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Therefore, this study used the optimal control theory to propose an order system and inventory management model. The model is presented from the company\u2019s resourcing stage with a desirable accountability level from the supplier side in a continuous review period with dynamic multi-item demand and budget constraints. In the present model, the order was regarded as a time-dependent function and a control variable. In addition, the need for each item is time-dependent and specified. The present model indicates the order and inventory system as an optimal control problem. In addition, Pontryagin\u2019s maximum principle for optimal control problems, Generalized Reduced Gradient Method (GRG), and Kuhn\u2013Tucker conditions were used to seek the optimal order. The model aimed to maximize the total order profit and inventory management systems. Finally, the results were presented numerically and graphically, and some management decisions were derived.<\/jats:p>","DOI":"10.1177\/01423312221109724","type":"journal-article","created":{"date-parts":[[2022,8,1]],"date-time":"2022-08-01T08:06:30Z","timestamp":1659341190000},"page":"104-119","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["Improvement of multi-item order systems and inventory management models using optimal control theory"],"prefix":"10.1177","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2108-0287","authenticated-orcid":false,"given":"Mahdi","family":"Nakhaeinejad","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering, Faculty of Engineering, Yazd University, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hassan","family":"Khademi Zare","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, Faculty of Engineering, Yazd University, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohsen","family":"Habibi","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, Faculty of Engineering, Science and Art University, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad Reza","family":"Khodoomi","sequence":"additional","affiliation":[{"name":"School of Industrial Engineering, Iran University of Science and Technology, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2022,8,1]]},"reference":[{"key":"bibr1-01423312221109724","doi-asserted-by":"publisher","DOI":"10.29015\/cerem.578"},{"key":"bibr2-01423312221109724","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(98)00202-1"},{"key":"bibr3-01423312221109724","doi-asserted-by":"publisher","DOI":"10.1080\/00207728508926662"},{"key":"bibr4-01423312221109724","doi-asserted-by":"publisher","DOI":"10.1080\/17509653.2018.1563873"},{"key":"bibr5-01423312221109724","first-page":"36","volume":"5","author":"Bounkhel M","year":"2005","journal-title":"Applied Mathematics E-Notes"},{"key":"bibr6-01423312221109724","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2021.104311"},{"key":"bibr7-01423312221109724","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2006.02.024"},{"key":"bibr8-01423312221109724","doi-asserted-by":"publisher","DOI":"10.1088\/1757-899X\/469\/1\/012115"},{"issue":"8","key":"bibr9-01423312221109724","first-page":"146","volume":"1","author":"Fredrick K","year":"2018","journal-title":"International Journal of Logistics and Procurement Management"},{"key":"bibr10-01423312221109724","volume-title":"Principles of Optimal Control Theory","volume":"7","author":"Gamkrelidze R","year":"2013"},{"issue":"1","key":"bibr11-01423312221109724","first-page":"43","volume":"51","author":"Ganji F","year":"2019","journal-title":"Journal of Algorithms and Computation"},{"key":"bibr12-01423312221109724","first-page":"143","volume-title":"Congress of APDIO, the Portuguese operational research society","author":"Gon\u00e7alves JN","year":"2018"},{"key":"bibr13-01423312221109724","unstructured":"Horoshkova L, Khlobystov Y, Volkov V, et al. 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