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:
2. Available data for each district
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
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.
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.
Maximum input quantity (MIQ) is established as a share of local availability. The maximum share is calculated by input as follows:
Quantity for district market this is established as follows: district population × per capita consumption × 0.15 × 1.055 (QDM).
Quantity for urban market (QUM). The quantity is equal to the total quantity produced less the quantity for district market.
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:
(i) | line | each line represents a production function for one distinct culture technology; |
(ii) | k,s,c | are constants indicating the quantity of input needed to raise fish in one hectare of ponds according to culture system 1 to 11 |
(iii) | x | a variable, indicating the number of units of the particular input that is going to be used in the particular solution/alternative under study. |
(iv) | K,S,C | are constants indicating the maximum quantity of the inputs (economically) available for fish farming in the district. |
(v) | P | are constants indicating the cost of transport per kg-km for respective inputs and outputs. |
(vi) | M | variable, indicating the total kgs of fish produced by the activity in the district. |
(vii) | y | constant, indicating the quantity (kgs of fish) to be marketed in the district. |
(viii) | z | variable, indicating the quantity (kgs of fish) to be market in the nearest urban area. |
Relationships:
(i) | M = Y + z | |
(ii) | K = k + k | + …. + k |
(iii) | S = s + s | + …. + s |
(iv) | C = c + c | + …. + c |
(v) | M = q × x | |
(vi) | M = q × x | |
(vii) | M = q × x |
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:
the total costs of transport required for any individual culture system can not exceed the total maximum net profit for the system; and,
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”.