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ULD Build-Up Scheduling with Logic-Based Benders Decomposition

  • We study a complex planning and scheduling problem arising from the build-up process of air cargo pallets and containers, collectively referred to as unit load devices (ULD), in which ULDs must be assigned to workstations for loading. Since air freight usually becomes available gradually along the planning horizon, ULD build-ups must be scheduled neither too early to avoid underutilizing ULD capacity, nor too late to avoid resource conflicts with other flights. Whenever possible, ULDs should be built up in batches, thereby giving ground handlers more freedom to rearrange cargo and utilize the ULD's capacity efficiently. The resulting scheduling problem has an intricate cost function and produces large time-expanded models, especially for longer planning horizons. We propose a logic-based Benders decomposition approach that assigns batches to time intervals and workstations in the master problem, while the actual schedule is decided in a subproblem. By choosing appropriate intervals, the subproblem becomes a feasibility problem that decomposes over the workstations. Additionally, the similarity of many batches is exploited by a strengthening procedure for no-good cuts. We benchmark our approach against a time-expanded MIP formulation from the literature on a publicly available data set. It solves 15% more instances to optimality and decreases run times by more than 50% in the geometric mean. This improvement is especially pronounced for longer planning horizons of up to one week, where the Benders approach solves over 50% instances more than the baseline
Author:Ricardo EulerORCiD, Ralf Borndörfer, Christian Puchert, Tuomo Takkula
Document Type:In Proceedings
Parent Title (English):Integration of Constraint Programming, Artificial Intelligence, and Operations Research
First Page:259
Last Page:276
Series:Lecture Notes in Computer Science
Year of first publication:2024
Page Number:17
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