Here kj is the lagrange multiplier

Here kj is the lagrange multiplier associated with the constraint
that ensures that customer j is serviced.
In Fisher et al. (1997) are presents an algorithm for solving
the VRPTW optimally where the problem is formulated as a
K-tree problem with degree 2K on the depot. A K-tree for a
graph containing n + 1 vertices is a set of n + K edges spanning
the graph. Informally, the VRPTW could be described
as finding a K-tree with degree 2K on the depot, degree 2 on
the customers and subject to time and capacity constraints.
A K-tree with degree 2K on the depot therefore becomes equal
to K routes.