Two-dimensional loading in vehicle routing problem with release and due dates

In this paper, we study a two-dimensional vehicle loading and routing problem in which customer orders with deadlines become available for dispatch as per their release dates. The objective is to minimize the sum of transportation, inventory, and tardiness costs while respecting various loading and routing constraints. This scenario allows us to study various tradeoffs that tend to arise due to temporal order aggregation across release dates. We thereby propose an integrated mathematical formulation to simultaneously model both the routing and loading requirements of the problem at hand. Specifically, as the problem is NP-hard, we propose a scatter search-based heuristic approach to solve large-size instances. Further, its performance is enhanced using problem-specific procedures and strategic oscillation approaches. Additionally, the numerical experiments illustrate the influence of cost structures on both the optimal loading configurations along with the optimal routes. Importantly, our experiments also suggest that the proposed scatter search method can produce good-quality solutions in less time.