Field Working Paper 8
Selecting the optimum combination of fish systems
for a district in Ghana

based on the work of

Ulf N. Wijkstrom (FAO Consultant Economist)
M.M.J. Vincke (FAO Senior Aquaculturist)

FOOD AND AGRICULTURE ORGANIZATION OF THE UNITED NATIONS
Rome, 1990

1. The problem

Those implementing a fish farm development strategy should have a clear concept of which combination of fish farming technologies that are best suited to the various parts of the country. In Ghana this means that the concerned fishery and agricultural extension staff should know which combination of tilapia farming systems that are most likely to suit a particular district and region.

The solution to this problem should take the following relationships into account:

• Income (sales revenue); the district (local) market for fresh tilapia and catfish is likely to be limited and although there will be markets in major urban areas, the cost of transport must be considered.
• Income (opportunity cost); the farmer will want to earn at least as much on the inputs he uses in fish farming as he could have obtained in the most rewarding alternative farming enterprise.
• Inputs; the quantity of agroindustrial byproducts/manures are limited and this must be acknowledged.
• Transport; the cost of transport may not exceed the net profit (after considering the opportunity costs of inputs).

2. Available data for each district

1. Net profit per ha/year for each of the eleven typical culture systems; (nation-wide)
2. Net profit per ha/year for the “best” alternative crop;
3. Kgs of fish produced per ha and year for each of the eleven culture systems (nation wide);
4. Human population;
5. Livestock population; cattle, pigs, chickens;
6. Availability of selected agro-industrial byproducts;
7. Per capita fish consumption
8. Transport cost for fish with ice in insulated containers, Cedis per kg-km;
9. Transport cost for manure and/or agroindustrial byproducts, Cedis per kg-km;

11. Distances in road-kilometres between district centres (geographical or administrative) and the following Urban markets: Accra, Tema, Takoradi-Sekondi, Kumasi, Tamale;

3. Problem solution

There are several steps in the algorithm needed to solve the above problem. First, several relationships, including maxima and minima, need to be calculated. These then need to be considered simultaneously for each district to discover the optimum combination of technologies for that district. Linear Programming might be used for a first approximation at a solution.

3.1 Calculations of maxima and minima

1. Net profit per ha/year for the best farming system multiplied by 2 gives the Minimum Net Profit for the Fish Farming Alternative (MNPFFA). This reasoning behind this constant of 2¹ is explained in Field Working Paper 9.

2. Maximum expenditure on transport (MET). The expenditure on transport for a particular fish farming system should not exceed the MNPFFA. Thus, for each farming system MET = MNPFFA.

3. Maximum input quantity (MIQ) is established as a share of local availability. The maximum share is calculated by input as follows:

   • cow manure: 1/3 × 16.000 × district cattle population;
   • pig manure: 1/3 × district population/100;
   • chicken manure: 0.2 × dist. ch. pop./30.000;
   • rice bran: 0.2 × mt rice/year × “yy”/“zzz”
   • palm kernel press cake: 0.2 × mt nuts/year × “yy”/“zzz”

4. Quantity for district market this is established as follows: district population × per capita consumption × 0.15 × 1.05⁵ (QDM).

5. Quantity for urban market (QUM). The quantity is equal to the total quantity produced less the quantity for district market.

¹ In fact the constant should reflect the specific water needs of each “opportunity” crop in relation to the needs for fish farming. The data needed for this refinement has not been available to the author.

3.2 Problem formulation

(x k p + x s p + x c p . . . . . y p × z p) < MEPxM
(x k p + x s p + x c p . . . . . y p + z p) <MEPxM

(x k p + x s p + x c p . . . . . y p + z p) < MEPxM

K p + S p + C p . . . . . Y p + Z p = TOTMEP

Significance:

Relationships:

Task:

(i) To maximise the “net (opportunity) profit”. This means that transport costs should be as small as possible per district.

This means that the difference between TOTMEP and the total costs of transport should be as large as possible. The “total sum of transport” is the combined value of all positive statements on the left-hand side of the “<” mark. This should be maximized respecting two types of conditions:

1. the total costs of transport required for any individual culture system can not exceed the total maximum net profit for the system; and,

2. the optimum culture system combination can not be allowed to use more feed/manure inputs than the maximum available in the district.

But the quantity produced “Y” is a function of inputs “x”.