Online Linear Optimization with Inventory Management Constraints

This paper considers the problem of online linear optimization with inventory management constraints. Specifically, we consider an online scenario where a decision maker needs to satisfy her timevarying demand for some units of an asset, either from a market with a time-varying price or from her own inventory. In each time slot, the decision maker is presented a (linear) price and must immediately decide the amount to purchase for covering the demand and/or for storing in the inventory for future use. The inventory has a limited capacity and can be used to buy and store assets at low price and cover the demand when the price is high. The ultimate goal of the decision maker is to cover the demand at each time slot while minimizing the cost of buying assets from the market. We propose ARP, an online algorithm for linear programming with inventory constraints, and ARPRate, an extended version that handles rate constraints to/from the inventory. Both ARP and ARPRate achieve optimal competitive ratios, meaning that no other online algorithm can achieve a better theoretical guarantee. To illustrate the results, we use the proposed algorithms in a case study focused on energy procurement and storage management strategies for data centers

Online Linear Optimization with Inventory Management Constraints

This paper considers the problem of online linear optimization with inventory management constraints. Specifically, we consider an online scenario where a decision maker needs to satisfy her time-varying demand for some units of an asset, either from a market with a time-varying price or from her own inventory. In each time slot, the decision maker is presented a (linear) price and must immediately decide the amount to purchase for covering the demand and/or for storing in the inventory for future use. The inventory has a limited capacity and can be used to buy and store assets at low price and cover the demand when the price is high. The ultimate goal of the decision maker is to cover the demand at each time slot while minimizing the cost of buying assets from the market. We propose ARP, an online algorithm for linear programming with inventory constraints, and ARPRate, an extended version that handles rate constraints to/from the inventory. Both ARP and ARPRate achieve optimal competitive ratios, meaning that no other online algorithm can achieve a better theoretical guarantee. To illustrate the results, we use the proposed algorithms in a case study focused on energy procurement and storage management strategies for data centers

The Voice of Optimization

We introduce the idea that using optimal classification trees (OCTs) and optimal classification trees with-hyperplanes (OCT-Hs), interpretable machine learning algorithms developed by Bertsimas and Dunn [2017, 2018], we are able to obtain insight on the strategy behind the optimal solution in continuous and mixed-integer convex optimization problem as a function of key parameters that affect the problem. In this way, optimization is not a black box anymore. Instead, we redefine optimization as a multiclass classification problem where the predictor gives insights on the logic behind the optimal solution. In other words, OCTs and OCT-Hs give optimization a voice. We show on several realistic examples that the accuracy behind our method is in the 90%-100% range, while even when the predictions are not correct, the degree of suboptimality or infeasibility is very low. We compare optimal strategy predictions of OCTs and OCT-Hs and feedforward neural networks (NNs) and conclude that the performance of OCT-Hs and NNs is comparable. OCTs are somewhat weaker but often competitive. Therefore, our approach provides a novel insightful understanding of optimal strategies to solve a broad class of continuous and mixed-integer optimization problems

A Practical Guide to Robust Optimization

Robust optimization is a young and active research field that has been mainly developed in the last 15 years. Robust optimization is very useful for practice, since it is tailored to the information at hand, and it leads to computationally tractable formulations. It is therefore remarkable that real-life applications of robust optimization are still lagging behind; there is much more potential for real-life applications than has been exploited hitherto. The aim of this paper is to help practitioners to understand robust optimization and to successfully apply it in practice. We provide a brief introduction to robust optimization, and also describe important do's and don'ts for using it in practice. We use many small examples to illustrate our discussions