Abstract
Physical Internet is a new fundamental paradigm to change global logistics and public storage is among the most critical operations in PI. We consider a public storage warehouse, facing a set of reservations for homogeneous or heterogeneous storage units over a certain time horizon with revenue rewards. The warehouse operation manager has to decide which storage requests to accept and schedule them in different storage units to maximize the revenue. We model warehouse operations as scheduling n independent multiprocessor tasks with given start and end times, with an objective to maximize total revenue. We identify 5 cases for basic operations and show that two polynomial algorithms can solve the basic problem optimally for all cases. If homogeneous storage units are considered, our algorithm has a time complexity of O((nlog n)2). For heterogeneous storage units, the time complexity of our algorithm is bounded by O(nm+1). We further consider more complex problems with upgrading operations, and employ column generation algorithm to solve the problem. Finally, we consider the application to self-storage warehouses in different countries, and show our algorithm can improve the revenue by 8.05% on average and at least 5.8% for warehouses with basic operations, and by 12.63% on average and at least 7.5% for warehouses with upgrading operations.