{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:36:29Z","timestamp":1760236589859,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,5]],"date-time":"2021-12-05T00:00:00Z","timestamp":1638662400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Volatile markets and uncertain deterioration rate make it extremely difficult for manufacturers to make the quantity of saleable vegetables just meet the fluctuating demands, which will lead to inevitable out of stock or over production. Aggregate production planning (APP) is to find the optimal yield of vegetables, shortage and overstock symmetry, are not conducive to the final benefit.The essence of aggregate production planning is to deal with the symmetrical relation between shortage and overproduction. In order to reduce the adverse effects caused by shortage, we regard the service level as an important constraint to meet the customer demand and ensure the market share. So an uncertain aggregate production planning model for vegetables under condition of allowed stockout and considering service level constraint is constructed, whose objective is to find the optimal output while minimizing the expected total cost. Moreover, two methods are proposed in different cases to solve the model. A crisp equivalent form can be transformed when uncertain variables obey linear uncertain distributions and for general case, a hybrid intelligent algorithm integrating the 99-method and genetic algorithm is employed. Finally, two numerical examples are carried out to illustrate the effectiveness of the proposed model.<\/jats:p>","DOI":"10.3390\/sym13122332","type":"journal-article","created":{"date-parts":[[2021,12,7]],"date-time":"2021-12-07T02:48:13Z","timestamp":1638845293000},"page":"2332","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Uncertain APP Model with Allowed Stockout and Service Level Constraint for Vegetables"],"prefix":"10.3390","volume":"13","author":[{"given":"Yufu","family":"Ning","sequence":"first","affiliation":[{"name":"School of Information Engineering, Shandong Youth University of Political Science, Jinan 250103, China"},{"name":"Key Laboratory of Intelligent Information Processing Technology and Security in Universities of Shandong, Jinan 250103, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Na","family":"Pang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Information Processing Technology and Security in Universities of Shandong, Jinan 250103, China"},{"name":"Business School, Shandong Normal University, Jinan 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuai","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Shandong Youth University of Political Science, Jinan 250103, China"},{"name":"Key Laboratory of Intelligent Information Processing Technology and Security in Universities of Shandong, Jinan 250103, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiumei","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Shandong Youth University of Political Science, Jinan 250103, China"},{"name":"Key Laboratory of Intelligent Information Processing Technology and Security in Universities of Shandong, Jinan 250103, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1287\/mnsc.2.1.1","article-title":"A linear decision rule for production and employment scheduling","volume":"2","author":"Holt","year":"1955","journal-title":"Manag. 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