Customer-Oriented Vehicle Routing Problem with Environment Consideration: Two-Phase Optimization Approach and Heuristic Solution

Algorithm 1

Fuzzy system clustering algorithm.

1 Step 1: Data initialization, input the fuzzy equivalent matrix . Let iterations =1.

2 Step 2: Find out the largest elements in the matrix , and chose the customer with the smaller number as the target

customer and denote it with .

3 Step 3: Mark the selected target customer and delete the corresponding row . Specifically, once a customer is chosen as

the target customer, its column is marked by , mark the corresponding elements in row as 0.

4 Step 4: Find out the largest element of matrix , denoted the similarity value as .

5 If (pre-given threshold value), then go to Step 5. Otherwise, calculate the total weight of the customers .

6 Make judgement, if , go to Step 5. Otherwise, put customers and in same group, then delete the corresponding

row of matrix , return to Step 4.

7 Step 5: Set the customer clustering termination conditions; if the matrix is empty, then clustering process stops; else let

= + 1 and got to Step 2.