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\begin{document}

\title{Uncertain optimal control problem of production and inventory under
time-varying customer demand}



\author[1]{Ting Jin}%
\author[1]{Zixuan Li}%
\author[2]{Tingqing Ye}%
\author[1]{Yifu Song}%
\author[3]{Shijun Xiao}%
\affil[1]{Nanjing Forestry University}%
\affil[2]{Beihang University}%
\affil[3]{University of Birmingham}%


\vspace{-1em}



  
  \date{May 20, 2024}


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\begin{abstract}
In the dynamic landscape of global trade and logistics, the optimization
of inventory control has risen as a crucial topic of academic discourse.
Acknowledging that inventory management functions as the intersection of
production and sales, these domains often manifest significant
uncertainty, which consequently poses formidable challenges to the
inventory management optimization. This paper leverages uncertainty
theory in a novel approach to articulate the optimal production strategy
for navigating time-varying demand with inherent fluctuations. And the
inventory state equation, characterized by fluctuations, is proposed as
a constraint condition. By factoring in the residual value of terminal
inventory, a production inventory model catering to time-varying demand
is devised, and the optimal production strategy is ascertained.
Simultaneously, solutions along the \selectlanguage{greek}\emph{α}- \selectlanguage{english}Path are introduced to
procure more intuitive numerical results. Finally, a case study of
Chinese clothing sales was harnedded to substantiate the reliability of
the model conclusion. This research amplifies the application of
uncertainty theory to the optimization of production strategies,
offering a novel perspective on inventory control in the ambit of
uncertain factors. It provides a theoretical paradigm for companies with
uncertain customer needs to orchestrate production, thereby bolstering
the operational efficiency and profitability of the company.%
\end{abstract}%



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