In a typical VRPTW MIP formulation there are constraints that keep service at each node between node-specific lower and upper bounds. Using $x_{ijk}$ as a binary variable representing whether or not vehicle $k$ travels from node $i$ to node $j$, $w_{ik}$ is a variable representing the starting time at node $i$, $s_{i}$ is the service time at node $i$, $a_{i}$ and $b_{i}$ are the lower and upper bounds for service at node $i$, and $M_{ij}$ is a large scalar. The time-consistency constraints are: $$ \begin{array} \\ w_{ik} + s_{i} + t_{ij} - w_{jk} \leq (1 - x_{ijk})M_{ij} \\ w_{ik} \geq a_{i} \\ w_{ik} \leq b_{i} \end{array} $$

Such constraints keep service within the time windows. But if a vehicle arrives at the node before the lower bound, it waits at the node until it can start service. Can someone point me to constraints that will prevent a vehicle from going to the node if it will get there too early? For example, is there a way to constrain the system so that vehicle $k$ will not arrive at node $i$ until $a_{i}$?