Search for: All records

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. Our first objective is to jointly optimize ordering decisions pertaining to regular, reverse and expedited flows of product in a stochastic, multi-stage inventory model of a logistics supply chain, in which the physical transformation of the product is completed at the most upstream location in the system. Due to those multiple flows of product, the feasible region for the problem acquires multi-dimensional boundaries that lead to the curse of dimensionality. To address this challenge, we develop a different solution method that allows us to reduce the dimensionality of the feasible region and, subsequently, 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 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 inherent demand volatility. Our second objective is to 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, so that the number of state and decisions variables increases with the square of the number of locations in the system. To analyze such a supply chain, 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. 

This paper studies an inventory management problem faced by an upstream supplier that is in a collaborative agreement, such as vendor-managed inventory (VMI), with a retailer. A VMI partnership provides the supplier an opportunity to manage in- ventory for the supply chain in exchange for point-of-sales (POS)- and inventory-level information from the retailer. However, retailers typically possess superior local market information and as has been the case in recent years, are able to capture and analyze customer purchasing behavior beyond the traditional POS data. Such analyses provide the retailer access to market signals that are otherwise hard to capture using POS information. We show and quantify the implication of the financial obligations of each party in VMI that renders communication of such important market signals as noncredible. To help insti- tute a sound VMI collaboration, we propose learn and screen—a dynamic inventory mechanism—for the supplier to effectively manage inventory and information in the supply chain. The proposed mechanism combines the ability of the supplier to learn about market conditions from POS data (over multiple selling periods) and dynamically de- termine when to screen the retailer and acquire his private demand information. Inventory decisions in the proposed mechanism serve a strategic purpose in addition to their classic role of satisfying customer demand. We show that our proposed dynamic mechanism significantly improves the supplier’s expected profit and increases the efficiency of the overall supply chain operations under a VMI agreement. In addition, we determine the market conditions in which a strategic approach to VMI results in significant profit im- provements for both firms, particularly when the retailer has high market power (i.e., when the supplier highly depends on the retailer) and when the supplier has relatively less knowledge about the end customer/market compared with the retailer. 

We consider a multi-stage inventory system with stochastic demand and processing capacity constraints at each stage, for both finite-horizon and infinite-horizon, discounted-cost settings. For a class of such systems characterized by having the smallest capacity at the most downstream stage and system utilization above a certain threshold, we identify the structure of the optimal policy, which represents a novel variation of the order-up-to policy. We find the explicit functional form of the optimal order-up-to levels, and show that they depend (only) on upstream echelon inventories. We establish that, above the threshold utilization, this optimal policy achieves the decomposition of the multidimensional objective cost function for the system into a sum of single-dimensional convex functions. This decomposition eliminates the curse of dimensionality and allows us to numerically solve the problem. We provide a fast algorithm to determine a (tight) upper bound on this threshold utilization for capacity-constrained inventory problems with an arbitrary number of stages. We make use of this algorithm to quantify upper bounds on the threshold utilization for three-, four-, and five-stage capacitated systems over a range of model parameters, and discuss insights that emerge.