Robust Approximation to Multiperiod Inventory Management

We propose a robust optimization approach to address a multi-period, 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 second order cone optimization problem (SOCP), with solution time, unlike dynamic programming approaches, is polynomial and independent on parameters such as replenishment lead time, demand variability, correlations, among others. The proposed truncated linear replenishment policy (TLRP), which is piecewise linear with respect to demand history, improves upon static and linear policies. Our computational studies also suggest that it performs better than simple heuristics derived from dynamic programming. ∗The April 2007 version of this paper went by the title “Robust Inventory Management using Tractable Replenishment Policies”. †Department of Industrial and Systems Engineering, National University of Singapore. Email: see [email protected] ‡NUS Business School, Singapore-MIT Alliance, NUS Risk Management Institute, National University of Singapore. Email: [email protected]. The research of the author is supported by SMA and NUS academic research grant R-314000-068-122.