Lp-Based Artificial Dependency for Probabilistic Etail Order Fulfillment

We consider an online multi-item retailer with multiple fulfillment facilities and finite inventory, with the objective of minimizing the expected shipping cost of fulfilling customer orders over a finite horizon. We approximate the stochastic dynamic programming formulation of the problem with an equivalent deterministic linear program, which we use to develop a probabilistic fulfillment heuristic that is provably optimal in the asymptotic sense. This first heuristic, however, relies on solving an LP that is exponential in the size of the input. Therefore, we subsequently provide another heuristic which solves an LP that is polynomial in the size of the input, and prove an upper bound on its asymptotic competitive ratio. This heuristic works by modifying the LP solution with artificial dependencies, with the resulting fractional variables used to probabilistically fulfill orders. A hardness result shows that asymptotically optimal policies that are computationally efficient cannot exist. Finally, we conduct numerical experiments that show that our heuristic's performance is very close to optimal for a range of parameters.http://deepblue.lib.umich.edu/bitstream/2027.42/108712/1/1250_ASinha.pd

Using Image Transformations to Learn Network Structure

Many learning tasks require observing a sequence of images and making a decision. In a transportation problem of designing and planning for shipping boxes between nodes, we show how to treat the network of nodes and the flows between them as images. These images have useful structural information that can be statistically summarized. Using image compression techniques, we reduce an image down to a set of numbers that contain interpretable geographic information that we call geographic signatures. Using geographic signatures, we learn network structure that can be utilized to recommend future network connectivity. We develop a Bayesian reinforcement algorithm that takes advantage of statistically summarized network information as priors and user-decisions to reinforce an agent's probabilistic decision.Comment: 11 pages, 6 figures, 5 tables, In Submission with International Journal of Data Science and Analytics, Special Issue: Domain Driven Data Minin

Near-Optimal Bisection Search for Nonparametric Dynamic Pricing with Inventory Constraint

We consider a single-product revenue management problem with an inventory constraint and unknown, noisy, demand function. The objective of the fi rm is to dynamically adjust the prices to maximize total expected revenue. We restrict our scope to the nonparametric approach where we only assume some common regularity conditions on the demand function instead of a speci fic functional form. We propose a family of pricing heuristics that successfully balance the tradeo ff between exploration and exploitation. The idea is to generalize the classic bisection search method to a problem that is a ffected both by stochastic noise and an inventory constraint. Our algorithm extends the bisection method to produce a sequence of pricing intervals that converge to the optimal static price with high probability. Using regret (the revenue loss compared to the deterministic pricing problem for a clairvoyant) as the performance metric, we show that one of our heuristics exactly matches the theoretical asymptotic lower bound that has been previously shown to hold for any feasible pricing heuristic. Although the results are presented in the context of revenue management problems, our analysis of the bisection technique for stochastic optimization with learning can be potentially applied to other application areas.http://deepblue.lib.umich.edu/bitstream/2027.42/108717/1/1252_Sinha.pd

Joint Inventory and Fulfillment Decisions for Omnichannel Retail Networks

With e-commerce growing at a rapid pace compared to traditional retail, many brick-and-mortar firms are supporting their online growth through an omnichannel approach, which integrates inventories across multiple channels. We analyze the inventory optimization of three such omnichannel fulfillment systems for a retailer facing two demand streams (online and in-store). The systems differ in the level of fulfillment integration, ranging from no integration (separate fulfillment center for online orders), to partial integration (online orders fulfilled from nearest stores) and full integration (online orders fulfilled from nearest stores, but in case of stockouts, can be fulfilled from any store). We obtain optimal order-up-to quantities for the analytical models in the two-store, single-period setting. We then extend the models to a generalized multi-store setting, which includes a network of traditional brick-and-mortar stores, omnichannel stores and online fulfillment centers. We develop a simple heuristic for the fully-integrated model, which is near optimal in an asymptotic sense for a large number of omnichannel stores, with a constant approximation factor dependent on cost parameters. We augment our analytical results with a realistic numerical study for networks embedded in the mainland US, and find that our heuristic provides significant benefits compared to policies used in practice. Our heuristic achieves reduced cost, increased efficiency and reduced inventory imbalance, all of which alleviate common problems facing omnichannel retailing firms. Finally, for the multiperiod setting under lost sales, we show that a base-stock policy is optimal for the fully-integrated model.With e-commerce growing at a rapid pace compared to traditional retail, many brick-and-mortar firms are supporting their online growth through an omnichannel approach, which integrates inventories across multiple channels. We analyze the inventory optimization of three such omnichannel fulfillment systems for a retailer facing two demand streams (online and in-store). The systems differ in the level of fulfillment integration, ranging from no integration (separate fulfillment center for online orders), to partial integration (online orders fulfilled from nearest stores) and full integration (online orders fulfilled from nearest stores, but in case of stockouts, can be fulfilled from any store). We obtain optimal order-up-to quantities for the analytical models in the two-store, single-period setting. We then extend the models to a generalized multi-store setting, which includes a network of traditional brick-and-mortar stores, omnichannel stores and online fulfillment centers. We develop a simple heuristic for the fully-integrated model, which is near optimal in an asymptotic sense for a large number of omnichannel stores, with a constant approximation factor dependent on cost parameters. We augment our analytical results with a realistic numerical study for networks embedded in the mainland US, and find that our heuristic provides significant benefits compared to policies used in practice. Our heuristic achieves reduced cost, increased efficiency and reduced inventory imbalance, all of which alleviate common problems facing omnichannel retailing firms. Finally, for the multiperiod setting under lost sales, we show that a base-stock policy is optimal for the fully-integrated model.http://deepblue.lib.umich.edu/bitstream/2027.42/136157/1/1341_Govindarajan.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136157/4/1341_Govindarajan_Apr2017.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136157/6/1341_Govindarajan_Jan18.pdfDescription of 1341_Govindarajan_Apr2017.pdf : April 2017 revisionDescription of 1341_Govindarajan_Jan18.pdf : January 2018 revisio

Dynamic Joint Pricing and Order Fulfillment for E-Commerce Retailers

We consider an e-commerce retailer (e-tailer) who sells a catalog of products to customers from different regions during a finite selling season and fulfills orders through multiple fulfillment centers. The e-tailer faces a Joint Pricing and Fulfillment (JPF) problem: At the beginning of each period, she needs to jointly decide the price for each product and how to fulfill an incoming order. The objective is to maximize the total expected profits defined as total expected revenues minus total expected shipping costs (all other costs are fixed in this problem). The exact optimal policy for JPF is difficult to solve; so, we propose two heuristics that have provably good performance compared to reasonable benchmarks. Our first heuristic directly uses the solution of a deterministic approximation of JPF as its control parameters whereas our second heuristic improves the first heuristic by adaptively adjusting the original control parameters at the beginning of every period. An important feature of the second heuristic is that it decouples the pricing and fulfillment decisions, making it easy to implement. We show theoretically and numerically that the second heuristic significantly outperforms the first heuristic and is very close to a benchmark that jointly re-optimizes the full deterministic problem at every period.http://deepblue.lib.umich.edu/bitstream/2027.42/117573/1/1310_Jasin.pd

Capacity Investment with Demand Learning

We study a firm’s optimal strategy to adjust its capacity using demand information. The capacity adjustment is costly and often subject to managerial hurdles which sometimes make it difficult to adjust capacity multiple times. In order to clearly analyze the impact of demand learning on the firm’s decision, we study two scenarios. In the first scenario, the firm’s capacity adjustment cost increases significantly with respect to the number of adjustments because of significant managerial hurdles, and resultantly the firm has a single opportunity to adjust capacity (single adjustment scenario). In the second scenario, the capacity adjustment costs do not change with respect to the number of adjustments because of little managerial hurdles, and therefore the firm has multiple opportunities to adjust capacity (multiple adjustment scenario). For both scenarios, we first formulate the problem as a stochastic dynamic program, and then characterize the firm’s optimal policy: when to adjust and by how much. We show that the optimal decision on when and by how much to change the capacity is not monotone in the likelihood of high demand in the single adjustment scenario, while the optimal decision is monotone under mild conditions and the optimal policy is a control band policy in the multiple adjustment scenario. The sharp contrast reflects the impact of demand learning on the firm’s optimal capacity decision. Since computing and implementing the optimal policy is not tractable for general problems, we develop a data-driven heuristic for each scenario. In the single adjustment scenario, we show that a two-step heuristic which explores demand for an appropriately chosen length of time and adjusts the capacity based on the observed demand is asymptotically optimal, and prove the convergence rate. In the multiple adjustment scenario, we also show that a multi-step heuristic under which the firm adjusts its capacity at a predetermined set of periods with exponentially increasing gap between two consecutive decisions is asymptotically optimal and show its convergence rate. We finally apply our heuristics to a numerical study and demonstrate the performance and robustness of the heuristics.http://deepblue.lib.umich.edu/bitstream/2027.42/122454/4/1231_Ahn_July162016.pdfDescription of 1231_Ahn_July162016.pdf : July 2016 revisionDescription of 1321_Ahn.pdf : [SUPERSEDED] Original version for reference onl

Investing in a Shared Supplier in a Competitive Market: Stochastic Capacity Case

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/116001/1/poms12348-sup-0001-Appendix.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/116001/2/poms12348.pd

To Share or Not to Share? Capacity Reservation in a Shared Supplier

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151965/1/poms13081_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151965/2/poms13081-sup-0001-OnlineAppendix.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151965/3/poms13081.pd

Approximating the Degree-Bounded Minimum Diameter Spanning Tree Problem

We consider the problem of finding a minimum diameter spanning treewith maximum node degree $B$ in a complete undirected edge-weightedgraph. We provide an $O(sqrt{log_Bn})$-approximation algorithm for theproblem. Our algorithm is purely combinatorial, and relies on acombination of filtering and divide and conquer.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41348/1/453_2004_Article_1121.pd

Prevalence, Response to Cysticidal Therapy, and Risk Factors for Persistent Seizure in Indian Children with Neurocysticercosis

Background. Neurocysticercosis (NCC) is the commonest cause of childhood acquired epilepsy in developing countries. The use of cysticidal therapy in NCC, except “single lesion NCC,” is still debated in view of its doubtful usefulness and potential adverse effects. Methods. Children presenting with first episode of seizure or acute focal neurological deficit without fever were screened for NCC and received appropriate therapy (followup done for 1 year to look for the response and side effects). Results. The prevalence of NCC was 4.5%. Most common presenting feature was generalized seizure and commonest imaging finding was single small enhancing lesion in the parietal lobe. Abnormal EEG and CSF abnormalities were found in almost half of the children. The response to therapy was very good with infrequent recurrence of seizure and adverse effects of therapy were encountered rarely. No risk factors for persistent seizure could be identified. Conclusion. Present study shows that the response to cysticidal therapy is very good in NCC as seizure recurrence was observed in only 5%, 4.2%, and 4.2% of cases at 3-month, 6-month, and 1-year followup. Adverse effects of therapy were observed in 20% of cases during therapy but they were mild and self-limiting