{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:00:34Z","timestamp":1760144434736,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,4,13]],"date-time":"2024-04-13T00:00:00Z","timestamp":1712966400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["NSFC12371338","NSFC11601001"],"award-info":[{"award-number":["NSFC12371338","NSFC11601001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Vegetables have a short period of freshness, and therefore, the purchase of vegetables has to be carefully matched with sales, especially in the \u201csmall production and big market\u201d setting prevalent in China. Therefore, it is worthwhile to develop a systematic and comprehensive mathematical model of replenishment plans and pricing strategies for each category of vegetables and individual products. In this paper, we analyze the following three questions: Question One: What is the distribution law and relationship between the sales volume of vegetable categories and single products? Question Two: What is the relationship between total sales volume and cost-plus pricing of vegetable categories? And is it possible to provide the daily total replenishment and pricing strategy of each vegetable category for the following week to maximize supermarket profit? Question Three: How can we incorporate the market demand for single vegetable products into a profit-maximizing program for supermarkets? Is it possible to further formulate the replenishment plan requirements for single products? To answer the first question, we created pivot tables to analyze occupancy. We found that mosaic leaves, peppers, and edible mushrooms accounted for a larger proportion of occupacy, while cauliflowers, aquatic rhizomes, and eggplants accounted for a smaller proportion. For the single items, lettuce, cabbage, green pepper, screw pepper, enoki mushroom, and shiitake mushroom accounted for a large proportion of their respective categories. We used the Pearson correlation coefficient and the Mfuzz package based on fuzzy c-means (FCM) algorithm to analyze the correlation between vegetable categories and single products. We found that there was a strong correlation between vegetable categories. Moreover, the sale of vegetable items belonging to the same category exhibited the same patterns of change over time. In order to address the second question, we established the LightGBM sales forecasting model. Combined with previous sales data, we forecasted and planned an efficient daily replenishment volume for each vegetable category in the coming week. In addition, we developed a pricing strategy for vegetable categories to maximize supermarket profits. For the third question, we built a dynamic programming model combining an optimal replenishment volume with a product pricing strategy for single items, which let the supermarket maximize its expected profits.<\/jats:p>","DOI":"10.3390\/axioms13040257","type":"journal-article","created":{"date-parts":[[2024,4,15]],"date-time":"2024-04-15T08:08:12Z","timestamp":1713168492000},"page":"257","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Research on the Optimization of Pricing and the Replenishment Decision-Making Problem Based on LightGBM and Dynamic Programming"],"prefix":"10.3390","volume":"13","author":[{"given":"Wenyue","family":"Tao","sequence":"first","affiliation":[{"name":"Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233000, China"}]},{"given":"Chaoran","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233000, China"}]},{"given":"Ting","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Economics, Anhui University of Finance and Economics, Bengbu 233000, China"}]},{"given":"Fuyuan","family":"Chen","sequence":"additional","affiliation":[{"name":"Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233000, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,13]]},"reference":[{"key":"ref_1","unstructured":"Zhang, S., and Zhou, J. (2023). Analysis of factors and strategies affecting the efficiency of \u201cagricultural super docking\u201d of bulk vegetables. Shanxi Agric. Econ., 263\u2013268."},{"key":"ref_2","unstructured":"Li, G. (2016). Research on Price Formation and Stabilization Measures of the Whole Vegetable Industry Chain. [Ph.D. Thesis, Nanjing University of Aeronautics and Astronautics]."},{"key":"ref_3","first-page":"69","article-title":"Research on vegetable revenue insurance risk and pricing in Shandong","volume":"32","author":"Wei","year":"2021","journal-title":"Rural Econ. Technol."},{"key":"ref_4","first-page":"234","article-title":"Dynamic planning model and application of solution for merchandising","volume":"3","author":"Zhu","year":"2002","journal-title":"J. Shijiazhuang Econ. Coll."},{"key":"ref_5","first-page":"322","article-title":"Cluster analysis of fuzzy C-mean seismic attributes","volume":"42","author":"Yang","year":"2007","journal-title":"Pet. Geophys. Explor."},{"key":"ref_6","unstructured":"Lu, Y. (2010). Research on Dynamic Pricing Problem of High Quality Fresh Vegetables in Supermarkets in China. [Ph.D. Thesis, Beijing Jiaotong University]."},{"key":"ref_7","first-page":"61","article-title":"Research on resource allocation of health service stations based on state transfer equation","volume":"31","author":"Yan","year":"2012","journal-title":"China Health Econ."},{"key":"ref_8","unstructured":"Wang, S. (2014). Research on the Formation Problem of Retail Price of Vegetables in Farmers\u2019 Market. [Ph.D. Thesis, Huazhong Agricultural University]."},{"key":"ref_9","unstructured":"Song, J. (2015). Research on Optimization of Inventory Management of Vegetable Supply Chain in Shouguang City. Coop. Econ. Sci. Technol., 138\u2013139."},{"key":"ref_10","first-page":"36","article-title":"Application of state transfer equation in multi-stage decision-making evaluation of emergencies","volume":"7","author":"Wu","year":"2020","journal-title":"Decis.-Mak. Explor."},{"key":"ref_11","first-page":"263","article-title":"Optimizable replenishment strategy based on dynamic matrix model","volume":"57","author":"Lu","year":"2021","journal-title":"Comput. Eng. Appl."},{"key":"ref_12","first-page":"250","article-title":"A parameter estimation method for multivariate linear models based on residual vector l1-paradigm minimization with basis tracking","volume":"35","author":"Feng","year":"2022","journal-title":"J. Hainan Norm. Univ. Nat. Sci. Ed."},{"key":"ref_13","unstructured":"Li, Y. (2023). Joint Replenishment and Pricing Collaborative Decision Making Considering Investment in Preservation Technology. [Ph.D. Thesis, Chongqing Jiaotong University]."},{"key":"ref_14","first-page":"833","article-title":"Optimized deep forest algorithm based on Lightgbm and XGBoost","volume":"59","author":"Xie","year":"2023","journal-title":"J. Nanjing Univ. Nat. Sci."},{"key":"ref_15","unstructured":"Xu, X., Zhang, Y., Fang, Y., and Liu, S. (2024). Research on Inventory Management Optimization of A Trading Company Based on k-means Clustering Algorithm. China Storage Transp., 143\u2013144."},{"key":"ref_16","first-page":"357","article-title":"Identification of residential electricity theft based on Pearson correlation coefficient and SVM","volume":"43","author":"Guo","year":"2023","journal-title":"J. Hebei Univ. Nat. Sci. Ed."},{"key":"ref_17","unstructured":"Liu, H. (2023). Research and application of network intrusion detection method based on deep learning. Comput. Program. Ski. Maint., 162\u2013165."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/4\/257\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:27:38Z","timestamp":1760106458000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/4\/257"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,13]]},"references-count":17,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["axioms13040257"],"URL":"https:\/\/doi.org\/10.3390\/axioms13040257","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2024,4,13]]}}}