Robust approximation to multiperiod inventory management

We propose a robust optimization approach to address a multiperiod inventory control problem under ambiguous demands, that is, only limited information of the demand distributions such as mean, support, and some measures of deviations. Our framework extends to correlated demands and is developed around a factor-based model, which has the ability to incorporate business factors as well as time-series forecast effects of trend, seasonality, and cyclic variations. We can obtain the parameters of the replenishment policies by solving a tractable deterministic optimization problem in the form of a second-order cone optimization problem (SOCP), with solution time; unlike dynamic programming approaches, it is polynomial and independent on parameters such as replenishment lead time, demand variability, and correlations. The proposed truncated linear replenishment policy (TLRP), which is piecewise linear with respect to demand history, improves upon static and linear policies, and achieves objective values that are reasonably close to optimal.