%0 Journal Article
%T 基于动态规划模型的蔬菜商品定价与补货问题<br>Vegetable Product Pricing and Replenishment Problem Based on Dynamic Programming Model
%A 王欣宇
%A 王子杰
%A 李宇鹏
%J Advances in Applied Mathematics
%P 3632-3640
%@ 2324-8009
%D 2024
%I Hans Publishing
%R 10.12677/aam.2024.138346
%X 本文研究了如何对蔬菜类商品进行自动定价与补货。通过分析近三年各蔬菜品类及各单品的销售信息，剔除掉不合理数据，整理出最优数据，建立动态规划模型，结合添加附加条件预测出未来特定时间内的最优补货量和最优定价策略。针对问题一，本文首先对数据进行预处理，通过箱线图查找异常值并剔除不合理数据，将销量进行量纲归一化处理，分析相关性。利用MATLAB数据可视化工具箱绘制销量随季度变化的图表和品类相关性矩阵图，揭示各品类销售总量变化规律和相关程度。对于单品销售量，利用归一化数据绘制归一化表并通过Excel数据透视表进行分析。结果显示花叶类商品销量稳定高，茄类销量较低；水生根茎类和花菜类相关性高，辣椒类与食用菌类相关性较高。在单品销售中，芜湖青椒与西兰花销量接近，金针菇与云南生菜销量最高。针对问题二，第一小问利用公式计算各蔬菜单品的成本加成价格，并通过MATLAB数据拟合分析品类销量与成本加成定价的关系。随着成本加成定价的降低，销售总量分布更分散且较低；成本加成定价提高后，销售总量更聚集，与拟合直线重叠较多。第二小问使用MATLAB创建动态规划的状态空间和价值函数矩阵，建立模型并通过内部嵌套循环程序分析，利用disp函数得出各蔬菜品类每天的最优补货量和定价，以获得商超的最大收益值，当销量超过前一天库存时，最优补货量设为0。针对问题三，首先对总表进行数据预处理，得到六天的蔬菜单品总销量、销售价格和成本加成定价数据矩阵；其次建立一个线性规划模型，通过定义目标函数和约束条件，得到蔬菜商超的收益最大值、当日蔬菜单品的最优补货量和最优定价。针对问题四，为了更好地帮助商超解决前三个问题，可以首先提出蔬菜需求量预测数据，并利用基于集成学习stacking方法的算法来预测未来顾客对蔬菜购买量的需求，以帮助商超调整蔬菜商品的定价。其次，统计供应商信息，考虑进货商可靠性等因素，以选择最优供应商，提高进货效率和蔬菜品质。然后，统计蔬菜商品市场价格竞争情况，帮助商超分析同行的定价策略。最后，考虑顾客满意度问题，统计顾客反馈和需求数据以及退货原因，不断改进以吸引更多忠实客户。<br />
This study explores how to automatically price and replenish vegetable products. By analyzing sales data of various vegetable categories and individual products over the past three years, filtering out unreasonable data, organizing optimal data, establishing a dynamic programming model, and adding additional conditions to predict the optimal replenishment quantity and pricing strategy for specific future time periods. For Problem 1, this paper first preprocesses the data, identifies outliers using box plots, normalizes sales quantities, and analyzes correlations. Using MATLAB’s data visualization toolbox, charts showing sales variation by quarter and category correlation matrices are generated to reveal the trends and correlations in total sales volumes by category. For individual product sales, normalized tables are created and analyzed using Excel pivot tables. Results show stable high sales for leafy vegetables, lower sales for tomato products; high correlation between aquatic root vegetables and cauliflower, and between chili peppers and edible fungi. Among individual product sales, sales are similar for Wuhu green peppers and broccoli, while enoki mushrooms and Yunnan lettuce have the highest sales. For Problem 2, in the first sub-question, the cost-plus pricing for each vegetable product is calculated using a formula, and the relationship between category sales and cost-plus pricing is analyzed through MATLAB data fitting. As cost-plus pricing decreases, total sales distribution becomes more dispersed and lower; with increased cost-plus pricing, total sales become more concentrated and overlap with the fitted line. In the second sub-question, a dynamic programming model is
%K 动态规划模型&#65292
%K 预测模型&#65292
%K 量纲归一化&#65292
%K 相关系数分析法&#65292
%K 拟合分析<br>Dynamic Programming Model
%K Forecasting Model
%K Normalization
%K Correlation Coefficient Analysis
%K Fitting Analysis
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=92918