A Bi‐Objective Analysis of Integer Programming Formulations for the Truck‐to‐Dock Door Assignment Problem

ABSTRACT

This paper addresses the Truck‐to‐dock Door Assignment Problem, an optimisation problem in supply chain management. The problem is characterized by two incommensurable business objectives: to maximise the volume of pallets transiting through the cross‐dock and to minimise the total transfer time required to perform the pallet 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 a monetary nature. However, these coefficients are inherently artificial, reflecting the impossibility of a pallet transfer through a penalty cost and a pallet transfer time through a transportation cost. To overcome this limitation, two bi‐objective lexicographic formulations, derived from these single‐objective formulations and free of any artificial cost coefficients, are proposed. The core of the paper 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 modelling 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 the basis of results collected after intensive numerical experiments, the analysis carried out reveals that the bi‐objective lexicographic formulations outperform the two single‐objective formulations published in 2009 and 2016.