## 1 Introduction
[PERSON] addressed a many-to-many hub location-routing problem where the best-found locations of hubs and the best-found tours for each hub are determined with a simultaneous pickup and delivery within the hard time window [23]; [PERSON] presented a multi-objective model for the green capacitated location-routing problem, considering drivers' satisfaction and time windows with an uncertain demand [24]. [PERSON] developed a mixed integer linear programming (MILP) model to solve the location-routing problem with time windows, and applied opportunity constraints to deal with the changes of service time and time windows of transmission facilities [25]. [PERSON] suggested the integration of a variable neighborhood search (VNS) with path relinking (PR) to solve the LRPTW [26]. This type of research takes into account both capacity and time limitations but overlooks the influence of obstacles on the real distribution route. The scheme's design relies on the direct distance between the warehouse and the distribution point, which does not align with the actual distribution conditions on the cruise deck. Addressing this issue requires further research. In addition, there are CLRP problems such as multi-stage and multi-vehicle types [27; 28], which solve the problems at the warehouse and customer level and are more in line with the actual distribution situation. At present, the latest research includes the multi-period CLRP and delayed location-routing problem [29; 30]. Given the emergence of two-echelon distribution systems in several practical contexts, this paper tackles, at the strategic level, a distribution network design problem under uncertainty. This problem is defined as the two-echelon stochastic multi-period capacitated location-routing problem (2E-SM-CLRP); the latency location-routing problem (LLRP) belongs to a relatively new branch of routing problems, where latency, defined as the sum of the arrival times at customer locations, is the objective function to be minimized. From the perspective of modeling, [PERSON] proposed two new mixed integer formulas and introduced a general variant of the problem. The above is the latest variant of CLRP research. This article introduces the impact of the obstacle blocking environment based on the actual construction situation of cruise ships as a new variant of the LPR. Although above methods solve the various LRP problems effectively, they are not suitable for the LRP of on-deck cabin construction. The central reason is that none of the existing methods for the LRP take the blocking environment into consideration, while the blocking caused by obstacles such as stairways and function cabins on the ship is ubiquitous on deck during construction, which impacts the distribution distances of the LRP to a large extent. For this reason, the LRP of on-deck cabin materials and components in this paper is defined as a BE-LRP (blocking environment location-routing problem), which can be seen as a new variant of the LRP, as shown in Figure 1. The classic LRP calculates the delivery distance by computing the Euclidean distance between points. However, when obstacles are present, such as between two points, the delivery route needs to detour around obstacles, resulting in a longer actual delivery distance. If existing LRP optimization algorithms are used to solve the BE-LRP, especially when the delivery distance is set as the optimization objective, inaccurate distance calculations can lead to suboptimal delivery solutions. Therefore, research is needed to develop optimization methods specifically for the BE-LRP. To solve this new BE-LRP, the impact of the blocking environment on the distribution distances should be modeled quantificationally first, and then the optimization method considering this impact should be designed. Only [PERSON] [31] integrates the location path issue with motion planning by utilizing the current path planning technique to generate an obstacle avoidance route map and subsequently derive the distance matrix.