In this paper we study a Monte Carlo simulation--based approach to stochastic discrete optimization problems. The basic idea of such methods is that a random sample is generated and the expected value function is approximated by the corresponding sample average function. The obtained sample average optimization problem is solved, and the procedure is repeated several times until a stopping criterion is satisfied. We discuss convergence rates, stopping rules, and computational complexity of this procedure and present a numerical example for the stochastic knapsack problem.

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The Sample Average Approximation Method for Stochastic Discrete Optimization

https://homepages.fhv.at/hgb/New-Papers/CMAME07_BS07b.pdf

Robust Optimization - A Comprehensive Survey

https://ira.lib.polyu.edu.hk/bitstream/10397/1269/1/SetupSurvey-2006%28June-19%29.pdf

A survey of scheduling problems with setup times or costs

Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.

Predictive Control for Linear and Hybrid Systems

http://www.optimization-online.org/DB_FILE/2003/06/670.pdf

A stochastic programming approach for supply chain network design under uncertainty

(1998). Introduction to Stochastic Programming. Journal of the Operational Research Society: Vol. 49, No. 8, pp. 897-898.

https://link.springer.com/content/pdf/10.1057%2Fpalgrave.jors.2600031.pdf

Introduction to Stochastic Programming

Lot sizing is one of the most important and also one of the most difficult problems in production planning. This subject has been studied extensively in the literature. In this article, we consider single-level lot sizing problems, their variants and solution approaches. After introducing factors affecting formulation and the complexity of production planning problems, and introducing different variants of lot sizing and scheduling problems, we discuss single-level lot sizing problems, together with exact and heuristic approaches for their solution. We conclude with some suggestions for future research.

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The capacitated lot sizing problem: a review of models and algorithms

The Process Modellera s Needs. Basic Concepts in Process Modelling. Modelling with RADs. Animating a Process Model. Micro--Modelling of Processes. Modelling Large Processes. Process Patterns. Modelling the Materials in the Process. Analysing a Process Model. Managing the Modelling. Epilogue. Index.

Business Processes : Modelling and Analysis for Re-Engineering and Improvement

The evolution of cell formation problem methodologies based on recent studies (1997–2008): Review and directions for future research

Foreword. Preface. 1. A Historical Sketch on Sensitivity Analysis and Parametric Programming T. Gal. 2. A Systems Perspective: Entity Set Graphs H. Muller-Merbach. 3. Linear Programming 1: Basic Principles H.J. Greenberg. 4. Linear Programming 2: Degeneracy Graphs T. Gal. 5. Linear Programming 3: The Tolerance Approach R.E. Wendell. 6. The Optimal Set and Optimal Partition Approach A.B. Berkelaar, et al. 7. Network Models G.L. Thompson. 8. Qualitative Sensitivity Analysis A. Gautier, et al. 9. Integer and Mixed-Integer Programming C. Blair. 10. Nonlinear Programming A.S. Drud, L. Lasdon. 11. Multi-Criteria and Goal Programming J. Dauer, Yi-Hsin Liu. 12. Stochastic Programming and Robust Optimization H. Vladimirou, S.A. Zenios. 13. Redundancy R.J. Caron, et al. 14. Feasibility and Viability J.W. Chinneck. 15. Fuzzy Mathematical Programming H.-J. Zimmermann. Subject Index.

/pdf/advances-in-sensitivity-analysis-and-parametric-programming-18w1i6ngae.pdf

John M. Wilson

Papers

Introduction to Stochastic Programming

The capacitated lot sizing problem: a review of models and algorithms

Business Processes : Modelling and Analysis for Re-Engineering and Improvement

The evolution of cell formation problem methodologies based on recent studies (1997–2008): Review and directions for future research

Advances in Sensitivity Analysis and Parametric Programming