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Cross-docking is a logistics strategy that minimizes the storage and picking functions of conventional warehouses. The objective is to unload the cargo from inbound trucks and directly load it into outbound trucks, with little or no storage. The success of the strategy depends on an efficient transshipment operation. This work undertakes a study of truck scheduling in a parallel dock cross-docking center. The problem is first modeled as a two-machine flow shop scheduling problem with precedence constraints, with the objective of minimizing the makespan, and later we generalize it to the parallel-dock case. We propose a hybrid method based on a Lagrangian relaxation technique through the volume algorithm. Using information from the Lagrangian multipliers, constructive heuristics with local search procedures generates good feasible solutions. With a series of cuts, the methodology finds tight bounds for small and large instance sizes, outperforming current results.

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The scheduling of jobs over a single machine with sequence dependent setups is a classical problem setting that appears in many practical applications in production planning and logistics. In this work, we analyze six mixed-integer formulation paradigms for this classical context considering release dates and two objective functions: the total weighted completion time and the total weighted tardiness. For each paradigm, we present and discuss a MIP formulation, introducing in some cases new constraints to improve performance. A dominance hierarchy in terms of strength of their linear relaxations bounds is developed. We report extensive computational experiments on a variety of instances to capture several aspects of practical situations, allowing a comparison regarding size, linear relaxation and overall performance. Based on the results, discussions and recommendations are made for the considered problems.

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