Abstract: A method for finding the optimal schedule and route to visit all constrained and unconstrained nodes of a graph only once while respecting the associated time windows and system constraints. The constrained nodes are first grouped in clusters based on their time windows and system constraints. Then, unconstrained nodes are optimally assigned to the clusters by using a greedy heuristic. Subsequently, enumeration is used to solve the TDTSPTW by cluster. Once all clusters are solved, the paths are joined and a local search heuristic is used to improve the solution. The result of the method is an ordered set of nodes to be visited with their associated start times.

Abstract: The push-back storage system includes an elongated storing lane defining opposite front and rear ends and at least one pair of spaced-apart parallel elongated rails extending between the front and rear ends of the storing lane and being inclined downwardly from the rear end towards the front end. Each rail includes a pair of elongated inclined side walls integrally linked at a common elongated top edge. At least one cart is rollably carried by the pair of rails and is rollable along the pair of rails between the storing lane front and rear ends, the cart having a load-bearing frame rollably carrying a number of wheels each engaging a corresponding one of the rails. Each wheel has a web rotatable about a rotational axis and a pair of side flanges radially extending from and axially spaced-apart along the wheel web so as to define a rail-engaging surface on the wheel web between the spaced-apart side flanges. The rail-engaging surface is wider than the top edge of the corresponding rail.