An Adaptive Tabu Search Algorithm for Solving the Two-Dimensional Loading Constrained Vehicle Routing Problem with Stochastic Customers

In practical logistic distributions, uncertainties may exist in each distribution process, and sometimes suppliers have to take undesirable measures to deal with the subsequent schedule variances. In light of the uncertainty of customers in logistics distribution and the widely applied two-dimensional loading patterns in transportation, we propose and formulate a two-dimensional loading-constrained vehicle routing problem with stochastic customers (2L-VRPSC), where each customer has a known probability of presence and customers’ demands are a set of non-stackable items. A stochastic modeling platform of 2L-VRPSC is established based on a Monte Carlo simulation and scenario analysis to minimize the expected total transportation cost. To achieve this, an enhanced adaptive tabu search (EATS) algorithm incorporating the multi-order bottom-fill-skyline (MOBFS) packing heuristic is proposed, where the EATS algorithm searches for the optimal routing combination and the MOBFS checks the feasibility of each route and guides the EATS to search for feasible solutions. The widely used two-dimensional loading-constrained vehicle routing problem (2L-VRP) benchmarks under different loading configurations considering items’ sequential and rotation constraints are applied for experiments, which demonstrates the comparable efficiency of the proposed EATS-MOBFS for solving 2L-VRP. Furthermore, the results and analysis of experiments based on the new 2L-VRPSC instances verify the versatility of the proposed solving approach, which is capable of providing more practical solutions to some real-life scenarios with customers’ uncertain information.