A beam search heuristics to solve the parcel hub scheduling problem

In this paper, a beam search scheduling heuristic (BSSH) is presented to solve the parcel hub scheduling problem (PHSP), which is a scheduling problem that is common in the parcel delivery industry (PDI). Companies in the PDI include the United States Postal Service, United Parcel Services, Federal Express, and Deutsche Post. Together, these companies move more than one trillion dollars of the United States' Gross Domestic Product. The PHSP involves scheduling a set of inbound trailers each containing a set of heterogeneous parcels to a set of unload docks. At the unload docks, the parcels are unloaded, sorted, and moved to the appropriate outbound trailers at the load docks. At the load docks, the parcels are loaded onto the outbound trailers. The objective is to minimize the timespan of the transfer operation at the transshipment terminal. The BSSH is compared to various scheduling approaches: random scheduling algorithm (RSA), genetic-based scheduling algorithm (GBSA), and simulation-based scheduling algorithm (SBSA). While GBSA and SBSA offer solutions that are superior to BSSH for smaller size problems, BSSH outperforms these algorithms on larger size problems requiring much less computational time. The results show that for larger size problems the BSSH is able to produce solutions that are from 4% to 8% of the known optimum solutions. In contrast, GBSA and SBSA, respectively offer solutions from 23% to 38% and from 6% to 47% of the known optimum solutions. The contribution of this paper is a scheduling heuristic to solve the PHSP. © 2011 Elsevier Ltd. All rights reserved.