Its input consists of a collection of ordered pairs of points in a metric space, and the goal is to connect these points into a cycle of minimum total length that includes all of the pairs, oriented consistently with each other.
It models problems of scheduling the pickup and delivery of individual loads of cargo, by a stacker crane, construction crane or (in drayage) a truck, in a simplified form without constraints on the timing of these deliveries.
Because it generalizes the traveling salesperson problem, it inherits the same computational complexity: it is NP-hard, and at least as hard to approximate.
[2] The problem of designing the back side of an embroidery pattern to minimize the total amount of thread used is closely related to the stacker crane problem, but it allows each of its pairs of points (the ends of the visible stitches on the front side of the pattern) to be traversed in either direction, rather than requiring the traversal to go through all pairs in a consistent direction.
[3] Another variation of the stacker crane problem, called the dial-a-ride problem, asks for the minimum route for a vehicle to perform a collection of pickups and deliveries while allowing it to hold some number k > 1 of loads at any point along its route.