## 1 Introduction
[11] also modeled the six types of requests where the destinations/origins of ER/ED requests are flexible, but their DAOV graph treats the terminal vertex as a bypass vertex and does not accommodate IE and OE requests. From the literature, the models considering IE and OE requests usually duplicate the terminal vertex according to the request number, while those not including IE and OE requests typically treat the terminal vertex as a bypass node or assume predetermined origins and destinations for all requests. To our knowledge, no study simultaneously incorporates the eight common types of requests into a single mathematical model, and thus, existing methods are not capable of solving them together. Additionally, most studies on the CDP focus on only one or two trucking operation modes and one or two empty container repositioning strategies. Furthermore, although half of the request types involve empty containers, researchers often ignore the scenario of multiple depots and the availability of empty containers [11]. To address this research gap, we are motivated to develop a DAOV-based model for the comprehensive CDP with diverse types of transport requests. The key contributions of this paper are threefold:1. A comprehensive CDP is mathematically formulated as an innovative MILP model based on the DAOV graph, which is capable of simultaneously accommodating all types of transport requests, two trucking operation modes, two empty container repositioning strategies, and empty container constraints across multiple depots. Given the non-pairing of IE and OE requests, the forbidden arc is introduced into the model. Although there is only one terminal, it is handled in two distinct ways, depending on the request types. The terminal vertices of IE and OE requests are uniquely numbered to ensure that each request is executed, while those of IF/OF-related requests are ignored by using hyperarcs to reduce unnecessary arcs. 2. From a methodological perspective, the inherent complexity of the comprehensive CDP renders the attainment of an exact solution for industrial-sized instances highly challenging. To efficiently solve the problem, an improved LNS algorithm is developed by incorporating the \"Sequential insertion\" and the \"Solution re-optimization\" methods. The \"Sequential insertion\" method is responsible for converting the solution into multiple truck routes, while the \"Solution re-optimization\" method is used to refine the quality of solutions and ensure the feasibility of the truck routing plan. 3. The performance of the proposed LNS is evaluated by comparing it with MILP and GA for varying scale instances. The results not only demonstrate the effectiveness and efficiency of the LNS but also reinforce its potential as a more optimal approach in solving the problem at hand. Moreover, a sensitivity analysis is carried out to investigate the effect of the number and distribution of depots and empty containers, offering useful managerial insights for decision makers. The remaining content of this paper is organized as follows. Section 2 provides a thorough review of the relevant literature. Following the problem description, Section 3 mathematically formulates the novel comprehensive CDP based on the DAOV graph. An improved LNS algorithm is designed in Section 4, and the MILP and the LNS are validated and evaluated through extensive randomly generated instances in Section 5. Finally, the paper is concluded in Section 6.