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

In rural areas, milk tankers collect milk from farms for processing at a central base.Collection runs are assigned to tankers, each tanker performing a series of runs. After eachrun, the tankers need to be emptied by pumps, which are limited in number. A schedulingsystem has been devised to allocate runs to tankers, despatch the tankers and determinewhen the tanker may be emptied on its return in order to minimise the total time taken(makespan) for all runs to be completed. The joint problem of scheduling and sequencing isposed as a linear integer programming (IP) problem with additional nonlinear constraints.The problem is then solved by embedding an IP algorithm within an overall branch andbound approach. The results of testing this algorithm will be discussed and compared to aproposed heuristic approach.

An exact algorithm for a milk tanker scheduling and sequencing problem

SUMMARY This paper demonstrates that integer programming can be used as a formulation and solution technique for designing efficient production lines by allocating tasks to multiple manned work stations. The paper considers a formulation of the problem by Shtub and reformulates it in a more straightforward way.

Formulation of a problem involving assembly lines with multiple manning of work stations

A series of approaches is presented to formulate statistical classification problems using integer programming. The formulations attempt to maximize the number of observations that can be properly classified and utilize single function, multiple function and hierarchical multiple function approaches to the problems. The formulations are tested using standard software on a sample problem and new approaches are compared to those of other authors. As the solution of such problems gives rise to various awkward features in an integer programming framework, it is demonstrated that new approaches to formulation will not be completely successful in avoiding the difficulties of existing methods, but demonstrate certain gains.

Integer programming formulations of statistical classification problems

Constraints and Optimization Loop Constructs Structured Linear Programming Conjunction and Implication Conditional Disjunction Negation Sensitivity Analysis Backtracking Classical Disjunction and Combinatorially Hard Problems Soundness and Completeness Depth-First Branch-and-Bound Search The Injury Method Tightening the Linear Relaxation Further Search Methods Mathematical Underpinnings Getting Started References List of Models Indexes.

Optimization and computational logic

In this paper we reflect on the last 10 years of the Journal of the Operational Research Society (JORS). We use metadata and citation analysis to profile OR research and practice published in this prestigious journal. The analysis of the published material includes examining variables such as the most productive authors, the papers having the highest number of citations, the universities and organisations associated with the most publications and their geographic diversity, OR techniques and their application areas, the number of authors per paper, the background of the authors, etc. Moreover, this work includes variables from a previously published study of JORS that profiled research from 1981 to 1999. Therefore, the analysis allows a comparison to be conducted between some of the findings of the two studies. This research has implications for researchers, journal editors and research institutions.

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John M. Wilson

Papers

An exact algorithm for a milk tanker scheduling and sequencing problem

Formulation of a problem involving assembly lines with multiple manning of work stations

Integer programming formulations of statistical classification problems

Optimization and computational logic

A profile of OR research and practice published in the Journal of the Operational Research Society