Single-stage approximations for optimal policies in serial inventory systems with nonstationary demand

Companies often face nonstationary demand due to product life cycles and seasonality, and nonstationary demand complicates supply chain managers' inventory decisions. This paper proposes a simple heuristic for determining stocking levels in a serial inventory system. Unlike the exact optimization algorithm, the heuristic generates a near-optimal solution by solving a series of independent single-stage systems. The heuristic is constructed based on three results we derive. First, we provide a new cost decomposition scheme based on echelon systems. Next, we show that the optimal base-stock level for each echelon system is bounded by those of two revised echelon systems. Last, we prove that the revised echelon systems are essentially equivalent to single-stage systems. We examine the myopic solution for these single-stage systems. In a numerical study, we find that the change of direction of the myopic solution is consistent with that of the optimal solution when system parameters vary. We then derive an analytical expression for the myopic solution and use it to gain insights into how to manage inventory. The analytical expression shows how future demand affects the current optimal local base-stock level; it also explains an observation that the safety stock at an upstream stage is often stable and may not increase when the demand variability increases over time. Finally, we discuss how the heuristic leads to a time-consistent coordination scheme that enables a decentralized supply chain to achieve the heuristic solution. © 2012 INFORMS.

Duke Scholars

Author Kevin H. Shang Fuqua School of Business