A Lagrangian Approach for The Airfreight Consolidation Problem Under Pivot-weight
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International airfreight forwarders are faced with the problem of consolidating ship- ments for efficient transportation by airline carriers. The use of standard unit loading devices (ULDs) is a solution adopted by the airfreight industry to speed up cargo loading, increase safety, and protect cargo. We study the airfreight consolidation problem from the forwarders perspective where a decision on the number of ULDs used and the assignment of shipments to ULDs is optimized. The cost of using a ULD consists of a fixed charge and depends on the weight of the cargo it contains. A ULD is charged at an under-pivot rate if the total weight is below a threshold limit, called the pivot-weight. Additional weight is charged at the over-pivot rate. We propose a solution methodology based on Lagrangian relaxation that is capable of providing high quality solutions in reasonable computational times. Besides, a high-quality lower bound, we propose three heuristics to generate feasible solutions, all based on the solution of the subproblems. The first, takes the solution of one of the subproblems and solves a restricted version of the original problem (LagHeur). The other two heuristics are a heuristic based on solving two knapsack problems (2knap) and a best-fit greedy heuristic (bestfit). Problems with up to 100 ULDs and 1000 shipments are solved to within an average of 1%, 2%, 2% of optimality in less than 51.05s, 50.57s and 589.16s by bestfit, 2knap and LagHeur, respectively.
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Mohammad Alqssem Alzaeem (2018). A Lagrangian Approach for The Airfreight Consolidation Problem Under Pivot-weight. UWSpace. http://hdl.handle.net/10012/13344