###### Abstract  
The shipping market is unpredictable and volatile due to some uncontrollable factors such as epidemic, conflicts and natural disasters. There is always an imperfect match between the supply capacity of liner companies and the actual demand of the market, which leads to a waste of slot resources and/or unsatisfied customer demand. Furthermore, the trade off between empty container transportation and laden container transportation is the crucial problem of strategic importance for liner companies. To deal with the above problem, this paper aims to develop a new solution to the collaborative optimization problem of container slot allocation and empty container repositioning by exploring the resource allocation, storage, and repositioning methods collaboratively. An online booking platform is introduced in this paper, and no-shows and customer preferences are considered in the analysis. An innovative integer programming model is established based on an online booking mode and a delivery-postponed strategy. A new branch-and-cut algorithm is then proposed to solve the problem. Finally, numerical experiments are conducted to verify the effectiveness of the proposed model and algorithm. The experimental results show that collaborative optimization can remarkably enhance the revenue of liner companies along with increasing the utilization of slot resources. collaborative optimization; slot allocation; empty container repositioning; online booking platform; delivery-postponed strategy; no-show 2024202414110920241410  
to increase freight rates in a fiercely competitive shipping market. Therefore, effective management of container slot allocation becomes an alternative method for lines to increase revenue [4]. The core part for the slot allocation problem of containers (SAPC) is that liner companies can dynamically receive and reject booking requirements to maximize revenue. The features of the SAPC include (1) liner's operating routes, schedules, and capacity, which are fixed in the short term; (2) varying freight rates for cargoes based on market segmentation; (3) transportation demand for laden containers that exhibits randomness and volatility within a certain range; and (4) the sale and reservation of seats occurring before the ship's arrival. Given that the market became more volatile in recent years more than ever, classical methods for container slot allocation need to be revisited. This would stimulate new research needs on the solutions to the SAPC. SAPC is a key topic that container lines have been focusing on [5] from different perspectives, but relatively less studies have been focused on from the perspective of concerning empty container repositioning [6; 7]. Empty container repositioning is an inevitable challenge addressed within the shipping industry [8; 9] due to imbalanced trades between import and export countries. Empty container repositioning is an internal operation for the liner company to redeploy empty containers from surplus ports to deficient ports, aiming to minimize the cost and maximize benefits. This is a multi-period dynamic decision-making and complex problem. The issue has recently attracted growing concerns [10] and has faced challenges from the aforementioned volatile market in recent years. It is becoming a critical operational problem for container lines. The world trade pattern has the following characteristics. (1) Spatial dimension differences between import and export sources. Take the Trans-Pacific containerized trade for instance, where container volume from East Asia to North America was 26.1 million TEUs in 2022, and 6.6 million TEUs in the reverse direction [3]. Apparently, East Asia is one of the major export regions in the world. On the contrary, North America is the part of main import area. (2) Time dimension differences between demand and supply of empty containers. According to [3], the ships made more port calls in the first half than the second half of the year from 2018 to 2021.