A flow based formulation and a reinforcement learning based strategic oscillation for cross-dock door assignment

Cross-dock door assignment is a critical warehouse optimization problem in supply chain management. It involves assigning incoming trucks to inbound doors and outgoing trucks to outbound doors to minimize the total pallet-handling cost inside the warehouse. This study investigates a flow based formulation and a reinforcement learning based heuristic approach to solve this problem. The flow based formulation relies on the flow of goods. It is significantly smaller than the existing mixed integer programming formulations in the literature. The proposed heuristic algorithm relies on a Q-learning reinforced procedure to guide the search toward promising areas, and a strategic oscillation method to adaptively explore feasible and infeasible search spaces. It also relies on an improved tabu strategy using attributive and explicit memories. The formulation and proposed heuristic algorithm were tested on two sets of benchmark instances widely used in the literature and compared with several state-of-the-art algorithms. The computational results demonstrated the high competitiveness of the proposed methods in solution quality and computation time. In particular, the flow based formulation can optimally solve more and larger instances and produce better lower and upper bounds than the existing mixed integer programming formulations in the literature. The heuristic approach improved the best solutions (new upper bounds) for 43 of the 99 tested instances while matching the other best-known solutions, except in two cases. The key components of the algorithm were analyzed to justify the algorithm design. The code of the proposed algorithm will be publicly available.