Algorithm Problem for arrival and departure time of a dataset

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Algorith for arrival and departure time I have got a piece of algorithms which consists of several equations to determine the arrival and departure times of a water vessel to a dock from AIS data. I have problem making out the second equation which starts with abbreviated "s.t." and follows with $s_i^t=0$. The equation 4 also has an identical first part.

Can anyone help me figuring out or give any idea what these means?

Thanks

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It stands for subject to and is the constraint on the optimization.

The problem says thay you should minimize $t_i$ with the constraint that $s_i^t$ is zero and $t=\lambda_{ij}^k$ for all $s_i^t$ in $\Gamma_{ij}$ and $k$ in $2,\ldots,n_{ij}$.