Postharvest loss is one major problem farmers in Adaklu Traditional Area that most Ghanaian farmers face. As a result, many farmers wallow in abject poverty. Warehouses are important facilities that help to reduce postharvest loss. In this research, Beresnev pseudoBoolean Simple Plant Location Problem (SPLP) model is used to locate a warehouse at Adaklu Traditional Area, Volta Region, Ghana. This model was used because it gives a straightforward computation and produces no iteration as compared with other models. The SPLP is a problem of selecting a site from candidate sites to locate a plant so that customers can be supplied from the plant at a minimum cost. The model is made up of fixed cost and transportation cost. Location index ordering matrix was developed from the transportation cost matrix and we used it with the fixed cost and differences between variable costs to formulate the Beresnev function. Linear term developed from the function which was partial is pegged to obtain a complete solution. Of the 14 notable communities considered,
Food crop production is the major occupation of the people of Adaklu. About 85% of the citizenry depend on these food crops for their wellbeing. Major food crops like maize, cassava, groundnut, and yam are produced.
The farmers largely depend on the natural rainfall for the cultivation of their crops. Food crops are cultivated annually. During bumper harvest, however, food crops are left exposed to bad weather and animals for destruction. Bushfire most of the time also destroys food crops stored in farm by farmers. Farm produce most of the time is stolen by thieves as there is no proper storage of the crops.
To prevent food crops going waste, most farmers do sell their food crops at very cheap prices, thereby making huge losses.
The objective of this study is to help locate a place where warehouse could be built to store farm produce. It is also to help farmers minimize cost of transporting farm produce to market centers. Warehouses are basically used for storing raw materials and finished goods [
Quite a number of studies dealing with location of warehouses and similar facilities have been carried out in many different countries [
On problem of Mathematical Standardization Theory, Beresnev [
Hajiaghayi et al. [
The data obtained for this project is from two main sources.
The first data is the distances between various (notable) towns in Adaklu Traditional Area. (refer to Appendix
The second data deals with the estimated cost for establishing a modern warehouse in each community in the area. Masons, carpenters, and dealers in building materials in the communities were engaged in providing estimates for putting up the warehouse.
Adaklu Traditional Area is located at the eastern part of Ho, the Volta Regional Capital. It is made up of 46 small towns and villages with Adaklu Abuadi as its traditional capital. The area is not opened to commercial activities as the communities are widely dispersed and the road network is in a very deplorable state. Food crop farming is the major occupation for the people. Unfortunately, due to its inaccessibility and noncommercial nature, food crops obtained are spoilt over time as a result of postharvest losses (a sketch map of the traditional area is shown in Figure
Fourteen notable communities (see Appendix
The figure shows the coded values of the fourteen communities with the distances linking them. The distances are shown on the arcs of the network and the fixed costs (in Gh
The Beresnev pseudoBoolean SPLP is formulated as follows [
with the following conditions:
if
if
if
In (
Input edge matrix and the vector of facility setup cost (Appendix
Do all pairs shortest path for the
All pairs shortest path for edge matrix (see Appendix














 


3600  0.0  12.0  17.0  19.5  20.5  22.5  13.0  18.0  25.0  30.0  32.5  33.5  34.0  40.5 

1800  12.0  0.0  5.0  7.5  8.5  10.5  25.0  30.0  23.5  18.5  21.0  21.5  22.5  29.0 

3800  17.0  5.0  0.0  2.5  3.5  5.5  30.0  25.5  18.5  13.5  16.0  16.5  17.5  24.0 

2100  19.5  7.5  2.5  0.0  1.0  3.0  28.0  23.0  16.0  11.0  13.5  14.0  15.0  21.5 

4600  20.5  8.5  3.5  1.0  0.0  2.0  27.0  22.0  15.0  10.0  12.5  15.0  14.0  20.5 

3050  22.5  10.5  5.5  3.0  2.0  0.0  29.0  24.0  17.0  12.0  14.5  17.0  16.0  22.5 

3200  13.0  25.0  30.0  28.0  27.0  29.0  0.0  5.0  12.0  17.0  19.5  32.0  21.0  27.5 

5100  18.0  30.0  25.5  23.0  22.0  24.0  5.0  0.0  7.0  12.0  14.5  27.0  16.0  22.5 

3700  25.0  23.5  18.5  16.0  15.0  17.0  12.0  7.0  0.0  5.0  7.5  20.0  9.0  15.5 

6200  30.0  18.5  13.5  11.0  10.0  12.0  17.0  12.0  5.0  0.0  2.5  15.0  4.0  10.5 

3700  32.5  21.0  16.0  13.5  12.5  14.5  19.5  14.5  7.5  2.5  0.0  12.5  6.5  13.0 

1500  33.5  21.5  16.5  14.0  15.0  17.0  32.0  27.0  20.0  15.0  12.5  0.0  17.0  23.5 

5950  34.0  22.5  17.5  15.0  14.0  16.0  21.0  16.0  9.0  4.0  6.5  17.0  0.0  6.5 

1015  40.5  29.0  24.0  21.5  20.5  22.5  27.5  22.5  15.5  10.5  13.0  23.5  6.5  0.0 
Find location index ordering matrix for the transportation cost matrix
Compute differences between elements of each column in the transportation cost matrix using the formula
Use the result in Step
Compute coefficients of the linear term
Peg partial solution to obtain complete solution and then draw conclusion.
Equation (
Equation (
Equation (
Computation of optimal site and objective function values is as follows.
We observe that the coefficients
Condition (b) holds; that is,
Now
To obtain complete solution, we peg the coefficients
We arrange the coefficients
We assign the solutions
From
For the cost, we substitute the solution
Result of (







114 



201 



235 



261 



263 



246.5 



148 



200.5 



248 







254 



168.5 



240.5 



159 

We observe that the smallest
Hence, by condition (c), the warehouse for the traditional area must be located at
The total cost involved is Gh
The Beresnev SPLP model is quicker and hence effective for the project. In view of the fact that the authors prefer Beresnev model to the other models, these other models were not used again in the modeling of the actual data.
The Beresnev pseudoBoolean SPLP was used to model the data. It was used because it is a straightforward computation and it produces no iteration. The time used for obtaining the expected solution is also quicker.
From the analysis, of the 14 candidate sites considered for the location of the warehouse, Adaklu Waya is the most suitable site for the location of the warehouse.
The total cost involved is Gh
See Figure
See Table
From  Waya  Anfoe  Waya  Torda  Kpetsu  Abuadi  Tserefe 


To  Torda  Akoete  Kpatove  Wudzedeke  Ahunda Boso  Tserefe  Xelekpe 


Distance (km)  4.0  12.5  5.0  6.5  12.0  1.0  2.5 
From  Xelekpe  Waya  Kpatove  Ablornu  Kordiabe  Waya 


To  Kpetsu  Abuadi  Ablonu  Kpeleho  Abuadi  Anfoe 


Distance (Km)  5.0  10.0  7.0  5.0  2.0  2.5 
See Table
Codes 









Communities  Ahunda Boso  Kpetsu  Xelekpe  Tserefe  Abuadi  Kordiabe  Kpeleho 
Codes 









Communities  Ablornu  Kpatove  Waya  Anfoe  Akoete  Torda  Wudzedeke 
Equation (
Consider
See Code
function lip(a)
% to arrange numbers in ascending order
n=length (a);
for j=n:1:1
for i=1:j1
if a(i)>a(i+1)
p=a(i);
a(i)=a(i+1);
a(i+1)=p;
end
end
end
disp(a)
See Code
% input transportation cost matrix c
functiongoslow(G)
for k=1:n
for i=1:n
for j=1:n
if i==j
G(i,j)=0;
elseif G(i,j)==inf
G(i,j)=min(G(i,j),G(i,k)+G(k,j))
end
end
end
end
end
(
The authors declare that they have no competing interests.