Modeling And Solving 3D Online Robotic Palletization Problem

In this study,the last missing link of automating material handling in the warehouse of ecommerce enterprises was addressed,namely packing heterogeneous cargo boxes onto pallets using robotic arms.In recent years,the development of e-commerce in mainland China has been extremely rapid,and the demand for efficient logistics operation in warehouses surges.As labor costs continue to rise,many material handling operations in large warehouses have been automated,while the last step of loading heterogeneous boxes onto pallets are still performed manually due to the complexity of the packing layout.In addition,the packing decision for each cargo boxes must be carried out in real time so as to keep the robotic arm operating at a constant rate,which complicates the problem as only partial information are available in each step.We first modeled the offline version of the problem using a mixed integer programming model,so that we can focus on the key challenges: avoiding collision between the robotic arm and existing boxes during the loading process,and keep the layout stable in each packing step.For small-scale offline problems,integer programming can be solved to optimality by commercial solver,which can serve as a lower bound for measuring the effectiveness of our algorithm.To extend our model to address the online nature of the practical applications,we adopt Monte Carlo simulation to choose the best decision that maximizes expected space utilization.An effective heuristic algorithm is developed to handle large scale online problem.Comprehensive numeric experiments are conducted to simulates various practical application scenarios and measure the effectiveness of our proposed algorithm in different scenarios.The impact of several key system parameters to the performance of the overall packing system are analyzed and practical suggestions are given to guide the practitioners for designing an effective robotic palletization system.