This talk addresses the Truck-to-dock Door Assignment Problem, which is an optimisation problem in supply chain management, whose business objectives aim to maximise the volume of pallets transiting through the cross-dock, and to minimize the time required to perform the pallets transfer operations. Two single objective integer programming formulations introduced after 2009 in the literature are examined. Both formulations share the same objective function, which is composed of two parts made commensurable using coefficients of monetary nature. However, these coefficients are somewhat artificial, reflecting an impossibility of pallet transfer through a penalty cost, and a pallet transfer time through a transportation cost.
In face of this single objective approach, a variant considering two lexicographic non-commensurable separated objectives, derived from these formulations, is proposed. The core of the talk is devoted to the analysis of the four formulations according to the two business objectives of the Truck-to-dock Door Assignment Problem. Mathematical formulations have been implemented in Julia, using the algebraic modeling language JuMP. Codes and datasets are available online on GitHub in open-source. Reproducible numerical experiments on instances from the literature have been conducted using Gurobi Optimizer as IP solver. On base of results collected after intensive numerical experiments, the analysis carried out reveals that bi-objective lexicographic formulations outrank performances of the two single objective formulations published in 2009 and 2016.