Inverse Optimization with Noisy Data

Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions of a convex optimization problem are corrupted by noise. We first provide a formulation for inverse optimization and prove it to be NP-hard. In contrast to existing methods, we show that the parameter estimates produced by our formulation are statistically consistent. Our approach involves combining a new duality-based reformulation for bilevel programs with a regularization scheme that smooths discontinuities in the formulation. Using epi-convergence theory, we show the regularization parameter can be adjusted to approximate the original inverse optimization problem to arbitrary accuracy, which we use to prove our consistency results. Next, we propose two solution algorithms based on our duality-based formulation. The first is an enumeration algorithm that is applicable to settings where the dimensionality of the parameter space is modest, and the second is a semiparametric approach that combines nonparametric statistics with a modified version of our formulation. These numerical algorithms are shown to maintain the statistical consistency of the underlying formulation. Lastly, using both synthetic and real data, we demonstrate that our approach performs competitively when compared with existing heuristics

Local Water Storage Control for the Developing World

Most cities in India do not have water distribution networks that provide water throughout the entire day. As a result, it is common for homes and apartment buildings to utilize water storage systems that are filled during a small window of time in the day when the water distribution network is active. However, these water storage systems do not have disinfection capabilities, and so long durations of storage (i.e., as few as four days) of the same water leads to substantial increases in the amount of bacteria and viruses in that water. This paper considers the stochastic control problem of deciding how much water to store each day in the system, as well as deciding when to completely empty the water system, in order to tradeoff: the financial costs of the water, the health costs implicit in long durations of storing the same water, the potential for a shortfall in the quantity of stored versus demanded water, and water wastage from emptying the system. To solve this problem, we develop a new Binary Dynamic Search (BiDS) algorithm that is able to use binary search in one dimension to compute the value function of stochastic optimal control problems with controlled resets to a single state and with constraints on the maximum time span in between resets of the system

A Supply Chain Design Model with Unreliable Supply

Uncertainties abound within a supply chain and have big impacts on its performance. We propose an integrated model for a three-tiered supply chain network with one supplier, one or more facilities and retailers. This model takes into consideration the unreliable aspects of a supply chain. the properties of the optimal solution to the model are analyzed to reveal the impacts of supply uncertainty on supply chain design decisions. We also propose a general solution algorithm for this model. Computational experience is presented and discussed

OM Forum-challenges and strategies in managing nonprofit operations: an operations management perspective

The operations management (OM) community is paying increasing attention to the analysis of nonprofit operations. However, what is it about this type of operation that makes it particularly interesting to OM scholars? We address this question by studying the objectives, actors, and main activities of nonprofit operations and the most common challenges they face. In addition, we suggest tactical and operational strategies to address these challenges by considering works in the for-profit sector and in different applied areas. The ultimate goal of this paper is to inspire and stimulate OM researchers to develop significant theoretical and empirical models in this novel stream of literature