In this note, we polynomially reduce an instance of the partition problem to a dynamic lot sizing problem, and show that solving the latter problem solves the former problem. By solving the dynamic program formulation of the dynamic lot sizing problem, we show that the instance of the partition problem can be solved with pseudo-polynomial time complexity. Numerical results on solving instances of the partition problem are also provided using an implementation of the algorithm that solves the dynamic program. We conclude by discussing polynomial time solvability of the partition problem through further observation on the dynamic program formulation of the dynamic lot sizing problem.

翻译：本文中，我们将划分问题的一个实例多项式归约至动态批量确定问题，并证明求解后者即可解决前者。通过求解动态批量确定问题的动态规划模型，我们证明该划分问题实例可在伪多项式时间复杂度内求解。我们还通过实现求解该动态规划的算法，提供了求解划分问题实例的数值结果。最后，我们通过对动态批量确定问题动态规划模型的进一步观察，探讨了划分问题的多项式时间可解性。