When Variability Trumps Volatility: Optimal Control and Value of Reverse Logistics in Supply Chains with Multiple Flows of Product
49 Pages Posted: 17 Nov 2017 Last revised: 21 Oct 2018
Date Written: June 15, 2018
Reverse logistics has been gaining recognition in practice (and theory) for helping companies better match supply with demand, and thus reduce costs in their supply chains. In this paper, we study reverse logistics from the perspective of a supply chain in which each location can initiate multiple flows of product. We formulate a stochastic, multi-stage inventory model to jointly optimize ordering decisions pertaining to regular, reverse and expedited flow of product throughout the system. Due to these multiple flows of product, the resulting feasible region acquires multi-dimensional boundaries that lead to the curse of dimensionality. To address this challenge, we develop a different solution method based on allowing long purchases of inventory in the supply chain. This method allows us to reduce the dimensionality of the feasible region and, subsequently, identify the structure of the optimal policy. This optimal policy represents a nested echelon basestock policy whose key feature is that decisions for different product flows are sequentially nested within each other. We show that this policy renders the model analytically and numerically tractable. Our results provide actionable policies for firms to jointly manage three different product flows in their supply chains, and allow us arrive at insights regarding the main drivers of the value of reverse logistics. One of our key findings is that, when it comes to the value generated by reverse logistics, demand variability (i.e., demand uncertainty across periods) matters more than demand volatility (i.e., demand uncertainty within each period). This is because, in the absence of demand variability, it is effectively never optimal to return product upstream, regardless of the level of demand volatility. Finally, we demonstrate that reverse logistics creates most value in supply chains that are characterized by higher demand variability, higher number of locations in the system, and lower reverse logistics and expediting order costs, as in such systems returning products upstream and expediting products downstream act as complements with regard to cost savings.
Keywords: Reverse Logistics; Multiechelon Inventory; Expediting; Secondary Markets; Optimal Policy
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