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

Stochastic lot sizing problems under monopoly

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 2009.Thesis (Master's) -- Bilkent University, 2009.Includes bibliographical references leaves 48-49.In this thesis, we study stochastic lot sizing problems under monopoly. We consider production planning of a single item using uncapacitated resources over a multi-period time horizon. The demand uncertainty is modeled via a scenario tree structure. Each node of the tree corresponds to a scenario of demand realization with an associated probability. We first consider the stochastic lot sizing problem under monopoly (SLS), which addresses the period based production plan of a manufacturer with uncertain demands and a monopolistic supplier. We propose an exact dynamic programming algorithm to solve the SLS problem in polynomial time. The second problem we consider, the stochastic lot sizing problem with extra ordering (SLSE), is based on two-stage stochastic programming. In addition to the period based production decision variables of the SLS model, there exist scenario based extra ordering decision variables in the problem setting of SLSE. We develop two families of valid inequalities for the feasible region of the introduced SLSE model. The required separation algorithms of both valid inequalities are presented along with their implementations with branch-and-cut algorithm in solving SLSE. An extensive computational analysis with branch-and-cut algorithms shows the effectiveness of these inequalities.Yanıkoğlu, İhsanM.S

Decision rule bounds for two-stage stochastic bilevel programs

Due to copyright restrictions, the access to the full text of this article is only available via subscription.We study two-stage stochastic bilevel programs where the leader chooses a binary here-and-now decision and the follower responds with a continuous wait-and-see decision. Using modern decision rule approximations, we construct lower bounds on an optimistic version and upper bounds on a pessimistic version of the leader's problem. Both bounding problems are equivalent to explicit mixed-integer linear programs that are amenable to efficient numerical solution. The method is illustrated through a facility location problem involving sellers and customers with conflicting preferences. Read More: https://epubs.siam.org/doi/10.1137/16M1098486TÜBİTAK ; Swiss National Science Foundation ; École Polytechnique Fédérale de Lausann

Load dependent lead time modelling: a robust optimization approach

Due to copyright restrictions, the access to the full text of this article is only available via subscription.Although production planning models using nonlinear CFs have shown promising results for semiconductor wafer fabrication facilities, the lack of an effective methodology for estimating the CFs is a significant obstacle to their implementation. Current practice focuses on developing point estimates using least-squares regression approaches. This paper compares the performance of a production planning model using a multi-dimensional CF and its robust counterpart under several experimental settings. As expected, as the level of uncertainty is increased, the resulting production plan deviates from the optimal solution of the deterministic model. On the other hand, production plans found using the robust counterpart are less vulnerable to parameter estimation errors

A survey of adjustable robust optimization

Static robust optimization (RO) is a methodology to solve mathematical optimization problems with uncertain data. The objective of static RO is to find solutions that are immune to all perturbations of the data in a so-called uncertainty set. RO is popular because it is a computationally tractable methodology and has a wide range of applications in practice. Adjustable robust optimization (ARO), on the other hand, is a branch of RO where some of the decision variables can be adjusted after some portion of the uncertain data reveals itself. ARO generally yields a better objective function value than that in static robust optimization because it gives rise to more flexible adjustable (or wait-and-see) decisions. Additionally, ARO also has many real life applications and is a computationally tractable methodology for many parameterized adjustable decision variables and uncertainty sets. This paper surveys the state-of-the-art literature on applications and theoretical/methodological aspects of ARO. Moreover, it provides a tutorial and a road map to guide researchers and practitioners on how to apply ARO methods, as well as, the advantages and limitations of the associated methods

Robust dual response optimization

This article presents a robust optimization reformulation of the dual response problem developed in response surface methodology. The dual response approach fits separate models for the mean and the variance, and analyzes these two models in a mathematical optimization setting. We use metamodels estimated from experiments with both controllable and environmental inputs. These experiments may be performed with either real or simulated systems; we focus on simulation experiments. For the environmental inputs, classic approaches assume known means, variances or covariances, and sometimes even a known distribution. We, however, develop a method that uses only experimental data, so it does not need a known probability distribution. Moreover, our approach yields a solution that is robust against the ambiguity in the probability distribution. We also propose an adjustable robust optimization method that enables adjusting the values of the controllable factors after observing the values of the environmental factors. We illustrate our novel methods through several numerical examples, which demonstrate their effectiveness

Robust strategic planning of dynamic wireless charging infrastructure for electric buses

Electromobility in public bus systems is growing rapidly and experiencing a fundamental transformation in their infrastructure and operations. The dilemma of limited driving range and charging time of battery electric buses (BEBs) hinders their adoption. A novel approach to address BEB limitations is to utilize dynamic wireless charging (DWC) technology that allows buses to charge while in motion. This paper aims to analyze robust strategic planning of DWC and BEB fleet scheduling based on a real bus network at Binghamton University. The problem is first formulated as a new deterministic mixed-integer linear programming model to simultaneously optimize both the charging planning problem and fleet scheduling problem in an integrated fashion. To address the uncertainty of energy demand and charging time, a robust counterpart model (RCM) has been derived. To increase RCM flexibility, the battery status variable is formulated in a cumulative form. Dependent and independent budget uncertainty sets have been developed to control the robustness. A sensitivity analysis has been conducted to study the system behavior in response to different charging types, auxiliary energy demand, depth of discharge, charging options at terminals, battery degradation, and electricity cost. The deterministic model shows that eight homogeneous BEBs are required to operate on the selected routes with a battery capacity of 54.01 kWh and a total cost of $3,636,347. The results show that joint planning of charging infrastructure and fleet scheduling can save 19.2% of total cost compared to disjoint planning. The RCM results in 10 BEBs to ensure feasiblility against uncertainty

Safe Approximations of Ambiguous Chance Constraints Using Historical Data

This paper proposes a new way to construct uncertainty sets for robust optimization. Our approach uses the available historical data for the uncertain parameters and is based on goodness-of-fit statistics. It guarantees that the probability the uncertain constraint holds is at least the prescribed value. Compared to existing safe approximation methods for chance constraints, our approach directly uses the historical data information and leads to tighter uncertainty sets and therefore to better objective values. This improvement is significant, especially when the number of uncertain parameters is low. Other advantages of our approach are that it can handle joint chance constraints easily, it can deal with uncertain parameters that are dependent, and it can be extended to nonlinear inequalities. Several numerical examples illustrate the validity of our approach