In this paper, we consider an automotive firm that moves cars from a parking lot to a mother ship in a limited period of time, in order to satisfy a customer’s requisition. Using a calculus of variations technique, the problems cast similarities with Ramsey [6] economic growth model. So, assuming polynomial costs, we show a closed form solution for the optimal number of movements that minimizes the cost of moving cars from the parking lot to the mother ship. Also, we show the associated optimal allocation from which a car has to be moved at each time.

transshipment, calculus of variations, Euler’s equation.