# A Multi-Strategy ALNS for the VRP with Flexible Time Windows and Delivery Locations
## 2 Literature Review
### The Vehicle Routing Problem with Delivery Options  
The integration of delivery options into vehicle routing problems (VRPs) introduces flexibility by allowing deliveries to the same customer to occur at different locations, each associated with distinct time windows. This feature is particularly relevant in last-mile logistics, where customer behavior and urban constraints demand adaptable delivery strategies. [PERSON] et al. [28] proposed a VRP with roaming delivery locations (VRPRDL), where the logistics provider chooses a location among several delivery options based on a schedule and delivers the goods to the trunk of the customer's car. This problem is solved using Large Neighborhood Search (LNS) heuristic algorithms and experimentally analyzed; the roaming delivery approach leads to significant economic and environmental benefits. It needs to be noted that they assumed that the customer does not move faster than the delivery vehicle, which helps them to propose a strategy to speed up the algorithm while also limiting the applicability of the problem. [PERSON] et al. [29] modeled the VRPRDL problem as a set covering the problem and developing a branch-and-price (B&P) algorithm to solve the problem with an average savings of 20% on the experimental dataset, a solution not suitable for large-scale problems. [PERSON] et al. [30] additionally allowed customers to specify preferred delivery locations in addition to considering delivery options, and finally solved this problem using a large neighborhood search algorithm, obtaining good results on both small and large problems, finally providing some management insights for the vehicle routing problem with delivery options. Several studies further explored delivery flexibility through customer-defined delivery preferences. [PERSON] et al. [31] applied the k-means clustering algorithm to evaluate potential locations for raw material collection points in the upstream supply chain. They formulated the problem as a vehicle routing problem with flexible time windows, aiming to minimize the total delivery cost while ensuring low delivery delays. [PERSON] et al. [32] allowed each customer to be associated with a set of delivery time windows in order to reflect the implicit requirement for customer presence in real-world delivery scenarios. They proposed a hybrid ALNS algorithm to solve this problem, which effectively reduced delivery costs while minimizing failed deliveries. [PERSON] et al. [33] observed that narrower time windows can enhance customer satisfaction but may restrict the delivery flexibility of logistics companies. To address this, they studied how to select the optimal time window for each customer from multiple available options, aiming to balance customer satisfaction and delivery cost. They proposed an improved large neighborhood search algorithm to solve this problem, and the results showed that offering multiple time windows can bring economic benefits to logistics providers. [PERSON] et al. [34] formulated a three-dimensional vehicle routing problem in last-mile delivery by incorporating vertical travel time, hard time window constraints, and delivery options, and proposed a crowding differential evolution algorithm to minimize cost while enhancing customer satisfaction. Other scholars introduced delivery option flexibility in various forms. [PERSON] et al. [35] considered customers' preferences for delivery locations and formulated a two-echelon vehicle routing problem, effectively balancing delivery costs with customer preferences. [PERSON] et al. [36] addressed the problem of simultaneous pickup and delivery by offering customers the option to choose self-pickup locations along with compensation incentives. They developed a customized adaptive large neighborhood search algorithm to effectively solve the problem. The results showed that this approach significantly reduced delivery costs. [PERSON] et al.