Shahin Gelareh

In this work, we study the dock-door assignment and truck scheduling problem in cross-docks with an intraday planning horizon. This timeframe allows us to view the problem as a repeating operation with a frequency of 24 h. In practice, this repeating process follows a certain distribution, which is largely sustained even if we extend the horizon. While several modeling approaches and efficient solution algorithms have been proposed for various problem variations, the utilization of decomposition techniques in exact mathematical programming methods has been the most effective. Surprisingly, none of these techniques have taken advantage of the repeating patterns inherent in the problem. We start with a recently proposed compact model that is well-designed and can be exploited in a primal (Benders) decomposition technique, although it cannot be directly used to solve a practical-sized problem. We show that its modeling deficiencies can be fixed and propose a Benders decomposition framework together with several Alternative Objective Functions (AOFs) to generate customized Benders cuts, along with other valid inequalities that can be identified and separated. A classifier is trained to identify the most efficient AOF to use at different stages of the Benders iterations, to help avoid saturation of the master problem with dominated Benders cuts. Our extensive computational experiments confirm the significant performance improvement in the comparable decomposition framework.

The notion of ‘resource’ plays an important role in the overall efficiency and performance of most cross-docks. The processing time can often be described in terms of the resources allocated to different trucks. Conversely, for a given processing time, different combinations of resources can be prescribed. We study the problem of truck scheduling and dock assignment in the presence of resource constraints. In the absence of a closed-form (or well-defined) linear formulation describing the processing times as a function of resources, expert’ knowledge has been mobilized to enable modelling of the problem as an integer linear model. Two cases are taken into account: In the first one, the expert believes in his/her estimation of the processing time for every truck and only proposes a different combination of resources for his/her estimation, while in the second one the expert proposes a limited number of resource deployment scenarios for serving trucks, each of which has a different combination of resources and different processing times. We propose a novel compact integer programming formulation for the problem, which is particularly designed with an embedded structure that can be exploited in dual decomposition techniques with a remarkably computationally efficient column generation approach in this case. The case in which a scenario with invariant processing time is considered and modelled as a special case of the proposed model. Since a direct application of commercial solvers such as CPLEX to solve instances of this problem is not realistic, we propose a branch-and-price framework and, moreover, several classes of valid inequalities. Our extensive computational experiments confirm that the proposed exact solution framework is very efficient and viable in solving real-size instances of the practice and in a reasonable amount of time.

Some implementations of variable neighborhood search based algorithms were presented in “Daquin et al. RAIRO: OR 55 (2021) 2291–2323”. This work is based on model in “Miao et al. Eur. J. Oper. Res. 192 (2009) 105–115” which has been proven to be incorrect. We reiterate and elaborate on the deficiencies in the latter and show that the authors in the former were already aware of the deficiencies in the latter and the proposed minor amendment does not overcome any of such deficiencies.