications of DP are problems of replacement, shipment, allocation of capital and other inputs. Numerical techniques have also been developed to formulate programmes and control projects. These techniques are: Critical Path Method (CPM) and Programme Evaluation and Review Technique (PERT). The latter is used in instances where it is impossible to make a precise estimate of time, costs and results, and probability and statistics concepts must be used to make predictions.

Example 6.5 Application of Dynamic Programming. Operation of an integrated fish processing plant (canning, salting and freezing)

As an example of the use of optimization techniques, an economic comparison of the operation of integrated and individual plants (Zugarramurdi and Lupin, 1976a) is presented. The integrated plant is composed of canning, salting and freezing plants. The first step in simplifying the system is to assume that the plant will process hake (annual species) and anchovy, mackerel or bonito (seasonal species) simultaneously.

By applying the Bellman principle of optimality, a sequential sub-optimization of a step-by-step process is arrived at, according to the Dynamic Programming strategy. Given that the problem can be divided into a series of identifiable steps, within each of the plants, it seems appropriate to apply this technique in the search for the optimum solution. The scheme of the system to be optimized is as shown in Figure 6.3 where:

CA = entry of anchovy, t/day;

CM = entry of hake, t/day;

AC = quantity of anchovy to be processed in the canning plant, t/day;

AS = quantity of anchovy to be processed in the salting plant, t/day;

A' = entry of anchovy in the salting and freezing plants, t/day;

AF = quantity of hake to be processed in the freezing plant, t/day;

GC = risk profit of the canning plant, US$/year;

GFS = risk profit of the freezing and salting plants, US$/year.


Figure 6.3 Dynamic Programming: Information Flow 

In this plan, freezing and salting plants have been considered together, with the restriction that all raw material received must be processed. The plan is currently much simpler, as hake has not been considered as raw material for the canning plants over the last few years. If this option was considered, the proposed system would be modified, with the introduction of the variable CM in the block corresponding to the canning plant, and another design variable, MC, being introduced in the same block.

The definition of any optimization problem is to maximize or minimize (optimize) the objective function acting on the decision variables, considering all the restrictions of the system to be optimized. The problem can thus be stated as follows:

Ma x G = NP - i x Iw - (i + h) x IF


G = risk profit
NP = net profit
i = rate of return
Iw = working capital
h = level of risk
IF = fixed investment

Once the problem has been presented in this way, it is obvious that there are infinite possibilities for the distribution of raw material among the different plants. The use of the Dynamic Programming technique allows the optimum combination of variables for each entry value of raw material to be known. The Bellman Principle of Optimality indicates that the last step (salting and freezing) must be optimized with respect to the supply that it receives from the variables A' and CM. This means that the value of AS and MS which succeeds in maximizing the partial objective function GFS for any value of CM and A' is optimum.

Once the final step is optimized, the value of AC, which will maximize the partial function of the canning step, plus the maximum of the last function, must be chosen.

The last step of this calculation strategy is the collection of the information in order to prepare an optimum plan for the operation of the integrated plant, as a function of the raw material entering the plant daily. This is outlined in the following calculation sequence:

Data = CA and CM

  1. From the graph or table resulting from the optimization of the canning stage, the optimum value of AC* is obtained.

  2. A' = CA - AC*

  3. From the table or graph resulting from the optimization of the salting and freezing steps, with the values of A' and CM, optimum values of AS* and MS* are obtained.

  4. From the design relationship in this last step, one obtains:

AF* = A' - AS*

MF* = CM - MS*

Table 6.4 lists the values of the design variables for a integrated plant and the corresponding values for individual plants. In both cases the operation is taking place with a saturation of raw material (CA = 184.5 t/day and CM = 34.5 t/day). A point to be discussed is the inclusion of the fishmeal plant. If it is added to the integrated plant (which is logical) the costs of raw material will be practically nil, since it will use trimmings, remains and material discarded by the other plants. If the individual plant operates with trimmings and remains, it will have to buy them.

The profit of the integrated plant compared to the individual plants working separately, when the fishmeal plant is not included, is increased by 28%, while if it is included, the profit would increase by 57%. It should be pointed out that eventually an integrated plant can operate with only one of its production lines, in this case the frozen line, with a profit lower than that of an equivalent plant operating alone.

This situation occurs, since the optimum point of all the plants taken together is not necessarily equal to the sum of the optimum points of the individual plants. As a result, the quantities to be processed in the integrated plant do not correspond to the maximum of the individual plants, but to those which result from the application of the method of dynamic programming to the system. On the other hand, the application of this method can be extended to determine the form in which costs will vary for a similar product manufactured by an individual plant and an integrated one. The result is a reduction of unit costs., For example, for the manufacture of canned products, the unit cost of the product in the integrated plant will be 20% lower than in the individual canning plant.

Table 6.4 Comparison of an Integrated Plant with Individual Plants


Individual Plants
Optimum Value (t/day)

Integrated Plants
Optimum Value (t/day)


AC = 150

AC = 131.1


AS = 4.32
MS = 4.68

AS = 4.4
MS = 4.6


AF = 31.78
MF = 28.22

AF = 49
MF = 30

Although optimization techniques are, with few exceptions, not utilized in developing countries, they are utilized in developed countries by medium and large food and fish companies, and consultant companies which provide technical advice to the fishery industry.

Optimization techniques require a sound technical and analytical knowledge of the system to be optimized. In most cases, it means the possibility to develop a mathematical model incorporating the most relevant variables. Application of optimization techniques is relatively common in today's most developed fishery industries.

The on-line simulation for product management that Scandinavian fishery industries expect to introduce by 1995 is basically a real time optimization programme. Some fish processing machines and equipment have already incorporated optimization techniques, e.g., in the robots that utilize vision techniques to eliminate bones and portion fillets.

Optimization is also already implicitly incorporated at the design stage in multi-stage compressors in refrigeration and multi-stage evaporators of fishmeal plants, improving efficiency and reducing costs. Optimization techniques have also been used, for instance, to calculate sterilization (or pasteurization) times in canned products, maximizing nutrient retention or texture characteristics, and to optimize packaging design (e.g., maximum strength vs minimum packaging material). In countries where information on nutrient composition on the labels is mandatory, as in the USA, processes that optimize nutrient retention are essential. In most cases, such procedures are the result of applied research at company level and therefore not available to the public.

Optimization techniques are also utilized in the design and production of fish feed for aquaculture in order to obtain a maximum in nutrient value at a minimum cost with the available raw materials. Optimization techniques are a part of modern management techniques. Although they are not yet a customarily used tool of the fish technologist in developing countries, they should be incorporated as such if self-sustainability is sought. The next step to the use of economic engineering is the application of optimization techniques.