## 3 Problem Definition and Formulations  
### Problem Description  
The comprehensive CDP with diverse types of transport tasks is defined as follows. A container transport company possesses a limited fleet of homogeneous trucks to serve container transport requests issued by customers (shippers and consignees) and shipping companies between the container terminal, multiple depots, and customers. The company manages multiple depots that can provide empty containers and serve as parking places for trucks. Because of the elevated expense associated with acquiring empty containers, the stock level of empty containers at each depot is finite and fluctuates dynamically as trucks pick up empty containers from the depot or deliver them back to it. The truck must depart from a depot and return to any depot by the end of the day. Each truck can only carry one container at a time, with all containers being of identical size. Each request is constrained by distinct time windows. The objective of the problem is to simultaneously optimize empty container repositioning, truck scheduling, and route planning to deal with all requests. A request in this study is defined as a container transport task issued by customers (shippers and consignees) or shipping companies. The eight types of requests consist of six basic requests (IF, ER, ED, OF, IE, and OE) and two composite requests (IFER and OFED), as illustrated schematically in Figure 1:  
1. IF request: This requires hauling the inbound full container from the terminal (Origin) to the consignee (Destination). This kind of request is very common, as sometimes a container cannot be unpacked on the same day as it is delivered, and the emptied container will need to be picked up the other day. 2. ER request: This refers to hauling back the emptied container from the consignee (Origin) to the terminal, a depot, or a shipper demanding an empty container after an IF container has been unpacked. The destination of an ER request is flexible, thus offering potential for optimization at the operational level. 3. ED request: This involves hauling an empty container from a terminal, a depot, or a consignee to a shipper (Destination) demanding it. The ED request is not always combined with OF request, as the empty container may not be packed immediately after its arrival, and thus the loaded container transport request can only be submitted afterward. Figure 1: Illustration of the eight types of transport requests. * OF request: This specifies hauling the outbound full container from the shipper (Origin) to the terminal (Destination). * IE request: This entails hauling the inbound empty container from the terminal (Origin) to a depot or a shipper who demands it. However, the destination of an IE request cannot be the terminal. If the destination is the terminal in a one-terminal scenario, the transportation will be handled by internal or in-port trucks, which are not managed by the trucking company. * OE request: This implies hauling the outbound empty container from a depot or a consignee to the terminal (Destination). The IE and OE requests are submitted by shipping companies due to the requirement of empty container repositioning between different terminals or regions. * IFER request: This is a composite request, which means that a consignee requires an IF container to be picked up from the terminal and delivered to their location, and the empty container to be picked up immediately after unpacking and repositioned to a suitable place. * OFED request: This is also a composite request, which indicates that a shipper requires an empty container to be delivered from the location where it is available to their location, and the OF container to be picked up immediately after packing and finally delivered to the terminal. Although an ER and an OE request may share the same origin and destination if they can be paired with each other, they should still be treated as individual requests.