Solving a constrained economic lot size problem by ranking efficient production policies

Abstract

<p style='text-indent:20px;'>We address the problem of finding the <inline-formula><tex-math id="M1">\begin{document}$ K $\end{document}</tex-math></inline-formula> best Zero-Inventory-Ordering (ZIO) policies of an Economic Lot-Sizing Problem (ELSP) with <inline-formula><tex-math id="M2">\begin{document}$ n $\end{document}</tex-math></inline-formula> time periods. To this end, we initially focus on devising an efficient algorithm to determine the Second Best ZIO policy. Based on both this latter algorithm and recent results from the state-of-the-art literature, we propose a solution method to compute the remaining <inline-formula><tex-math id="M3">\begin{document}$ K $\end{document}</tex-math></inline-formula> Best ZIO policies in <inline-formula><tex-math id="M4">\begin{document}$ O(n(K+n)) $\end{document}</tex-math></inline-formula> time and <inline-formula><tex-math id="M5">\begin{document}$ O(K+n^2 ) $\end{document}</tex-math></inline-formula> space. One claimed advantage of this approach is that it would efficiently solve a family of ELS problems, which includes a basic knapsack type constraint. A computational experiment is carried out to test the performance of the new algorithm <inline-formula><tex-math id="M6">\begin{document}$ K $\end{document}</tex-math></inline-formula>-ZIO and Constrained-ZIO for different values of <inline-formula><tex-math id="M7">\begin{document}$ K $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M8">\begin{document}$ n $\end{document}</tex-math></inline-formula>. For the particular case when the left-hand side coefficients in that constraint are equal, we provide an <inline-formula><tex-math id="M9">\begin{document}$ O(n^3 ) $\end{document}</tex-math></inline-formula> solution method.</p>