###### Abstract
This, however, may not be consistent with some real-world scenarios involved with uncertain information. In this context, deterministic models for 2L-VRP cannot capture these uncertainties observed in practice. As stated in [20], the uncertain vehicle routing problem contains two kinds of important uncertain information: information quality and information evolution. Information evolution refers to the fact that some information may not be known in advance and will be revealed over time during the transportation process, which is known as the dynamic VRP. Information quality refers to the uncertainty of some information; for example, the distribution of some information, which is usually modeled as a probability function. This is generally known as the stochastic VRP (SVRP). Taking the uncertainty and the prior knowledge of the uncertain information into account is of significant importance for optimizing the routing schedule that avoids infeasibility and saves transportation costs. At present, one of the most common solution frameworks for stochastic routing problems is prior optimization. It models the problem in two stages: determining a set of prior routes with uncertain information and making decisions as deterministic information is obtained based on pre-determined policies. Generally, stochastic programming with recourse (SPR) and chance-constrained programming (CCP) are used to determine the \"prior solution\" [21]. In the CCP, the problem is solved so that the probability of route failure is below a certain level, and the cost of failures is ignored. In the SPR, it determines the first-stage solution that minimizes the expected cost of the second-stage solution. Although the SPR is more difficult to solve than the CCP, the SPR objectives are more meaningful [21]. Therefore, most of the research focused on studies using the SPR approach to address the SVRP. For example, [PERSON] [22; 23; 24] studied the VRP with stochastic customers, stochastic travel time and stochastic demand, respectively, which were modeled as stochastic programming and the corresponding solution algorithms were proposed. However, the above studies did not consider the loading problem, which limited the applicability of these studies to certain scenarios, where each customer consists of a certain number of weighed items with a given width and length. In [25], the authors investigated a SVRP with uncertain demands, where a discrete probability distribution was adopted to characterize the height and width. In this work, the authors presented a two-stage stochastic program to describe this problem and proposed an inter L-shaped method to solve it. [PERSON] et al. in [26] studied a 2L-VRP considering stochastic travel time, which was modeled as a two-stage stochastic program. However, only the 2\(|\)UO\(|\)L and 2\(|\)UR\(|\)L loading configurations were studied in this work, while the two-dimensional sequential loading configuration was not considered. It is also commonly encountered, for example, in less-than-truckload operations, where a stable set of customers is served on a regular basis, but not every customer requires a visit every day; namely, the presence of customers is probabilistic. With the aforementioned problems and main purpose of this study, the main contribution of this study is fourfold: (i) By addressing the characteristics of customer-presence uncertainty and two-dimensional patterns in logistics distribution, this study investigates novel extensions of the vehicle routing problem known as the 2L-VRPSC. (ii) A stochastic programming model of 2L-VRPSC is first proposed based on Monte Carlo simulation and scenario analysis. (iii) To solve this problem, an enhanced adaptive tabu search algorithm incorporating a multi-order bottom-fill-skyline packing heuristic, i.e., EATS-MOBFS, is proposed, where multiple neighborhood operators are designed.