中文摘要：

在LMRPVCC问题优化模型基础上,在目标函数与约束条件中引入运输补偿成本项及服务半径Dr,将模型扩展为引入补偿策略的LMRPVCC选址-库存问题的非线性整数规划模型。利用所设计的粒子群算法对Daskin和Shen的文章中的49节点、88节点算例求解,并对补偿系数W、服务半径Dr及运输成本系数β进行敏感性分析,认为服务半径Dr越小,超出服务半径的零售商数量越多,配送中心需额外支出的补偿费用越高;服务半径Dr越大,超出服务半径的零售商数量越少,配送中心需支出的补偿费用越少。补偿成本系数W、运输成本系数β与模型目标函数值正相关。

英文摘要：

Based on LMRPVCC optimization model,by introducing compensation cost and service radius Dr into objective function and constraint condition,the model was expanded to a nonlinear integer-programming model for solving LMRPVCC location-stock problem with compensation policy.Using particle swarm optimization algorithm and 49-node and 88-node computational instances,the suboptimum solutions wer obtained.The numerical examples were given to evaluate the effectiveness of the models by changing compensation cost factor W,service radius Dr and transportation cost factor β.It is concluded that（1） When Dr is shorter,there will be more retailers out of Dr,and distribution centers will cost more additional compensation costs;while when Dris longer,there will be less retailers out of Dr,and distribution centers requires less compensate costs.（2） W and β are positively correlated with the objective function value.