Research on optimization of Pricing and Replenishment Decision Making Problem Based on LightGBM and Dynamic Programming

Abstract The fresh-keeping period of vegetable commodities was relatively short, and its sales problem had always been of great concern under the vegetable production and distribution pattern of ”small production and big market” in China. Therefore, it was necessary to establish a systematic and comprehensive mathematical model, and rationally formulate the replenishment plans and pricing strategies for each category and individual product of vegetables. In this paper, we mainly solved the following three questions: Question One: What was the distribution law and relationship between the sales volume of vegetable categories and single products? Question Two: What was the relationship between total sales volume and costplus pricing of vegetable categories? Could you give the daily total replenishment and pricing strategy of each vegetable category in the next week, so that the supermarket would have the greatest profit? Question Three: On the premise of meeting the market demand for various categories of vegetable products, how to further formulate the replenishment plan requirements of single products to maximize the revenue of supermarkets? For the first question, we used the Pearson correlation coefficient and the Mfuzz package based on fuzzy c-means clustering to analyze the distribution law and correlation between vegetable categories and single products.We found that mosaic leaves, peppers and edible mushrooms accounted for a larger proportion, while cauliflower, aquatic rhizomes and eggplants accounted for a small proportion. And for single items, lettuce, cabbage, green pepper, screw pepper, enoki mushroom and shiitake mushroom accounted for a large proportion of their respective categories. We also found that there was a strong correlation between vegetable categories. And the sales of vegetable items belonging to the same category showed the same change pattern over time. For the second question, we established the LightGBM sales forecasting model to solve it. Combined with previous sales data, we forecasted the daily replenishment volume of each vegetable category in the coming week. And we developed a pricing strategy for vegetable categories to maximize the benefits of the supermarket. For the third question, we built a dynamic programming model to solve it. We developed an optimal replenishment volume and pricing strategy for single items, which let the supermarket maximize its income on the premise of meeting the constraints. Mathematics Subject Classification (2020) 68M07 · 91B03 · 91B24