3.1. Proposed System Model for Distributed Retail Enterprises
This section explores the proposed system model for BI analytics in distributed retail enterprises. The proposed model has three layers, namely data cleaning and formatting, intelligent model and distributed product shops, as shown in
Figure 3. The data cleaning and formatting layer is found at the bottom of the proposed model. In this proposed model, data is collected from transactional systems branch per branch. The data is cleaned and formatted to the appropriate file type accepted by the proposed model. Processed data is input into the ARANN model branch per branch at the middle layer of the analytical model. The ARANN model cooperatively works between AR and ANN. Processed data from the bottom layer is passed into the AR model and it outputs confidence and support values. These values are passed into the ANN model as inputs in order to get the degree of belief (DoB). The DoB of sets generated is compared to the ARANN activations set. The accepted sets generated are applied on the top layer of the proposed model. This proposed model is deployed to each branch and patterns are generated independently. The choice is left for every retail enterprise branch to adopt the best results, depending on the market competitiveness and profit levels.
Figure 3.
Proposed intelligent analyticsbased framework.
Figure 3.
Proposed intelligent analyticsbased framework.
The proposed intelligent analyticsbased framework has the following benefits: reduction in risk of passing misleading results to all branches, no one point of failure, consumption of fewer resources, faster construction of distributed systems and no need for data integration.
This proposed analyticsbased model can be implemented using the pseudocode presented in
Table 1.
Table 1 shows how ARANN generates product arrangement sets that can be used by retail enterprise managers to arrange products on shop shelves so as to attract customers to purchase more products than planned. The pseudocode is further presented mathematically, as shown in Equations (5)–(14).
Table 1.
Pseudocode for ARANN model.
Table 1.
Pseudocode for ARANN model.
 Pseudocode 

Steps  Input: Transactional data in database (D) = {t_{1}, t_{2}, t_{3}, .., t_{n}} 
Support () 
Confidence () 
Weights (W) = {w_{1}, w_{2}, w_{3}, .., w_{n}} 

Output: Products pattern 
 Step 1: D = {t_{1}, t_{2}, t_{3}, .., t_{n}} //Transactions in the database 
Step 2: C_{k} = Candidate item set of size k 
Step 3: F_{k} = frequent item set of size k 
{ 
for (k =1; F_{k} != Ø; k++) // F_{k} is not equal to empty set. 
{ 
Scan the entire D to generate candidate sets C_{k} 
{ 
Compare candidate support count from C_{k} with the minimum support count to generate F_{k} 
} 
} 
Step 4: Generate Support () & Confidence () 
{ 
Step 5: Input Support () & Confidence () into Neuron 1 (N_{1}) and Neuron 2 (N_{2}) as inputs 
Step 6: Generate N_{1} by summing of the inputs with the corresponding weights and apply the output into sigmoid function 
Step 7: Generate N_{2} by summing of the inputs with the corresponding weights and apply the output into sigmoid function 
Step 8: Generate the summation of N_{1} & N_{2} after the sigmoid function and apply the output into sigmoid function to obtain Degree of Belief (DoB) 
Step 9: Display products pattern where
DoB ≥ ARANN activation 
} 
} 
Mathematical description for the ARANN Model
The sup and con values feed the N_{1} as the inputs and are multiplied with the corresponding weights.
The output of N
_{1} after the sigmoid function
The sup and con values feed the N
_{2} as the inputs and are multiplied with the corresponding weights:
The output of N
_{2} after the sigmoid function
where
N_{1} and
N_{2} are Neuron 1 and 2 respectively;
W_{1},
W_{2}_{,} W_{3}, W_{4},
W_{5} and
W_{6} are the corresponding weights;
O_{1} is Neuron 1 output after sigmoid function;
O_{2} is Neuron 2 output after sigmoid function,
F is input to final Neuron and
ARANN activation is the threshold value set.
3.3. Scenario—Arrangement of Products on Shelves for Distributed Retail Branches
Figure 4 shows a scenario of how the analytical model displays placement results in distributed branches. Transactional data from each retail branch is loaded into the ARANN model to determine the arrangement sets.
Figure 4.
Intelligent Analyticsbased Model for Four Branches.
Figure 4.
Intelligent Analyticsbased Model for Four Branches.
Table 3.
Market basket transactional data for branch 3 of a retail enterprise.
Table 3.
Market basket transactional data for branch 3 of a retail enterprise.
Marketbasket Transaction Data—Branch 3 

TID  ITEMS 
T300  Colgate, Vaseline, Geisha, Margarine, Bread 
T301  Margarine, Bread, Coke, Colgate, Vaseline 
T302  Coke, Colgate, Chocolate, Bread, Sweets, Margarine 
T303  Geisha, Colgate, Chocolate, Towel, Vaseline, Sweets 
T304  Colgate, Vaseline, Sweets, Chocolate, Bread, Margarine, Coke 
Even weights were applied to each corresponding input to avoid bias on products. This was obtained by dividing the count of a_union_b over a number of records within the data set, where
a, and
b are different products. The following ARANN activation was used:
>= 0.75 strongly connected products (strongly accepted)
>= 0.65 moderately connected products (accepted)
< 0.65 weakly connected products (rejected)
{Colgate, Vaseline} => {Bread}
Support = $\frac{n(A\cup B)}{N}=\frac{3}{5}=0.6$ Confidence = $\frac{n(A\cup B)}{n(A)}=\frac{3}{4}=0.75$
N_{1} = Supw_{1} + Conw_{3} N_{2} = Conw_{4} + Supw_{2}
= (0.6 × 0.6) + (0.75 × 0.6) = (0.75 × 0.6) + (0.6×0.6)
= 0.81 = 0.81
O_{1} = $\frac{1}{1+{{\displaystyle e}}^{N1}}=\frac{1}{1+{{\displaystyle e}}^{0.81}}=0.69$ O_{2} = $\frac{1}{1+{{\displaystyle e}}^{N2}}=\frac{1}{1+{{\displaystyle e}}^{0.81}}=0.69$
F = w5O_{1} + w6O_{2}
= (0.6 × 0.69) + (0.6 × 0.69) = 0.83
DoB = $\frac{1}{1+{{\displaystyle e}}^{F}}=\frac{1}{1+{{\displaystyle e}}^{0.83}}=0.70$
Product pattern => 0.70 >= 0.65
Therefore it is moderately connected and is accepted.
{Coke} => {Bread}
Support = $\frac{3}{5}=0.6$ Confidence = $\frac{3}{3}=1.0$
N1 = (0.6 × 0.6) + (1.0 × 0.6) N2 = (1.0 × 0.6) + (0.6 × 0.6)
= 0.96 = 0.96
01 = $\frac{1}{1+{{\displaystyle e}}^{0.96}}=0.72$ O2 = $\frac{1}{1+{{\displaystyle e}}^{0.4}}=0.72$
F = w5O_{1} + w6O_{2}
= (0.6 × 0.72) + (0.6 × 0.72) = 0.86
DoB = $\frac{1}{1+{{\displaystyle e}}^{86}}=0.70$
Product pattern => 0.70 >= 0.65
Therefore it is moderately connected and is accepted.
Table 4.
Market basket transactional data for branch 4 of a retail enterprise.
Table 4.
Market basket transactional data for branch 4 of a retail enterprise.
Marketbasket Transaction Data—Branch 4 

TID  ITEMS 
T400  Maize meal, Beef, Fish, Cooking oil, Soups, Bread, Coke 
T401  Cooking oil, Beans, Beef, Soups, Maize meal 
T402  Rice, Fish, Soups, Cooking oil, Bread 
T403  Fruits, Coke, Bread, Milk, Chocolate, Soups 
T404  Bread, Beef, Fruit, Coke, Sweets, Maize meal 
{Maize meal} => {Beef}
Support = $\frac{3}{5}=0.6$ Confidence = $\frac{3}{3}=1.0$
N1 = (0.6 × 0.6) + (1.0 × 0.6) N2 = (1.0 × 0.6) + (0.6 × 0.6)
= 0.96 = 0.96
01 = $\frac{1}{1+{{\displaystyle e}}^{0.96}}=0.72$ O2 = $\frac{1}{1+{{\displaystyle e}}^{0.4}}=0.72$
F = w5O_{1} + w6O_{2}
= (0.6 × 0.72) + (0.6 × 0.72) = 0.86
DoB = $\frac{1}{1+{{\displaystyle e}}^{86}}=0.70$
Product pattern => 0.70 >= 0.65
Therefore it is moderately connected and is accepted.
{Chocolate} => {Towel}
Support = $\frac{1}{5}=0.20$ Confidence = $\frac{1}{3}=0.33$
N_{1} = (0.20 × 0.20) + (0.33 × 0.20) N_{2} = (0.33 × 0.20) + (0.20 × 0.20)
= 0.11 = 0.11
O_{1} = $\frac{1}{1+{{\displaystyle e}}^{0.11}}=0.53$ O_{2} = $\frac{1}{1+{{\displaystyle e}}^{0.11}}=0.53$
F = (0.2 × 0.53) + (0.2 × 0.53) = 0.212
DoB = $\frac{1}{1+{{\displaystyle e}}^{0.212}}=0.55$
Product pattern => 0.55 < 0.65
Therefore it is weakly connected and is rejected.