When Variability Trumps Volatility: Optimal Control and Value of Reverse Logistics in Supply Chains with Multiple Flows of Product

Abstract

Problem definition: We study how to optimally control a multistage supply chain in which each location can initiate multiple flows of product, including the reverse flow of orders. We also quantify the resulting value generated by reverse logistics and identify the drivers of that value. Academic/practical relevance: 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. Nevertheless, there remains a lack of clarity in practice and the research literature regarding precisely what in reverse logistics is so important, exactly how reverse logistics creates value, and what the drivers of that value are. Methodology: We first formulate a multistage inventory model to jointly optimize ordering decisions pertaining to regular, reverse, and expedited flows of product in a logistics supply chain, where the physical transformation of the product is completed at the most upstream location. With multiple product flows, the feasible region for the problem acquires multidimensional boundaries that lead to the curse of dimensionality. Next, we extend our analysis to product-transforming supply chains, in which product transformation is allowed to occur at each location. In such a system, it becomes necessary to keep track of both the location and stage of completion of each unit of inventory; thus, the number of state and decision variables increases with the square of the number of locations. Results: To solve the reverse logistics problem in logistics supply chains, we develop a different solution method that allows us to reduce the dimensionality of the feasible region and identify the structure of the optimal policy. We refer to this policy as a nested echelon base stock policy, as 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 the three different product flows in their supply chains and allow us to 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). To analyze product-transforming supply chains, we first identify a policy that provides a lower bound on the total cost. Then, we establish a special decomposition of the objective cost function that allows us to propose a novel heuristic policy. We find that the performance gap of our heuristic policy relative to the lower-bounding policy averages less than 5% across a range of parameters and supply chain lengths. Managerial implications: Researchers can build on our methodology to study more complex reverse logistics settings, as well as tackle other inventory problems with multidimensional boundaries of the feasible region. Our insights can help companies involved in reverse logistics to better manage their orders for products, and better understand the value created by this capability and when (not) to invest in reverse logistics.