Flexible dock-out time

A system comprising:

• one or more processors;
• and
• one or more non-transitory computer-readable media storing computing instructions that, when executed on the one or more processors, cause the one or more processors to perform operations comprising:
• generating, using simulated annealing, a stack building plan, for an order of one or more orders, that minimizes a total number of stacks that are to be created for the order using pallets to be used to fulfill the order and that minimizes a portion of a trailer to be used for the total number of stacks;
• generating, using a routing system and based on generating the stack building plan, a dock-out plan designed to deliver the one or more orders to one or more locations, wherein the dock-out plan comprises a flexible period of time within which to dispatch the trailer, wherein the routing system is configured to communicate with a communication system to deliver within the flexible period of time, and wherein generating the dock-out plan comprises:
• generating, using the routing system, a preliminary dock-out time boundary based on one or more delivery time windows for one or more deliveries;
• and
• processing, using the routing system, two parallel data flow paths to locate a range of dock-out times associated with one or more time constraints of the one or more delivery time windows for the one or more deliveries, wherein the two parallel data flow paths further comprise:
• determining, using a backward search, an earliest dock-out time based at least in part on the preliminary dock-out time boundary;
• and
• determining, using a forward search, a latest dock-out time based at least in part on the preliminary dock-out time boundary;
• and
• transmitting, using the communication system, the range of dock-out times to a user, wherein the trailer is dispatched to a distribution center between the range of dock-out times to load the trailer and deliver the one or more deliveries within the one or more time constraints of the one or more delivery time windows based on the flexible period of time.