informs doi 10.1287/moor.1080.0360

We develop a framework for obtaining (deterministic) Fully Polynomial Time Approximation Schemes (FPTASs) for stochastic univariate dynamic programs with either convex or monotone single-period cost functions. Using our framework, we give the first FPTASs for several NP-hard problems in various fields of research such as knapsack-related problems, logistics, operations management, economics, and mathematical finance. 1

Using the well-known product-limit form of the Kaplan-Meier estimator from statistics, we propose a new class of nonparametric adaptive data-driven policies for stochastic inventory control problems. We focus on the distribution-free newsvendor model with censored demands. The assumption is that the demand distribution is not known and there is only sales data available. We study the theoretical performance of the new policies and show that for discrete demand distributions they converge almost surely to the set of optimal solutions. Computational experiments suggest that the new policies converge for general demand distributions, not necessarily discreet, and demonstrate that they are significantly more robust than previously known policies. As a byproduct of the theoretical analysis, we obtain new results on the asymptotic consistency of the Kaplan-Meier estimator for discrete random variables that extend existing work in statistics. To the best of our knowledge, this is the first application of the Kaplan-Meier estimator within an adaptive optimization algorithm, in particular, the first application to stochastic inventory control models. We believe that this work will lead to additional applications in other domains.

This issue’s column is written by guest columnists, David Shmoys and Chaitanya Swamy. I am delighted that they agreed to write this timely column on the topic related to stochastic optimization that has received much attention recently. Their column introduces the reader to several recent results and provides references for further readings.

We consider a repeated newsvendor problem where the decision-maker (DM) does not have access to the underlying distribution of discrete demand. We analyze three informational set-tings: 푖.) the DM observes realized demand in each period; 푖푖.) the DM only observes realized sales; and 푖푖푖.) the DM observes realized sales but also a lost sales indicator that records whether demand was censored or not. We provide a characterization of the best achievable performance in each of these cases, where we measure performance in terms of regret: the worst case difference between the cumulative costs of any policy and the optimal cumulative costs with knowledge of the demand distribution. In particular, we show that for both the first and the third settings, the best achievable performance is bounded (i.e., does not scale with the number of periods) while in the second setting, it grows logarithmically with the number of periods. The results enable one to quantify the performance degradation stemming from demand censoring and identifies minimal information through the lost sales indicator that mitigates some of this degradation.

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Confidence-based optimization for the Newsvendor problem Citation for published version:

Abstract In this paper we study a dynamic pricing problem, where a firm offers a product to be sold over a fixed time horizon. The firm has a given initial inventory level, but there is uncertainty about the demand for the product in each time period. The objective of the firm is to determine a robust and dynamic pricing strategy that maximizes revenue over the entire selling season. We develop a tractable optimization model that directly uses demand data, therefore creating a practical decision tool. Furthermore, we provide theoretical performance guarantees for this sampling-based solution, based on the number of samples used. Finally, we compare the revenue performance of our model using numerical simulations, exploring the behavior of the model with different robust objectives, sample sizes, and sampling distributions. This modeling approach could be particularly important for risk-averse managers with limited access to historical data or information about the demand distribution.

The increasing material costs and the rapid advances in computing technology have both motivated and promoted the study of network problems that arise in several different application domains. This dissertation consists of four chapters on network applications in transportation, telecommunications, and supply chain management. The core of our research is to apply heuristic search procedures and combinatorial optimization techniques to various practical problems. In the second chapter we investigate the split delivery vehicle routing problem (SDVRP), where a customer’s demand can be split among several vehicles. The third chapter deals with the regenerator location problem (RLP) that arises in optical networks. The fourth chapter solves the parametric uncapacitated network design problems on series-parallel graphs, which have potential application in supply chain management. In the fifth chapter we study the arc routing problem that arises in the small package delivery industry. The last chapter summarizes the dissertation. The results in this dissertation indicate that the methodologies developed to solve the network problems in the four different applications are quite efficient. Con-sequently, when applied in practice, they have the potential to significantly improve the operational efficiency of organizations in the relevant application domains.