Polynomial policies in supply chain networks

Abstract

This thesis aims to solve the periodic-reviewed inventory control problem in supply chain networks with uncertain demand so as to minimize the overall cost of the system over a fixed planning time horizon. In such problems, one seeks to optimally determine ordering quantities at different stages in time. We investigate the class of polynomial policies, where the control policy is directly parametrized polynomially in the observed uncertainties of previous stages. We use sum-of-square relaxations to reformulate the problem into a single semidefinite optimization problem for a specific polynomial degree. We consider both robust and stochastic approaches in order to address the uncertainties in demand. In extensive numerical studies, we find that polynomial policies exhibit better performance over basestock policies across a variety of networks and demand distributions under the mean and standard deviation criteria. However, when the uncertainty set turns out to be larger than planned, basestock policies start outperforming polynomial policies. Comparing the policies obtained under the robust and stochastic frameworks, we find that they are comparable in the average performance criterion, but the robust approach leads to better tail behavior and lower standard deviation in general.