A discrete time Markov chain model for a periodic inventory system with one-way substitution.

This paper studies the optimal design of an inventory system with “one-way substitution”, in which a high-quality (and hence, more expensive) item fulfills its own demand and simultaneously acts as backup safety stock for the (cheaper) low-quality item. Through the use of a discrete time Markov model we analyze the effect of one-way substitution in a periodic inventory system with an (R,s,S) or (R,S) order policy, assuming backorders, zero replenishment leadtime and correlated demand. In more detail, the optimal inventory control parameters (S and s) are determined in view of minimizing the expected total cost per period (i.e. sum of inventory holding costs, purchasing costs, backorder costs and adjustment costs). Numerical results show that the one-way substitution strategy can outperform both the “no pooling” (only product-specific stock is held, and demand can never be rerouted to stock of a different item) and “full pooling” strategies (implying that demand for a particular product type is always rerouted to the stock of the flexible product, and no product-specific stock is held) − provided the mix of dedicated and flexible inputs is chosen adequately − even when the cost premium for flexibility is significant. Furthermore, we can observe that decreasing the demand correlation results in rerouting more demand to the flexible product and because of the risk-pooling effect reduces the optimal expected total cost.Inventory management; One-way substitution;

The Multi-Location Transshipment Problem with Positive Replenishment Lead Times

Transshipments, monitored movements of material at the same echelon of a supply chain, represent an effective pooling mechanism. With a single exception, research on transshipments overlooks replenishment lead times. The only approach for two-location inventory systems with non-negligible lead times could not be generalized to a multi-location setting, and the proposed heuristic method cannot guarantee to provide optimal solutions. This paper uses simulation optimization by combining an LP/network flow formulation with infinitesimal perturbation analysis to examine the multi-location transshipment problem with positive replenishment lead times, and demonstrates the computation of the optimal base stock quantities through sample path optimization. From a methodological perspective, this paper deploys an elegant duality-based gradient computation method to improve computational efficiency. In test problems, our algorithm was also able to achieve better objective values than an existing algorithm.Transshipment;Infinitesimal Perturbation Analysis (IPA);Simulation Optimization

The Multi-Location Transshipment Problem with Positive Replenishment Lead Times

Transshipments, monitored movements of material at the same echelon of a supply chain, represent an effective pooling mechanism. With a single exception, research on transshipments overlooks replenishment lead times. The only approach for two-location inventory systems with non-negligible lead times could not be generalized to a multi-location setting, and the proposed heuristic method cannot guarantee to provide optimal solutions. This paper uses simulation optimization by combining an LP/network flow formulation with infinitesimal perturbation analysis to examine the multi-location transshipment problem with positive replenishment lead times, and demonstrates the computation of the optimal base stock quantities through sample path optimization. From a methodological perspective, this paper deploys an elegant duality-based gradient computation method to improve computational efficiency. In test problems, our algorithm was also able to achieve better objective values than an existing algorithm

Inventory planning for low demand items in online retailing

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2007.Includes bibliographical references (p. 81).A large online retailer strategically stocks inventory for SKUs with low demand. The motivations are to provide a wide range of selections and faster customer fulfillment service. We assume the online retailer has the technological capability to manage and control the inventory globally: all warehouses act as one to serve the global demand simultaneously. The online retailer will utilize its entire inventory, regardless of location, to serve demand. We study inventory allocation and order fulfillment policies among warehouses for low-demand SKUs at an online retailer. Thus, given the global demand and an order fulfillment policy, there are tradeoffs involving inventory holding costs, transportation costs, and backordering costs in determining the optimal system inventory level and allocation of inventory to warehouses. For the case of Poisson demand and constant replenishment lead time, we develop methods to approximate the key system performance metrics like transshipment, backorders and average system inventory for one-for-one replenishment policies when warehouses hold exactly one unit of inventory. We run computational experiments to test the accuracy of the approximation. We develop extensions for cases when more than one unit of inventory is held at a warehouse.(cont.) We then use these results to develop guidelines for inventory stocking and order fulfillment policies for online retailers. We also compare warehouse allocation policies for conditions when an order arrives but the preferred warehouse does not have stock although there is stock at more than one other location in the system. We develop intuition about the performance of these policies and run simulations to verify our hypotheses about these policies.by Pallav Chhaochhria.S.M

Distribution-free Inventory Risk Pooling in a Multi-location Newsvendor

With rapidly increasing e-commerce sales, firms are leveraging the virtual pooling of online demands across customer locations in deciding the amount of inventory to be placed in each node in a fulfillment network. Such solutions require knowledge of the joint distribution of demands; however, in reality, only partial information about the joint distribution may be reliably estimated. We propose a distributionally robust multi-location newsvendor model for network inventory optimization where the worst-case expected cost is minimized over the set of demand distributions satisfying the known mean and covariance information. For the special case of two homogeneous customer locations with correlated demands, we show that a six-point distribution achieves the worst-case expected cost, and derive a closed-form expression for the optimal inventory decision. The general multi-location problem can be shown to be NP-hard. We develop a computationally tractable upper bound through the solution of a semidefinite program (SDP), which also yields heuristic inventory levels, for a special class of fulfillment cost structures, namely nested fulfillment structures. We also develop an algorithm to convert any general distance-based fulfillment cost structure into a nested fulfillment structure which tightly approximates the expected total fulfillment cost.https://deepblue.lib.umich.edu/bitstream/2027.42/146785/1/1389_Govindarajan.pd