Shipping oil a thousand miles with leaky relays

A tanker must move oil from port X to port Y, $1000$ miles away. It starts with $3000$ gallons at X, can carry at most $1000$ gallons at a time, and while carrying oil it leaks $1$ gallon per mile travelled (it loses nothing when sailing empty). It may set up any number of depots along the route, leaving oil there to collect later. With an optimal plan, how many gallons can reach Y, to the nearest gallon?

$833$. While $3000$ to $2000$ gallons remain, three loaded legs are needed per mile, costing $3$ gallons per mile, so after $\tfrac{1000}{3}$ miles $2000$ remain. Then two loaded legs cost $2$ per mile, so after $500$ more miles $1000$ remain. The last $\tfrac{500}{3}$ miles are done in one load, arriving with $1000-\tfrac{500}{3}\approx833$ gallons.