液化天然气库存路径问题建模与算法

考虑液化天然气（LNG）的在途挥发、转移挥发与库存挥发对配送成本与风险的影响，根据LNG风险特性采用蒸汽爆炸模型量化库存和运输风险，并针对传统单因素风险评估方法的不足，结合多源数据（兴趣点密度、土地生产总值产出率和人口密度）构建多因素复合风险评估指标反映事故严重程度的空间异质性，建立库存路径问题双目标优化模型，实现多周期LNG库存和配送方案的联合优化。根据问题的特征，设计基于贪婪策略预优化并结合变邻域搜索（VNS）的多目标粒子群（MOPSO）混合优化算法，且通过标准测试函数对改进前后的MOPSO算法和非支配遗传算法（NSGA-Ⅱ）进行比较；与NSGA-Ⅱ相比，MOPSO在结合VNS前后分别具有32%和42%的收敛性优势，结合VNS混合优化相比原始MOPSO有15%的收敛性优势。最后，以广州地区LNG加气站供应体系进行案例分析。研究结果表明：库存与运输成本存在利益背反关系，且在短暂缺货时总成本较低；忽略挥发的影响会导致小批量频繁补货，从而增加不必要的运输成本；LNG挥发成本占总成本的10%~20%，库存挥发率对成本影响较大，但对风险影响很小，当库存挥发率低于2%时投资降低挥发率带来的经济效益较大，当超过2%时，投入产出比迅速降低；风险限值约束对路径选择和成本影响较大，20%风险限值的降低带来了10%总成本的提高，但20%风险限值的提高仅降低5%的总成本，说明总成本在逐步接近不考虑风险时的最低值，存在优化上限。

Model and Algorithm for Inventory Routing Problem of Liquified Natural Gas

In this study, we considered the impact of in-transit, transfer, and inventory volatilization of liquefied natural gas (LNG) on distribution costs and risks. According to the risk characteristics of LNG, a steam explosion model was adopted to quantify the inventory and transportation risks. To overcome the drawbacks of traditional single-factor risk assessment methods, we developed a multi-factor compound risk assessment index combining multi-source data (point of interest density, gross domestic product output rate, and population density) to capture the spatial heterogeneity of accidents. In this study, a two-objective optimization model of the inventory routing problem was developed to jointly optimize the multi-period LNG inventory and distribution schemes. Based on the characteristics of the problem, a hybrid optimization algorithm of multi-objective particle swarm optimization (MOPSO) based on greedy strategy pre-optimization and integration of variable neighborhood search (VNS) was designed. The MOPSO algorithm and NSGA-Ⅱ (non-dominated sorting genetic algorithm II) algorithm were tested using the standard test functions. Compared to NSGA-Ⅱ, MOPSO shows a convergence advantage of 32% before combining VNS, which increases to 42% when VNS is combined. Combining the VNS hybrid optimization also leads to a 15% convergence advantage over the original MOPSO. Finally, the case analysis of the LNG filling station supply system in Guangzhou shows the existence of a trade-off between the inventory and transportation costs; when there is a short-term shortage, the total cost is lower. Neglecting volatilization leads to frequent small-volume replenishment, which increases unnecessary transportation costs. The cost of LNG volatilization accounts for 10%-20% of the total cost. The inventory volatilization rate has a significant impact on the cost but has little impact on the risk. When the inventory volatilization rate is lower than 2%, the economic benefit, brought by the investment reduction in the volatilization rate, is greater, and when it exceeds 2%, the input-output ratio decreases rapidly, and the risk limit constraint has a greater impact on routing and cost. The 20% risk limit reduction results in a 10% increase in the total cost, but the 20% risk limit increase only reduces the total cost by 5%. This indicates that the total cost gradually approaches the lowest value without considering the risk factor, and that there is an upper limit for optimization.