Two-Echelon Location-Routing Problem with Time Windows and Transportation Resource Sharing

Algorithm 1

K-means clustering.

	Input: the number of clusters k and set of |J| customer points J = {1, 2, 3, …, |J|}
	Output: clustering results including k centers, k clusters, and membership matrix
	Steps:
(1)	Initialize the k centers by selecting k customer points from J randomly
(2)	Repeat:
(i)	Assign each customer point to the closest cluster by calculating and comparing the distance between the customer point and each cluster center
(ii)	Calculate the objective function B using equation (2)
(iii)	Update each cluster center
(3)	Until each center stays unchangeable
(4)	Export the results