{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T13:06:50Z","timestamp":1775912810616,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,5,25]],"date-time":"2022-05-25T00:00:00Z","timestamp":1653436800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71761024"],"award-info":[{"award-number":["71761024"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["21JR1RA236"],"award-info":[{"award-number":["21JR1RA236"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["GSSYLXM-04"],"award-info":[{"award-number":["GSSYLXM-04"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Gansu Province of China","award":["71761024"],"award-info":[{"award-number":["71761024"]}]},{"name":"Natural Science Foundation of Gansu Province of China","award":["21JR1RA236"],"award-info":[{"award-number":["21JR1RA236"]}]},{"name":"Natural Science Foundation of Gansu Province of China","award":["GSSYLXM-04"],"award-info":[{"award-number":["GSSYLXM-04"]}]},{"name":"Double-First Class Major Research Programs, Educational Department of Gansu Province","award":["71761024"],"award-info":[{"award-number":["71761024"]}]},{"name":"Double-First Class Major Research Programs, Educational Department of Gansu Province","award":["21JR1RA236"],"award-info":[{"award-number":["21JR1RA236"]}]},{"name":"Double-First Class Major Research Programs, Educational Department of Gansu Province","award":["GSSYLXM-04"],"award-info":[{"award-number":["GSSYLXM-04"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Due to the influence of insufficient production capacity or shortage of production materials, production enterprises may produce products in advance or be backordered. In order to improve the adaptability of enterprises and reduce production costs, the impacts of early delivery and delayed delivery are analyzed, and the method to determine the loss threshold is put forward. Moreover, the maximum allowable shortage of customers with different tardiness is calculated, and the cost of delayed delivery and loss of sales is determined. Considering the production cost, raw material cost, inventory cost, staff cost, stockout, and lost sales cost, an early\/delay multi-objective optimization model is developed for an aggregate production planning (APP) problem to minimize total production costs and instability in the workforce. Three algorithms and three different hybrid strategies are designed to solve the model. Finally, some test experiments are employed in order to validate the performance of the proposed evaluation of the three algorithms. The results show that: The method of determining the loss threshold can effectively reflect the double influence of customer satisfaction with waiting time and shortage quantity. The definition of unit tardiness cost reflects the law that it increases gradually with waiting time. The determination of the feasible range of product output and the number of workers in the workforce can reduce the search scope of the algorithm and improve the efficiency of the algorithm.<\/jats:p>","DOI":"10.3390\/a15060182","type":"journal-article","created":{"date-parts":[[2022,5,25]],"date-time":"2022-05-25T08:41:33Z","timestamp":1653468093000},"page":"182","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Multi-Objective Model and Algorithms of Aggregate Production Planning of Multi-Product with Early and Late Delivery"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0864-4110","authenticated-orcid":false,"given":"Lanfen","family":"Liu","sequence":"first","affiliation":[{"name":"School of Traffic & Transportation Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4744-5459","authenticated-orcid":false,"given":"Xinfeng","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Traffic & Transportation Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,25]]},"reference":[{"key":"ref_1","first-page":"309","article-title":"Aggregate production planning: A literature review and future research directions","volume":"10","author":"Cheraghalikhani","year":"2019","journal-title":"Int. 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