Abstract: In order to minimize the expected logistics cost of the supplier alliance, the Inventory Routing Problem (IRP) of multiple suppliers and multiple products under random fluctuations of demand was studied. Based on the horizontal collaboration strategy, a reasonable share method of vehicle distribution costs among the members of the supplier alliance was designed. By considering the retailer's distribution soft and hard time windows and inventory service level requirements, a heterogeneous vehicle inventory routing mixed-integer stochastic programming model of multiple suppliers and multiple products was established, and the inverse function of demand cumulative distribution was employed to transform this model into a deterministic programming model. Then an improved genetic algorithm was designed to solve the programming model. The results of example analysis show that the use of heterogeneous vehicles for distribution can reduce the total cost of supplier alliance by 8.3% and 11.92% respectively and increase the loading rate of distribution vehicles by 24% and 17% respectively, compared with the use of homogeneous heavy-duty and light-duty vehicles. The sensitivity analysis results indicate that no matter how the proportion of suppliers' supply to the total supply of the alliance and the variation coefficient of retailers' commodity demand change, the total cost of the supplier alliance can be effectively reduced by using heterogeneous vehicles for distribution; and the greater the demand variation coefficient is, the more obvious the advantage of using heterogeneous vehicles for distribution has.

Key words: horizontal collaboration, heterogeneous vehicle, Inventory Routing Problem (IRP), stochastic optimization model, improved genetic algorithm

摘要： 以实现供货商联盟期望物流成本最小化为目标，针对需求随机波动下的多供货商多产品库存路径问题（IRP）进行了研究。基于横向整合战略，设计了供货商联盟成员间车辆配送成本的合理分摊方式。考虑零售商配送软硬时间窗和库存服务水平要求，构建了多供货商多产品的异质车辆库存路径混合整数随机规划模型，并利用需求累积分布逆函数将其转化为确定型规划模型。然后设计改进遗传算法求解该确定型规划模型。算例分析结果显示，使用异质车辆配送可以比使用同质重型和轻型车辆分别降低供货商联盟总成本8.3%和11.92%，分别提升配送车辆装载率24%和17%。敏感性分析结果表明，无论供货商供货数量占联盟总供货数量比例和零售商商品需求变异系数如何变化，采用异质车辆配送的供货商联盟总成本都能得到有效降低；且需求变异系数越大，采用异质车辆配送的优势越明显。

关键词: 横向整合, 异质车辆, 库存路径问题, 随机优化模型, 改进遗传算法