Analysis of a two-echelon inventory system with returns

Product take-back and recovery activities have grown in recent times as a consequence of stringent government regulations and increased customer awareness of environmental pollution. Inventory management in the context of product returns has drawn the attention of many researchers. However, the inherent complexity of the system with uncertain returns makes the analysis of the system extremely difficult. So far, the literature on this type of system is mostly limited to single echelons. The few papers available in literature on multi-echelon systems with returns base their analyses on simplified assumptions such as non-existence or non-relevance of set-up and holding costs at different levels. In this paper, we relax these assumptions and consider a two-echelon system with returns under more generalized conditions. We develop a deterministic model as well as a stochastic model under continuous review for the system, and provide numerical examples for illustration.